Corrections appear in this file in this order:
* NATIONAL 5 APPLICATIONS OF MATHEMATICS REVISION PACK CORRECTIONS/UPDATES
* ADVANCED HIGHER MATHEMATICS REVISION NOTES CORRECTIONS/UPDATES
* HIGHER MATHEMATICS REVISION NOTES CORRECTIONS/UPDATES
* NATIONAL 5 MATHEMATICS REVISION NOTES CORRECTIONS/UPDATES
* NATIONAL 5 APPLICATIONS OF MATHEMATICS REVISION NOTES CORRECTIONS/UPDATES
* NATIONAL 4 APPLICATIONS OF MATHEMATICS REVISION NOTES CORRECTIONS/UPDATES
* NATIONAL 4 MATHEMATICS REVISION NOTES CORRECTIONS/UPDATES
NATIONAL 5 APPLICATIONS OF MATHS REVISION PACK CORRECTIONS/UPDATES
[In the event mistakes have been found on the answer sheet, it is kept constantly updated at https://www.dynamicmaths.co.uk/n5amrevisionpackANSWERS.pdf]
between version 1.0 and 1.1
ADVANCED HIGHER MATHEMATICS REVISION NOTES CORRECTIONS
between Version 2.0 and 2.1
* various minor formatting changes
* various minor typing errors with words
* the formula for vector product was wrong on pages 4 and 141 (b_2 appeared in top right of the 'i' submatrix, should be a_3). Now corrected.
* the formula for parametric differentiation on pages 5 and 32 was wrong: dy/dx = dy/dt / dx/dx changed to dy/dx = dy/dt / dx/dt
* page 8: "in a Higher maths exam" changed to "in an Advanced Higher maths exam!
* page 80: mistake in Example 4. Question said S_n = -195, now corrected to say S_n = 195.
* page 106: "are reflected in the line y = f(x)" was wrong; now corrected to "are reflected inthe line y = x"
* page 113: in example it said "lines x = 2 and x = 5", now corrected to "lines y = 2 and y = 5"
* p128: "will lead to redundancy" changed to "will lead to inconsistency"
* page 129 Example 1: top-left element of final answer should be 20, not 4
* page 136 Example 2: line A - 5A = 2I should have read A - 5A = 2I, with all other lines being adjusted accordingly
* page 137 solution had 4 and -1 the wrong way around in the matrix; now corrected
* page 140 Example 2. In final answers to both (a) and (c) the bottom-left element should be (not )
* page 143 Example 2, an incorrect 'k' was removed from the end of line 2 of the solution
* page 147 Example 3: in step two, PQ x QP changed to PQ x QR
* page 147 Example 3: final answer changed from 7x+10y+11z=-20 to 7x+10y-8z=-20
* page 151 Question type A Example 1: question used parameter lambda, working used parameter t. Now changed to use 't' throughout.
* page 163 Example 2. 'a' and 'b' were wrong way around. Final answer changed to 2sqrt3 + 2i
* page 164 Question type A, signs wrong in all working for sin theta, now corrected
* page 168 Locus example. Both sketches had centres (3, 0) when they should have been (0, 3). Now corrected.
* Proof chapter: add in some missing references to the sets N, Z in some proofs
between Version 1.1 and 2.0
[VERSION 2.0 now complete and published]
* adjust font to be sans-serif (Calibri) rather than Times New Roman
* most examples rephrased to be clearer or more step-by-step
* many minor layout/phrasing issues
* make wording/examples more consistent between Higher and Advanced Higher, in sections where the content is the same/similar
* most assessment-style questions rephrased to have a clear command word in line with SQA strategies. e.g. "how many..." changed to "Calculate how many..."; "is the..." changed to "determine whether the..."
* removed "which will be examined in May 2016"
* switch order of the two examples in the "differentiation using more than one rule" section and change the function involvign sin x to sin-1(4x) instead as there had been no inverse trigonometric examples in the chapter
* add in table showing the basic principles of implicit differentiation before the examples
* implicit differentiation, example 2, change the function to make slightly more complicated to try and draw out the key features of the method more
* implicit differentiation, example 3, change the dy/dx expression to be a quotient, given that previous paragraph said quotients would usually be involved
* logarithmic differentiation, example 2, change to make more complicated so that it was more obvious that the chain/product/quotient rules would not be as straightforward
* move the speed example from the parametric differentiation section to the rectilinear motion section; replace in original section with an example of a tangent to a parametric curve
* add in one extra slightly more straightforward example to section on related rates of change to help focus on the key aspects. also be more accurate with units across the section.
* add in two very basic integrals towards the start of integration chapter that use the basic rules outlined there
* switch order of examples 3 and 4 in the integration by substitution so that all indefinite integrals come before all definite integrals.
* add in two more examples in inverse trigonometric integration section to cover the more complex substitutions that may come up in exams
* Example 2 of separable equations changed from dy/dx=y to dy/dx=ycosx to make it a tiny bit more complex
* remove Example 3 (separable DE with partial fractions) from separable equations chapter; as it's a good interleaving example for teaching pupils in class; but not really adding anything new to these specific notes
* add in extra example of stating binomial coefficients from Pascals triangle
* adapt binomial theorem example 2 so that one of the terms in the bracket has a power
* Add in example 2 in "binomial specific terms" section involving a term independent of x
* switch Examples 2 and 3 in the arithmetic sequences section
* change Example 4 in the arithmetic sequences section to be of the form "Sn=___, find n".
* make minor changes to phrasing of the questions in Examples 2 and 3 in the Maclaurin series section
* move Example 1 in'sketching rational functions' section to the previous section ('rational functions and asymptotes') instead, as it does not involve sketching
* add in new Example 2 in the "Rational functions and asymptotes" section to cover completing a half-drawn graph using given facts.
* add in an example exam question of sketching the graph of an inverse function.
* add in second example for solids of revolution so that there was one around x-axis and one around y-axis.
* remove entire section on velocity-time graphs as this is not on the CfE Advanced Higher syllabus.
* move entire section on Integration and Areas to the "Applications of Integration" chapter as per syllabus
* remove Example 2 of Gaussian Elimination (parabola equation) as the method added nothing new; the context only affected the first few and last few lines of the equation. Replace with an example involving a letter as a coefficient.
* add in a second example in both the redundancy and inconsistency sections to match the usual style of SQA exam questions ("for what value of lambda....")
* remove example question relating to ill-conditioning; and instead expand upon the example given in the text.
* add in Example 2 in basic matrix algebra section, using the transpose
* add in various sub-parts to various matrices questions to better match the style of questions used in recent SQA papers; also include letters inside various matrices, again in line with the style of recent SQA questions
* add in brief section about orthogonality, since this is mentioned in the syllabus
* add in second example of scalar triple product (same question, using quicker method)
* Example 1 in equation of a line: now includes all three forms of the equation explicitly
* shuffle order of examples in equation of a line section
* adapt one example to demonstrate how if question involves two lines, the letter chosen for the parameter cannot be the same
* make angles between lines/planes, make more specific about whether acute/obtuse angle required
* for intersection of two planes example, change method from Gaussian elimination to substitution
* add in example involving intersection of three planes
* adapt all locus questions to include a sketch
* add in extra Euclidean example where there is not a part (a) and where the gcd isn't 1
* add in second number base example, using hexadecimal
* in points of inflection p94, "the fact that f''(x) indicates" changed to "the fact that f''(x) changes sign indicates"
between Version 1.0 and 1.1
[VERSION 1.1 now complete and published]
* p152 concluding line added to proof by contrapositive section
* formula list updated to match revised SQA formula list
* changed so modulus is always -180< not -180<=
* adjusted layout of algebraic division so that lines worked better
* add in another example of factorising complex polynomials (cubic)
* added a new section clarifying logic and negation
* new example of direct proofs involving factors/multiples
* mod(g(x_0))<1 changed to mod(g'(x_0))<1
HIGHER MATHEMATICS (CfE) REVISION NOTES CORRECTIONS/UPDATES
between Version 2.0 and 2.1
* various minor formatting changes
* title on front page changed from "Higher Maths Course Notes" to "Higher Maths Revision Notes" to match all other notes in the series
*
between Version 1.4 and 2.0
[version 2.0 NOW COMPLETE AND PUBLISHED]
* adjust font to be sans-serif (Calibri) rather than Times New Roman
* make wording/examples more consistent between Higher and N5 Maths, in sections where the content is the same/similar
* most examples rephrased to be clearer or more step-by-step
* most assessment-style questions rephrased to have a clear command word in line with SQA strategies. e.g. "how many..." changed to "Calculate how many..."; "is the..." changed to "determine whether the..."
* many minor layout/phrasing issues
* change title on front page from "New (CfE) Higher Mathematics Course Notes" to "Higher Mathematics Course Notes"
* add in very brief example "if f(5)=8, state f-1(8).
* expand the 'alternative' method for inverse functions to explicitly show all working by adding in an Example 2b
* add in section under 'essential skills' on rationalising the denominator; as this is occasionally required in a 'show that' question
* move the logarithms/exponentials part of the inverse function section into the (adjacent) Exponentials and Logarithms section
* for the "experimental data" (log transforms) section: adapt method; and adapt Example 2 so that the two examples do not have the same base.
* in 'completing the square' section, adapt letters to match those asked by sqa (i.e. a(x+b) +c rather than p(x+q) +r )
* change numerator in Example 1 on page 23 to '5 + x' rather than '3 + x' as previously the fraction inadvertently could be cancelled
* throughout 'wave function' chapter, adapt letters being used to match SQA questions (no longer any use of alpha)
* rearrange the wave function examples so that Example 1 (degrees) is in first quadrant and Example 2 (radians) is not so that Example 1 can be the most routine
* for the wave function questions where part (b) is the focus [including those in the Relationships and Calculus chapter], the method for part (a) is no longer repeated in full. Instead the answer is given, with a direction to read the examples in the previous section if more detail is needed.
* minor change to numbers in the magnitude of a vector section in Example 1; as the numbers were exactly the same as those in Example 2.
* adjust Examle 2 in 'angle between two vectors' to match SQA exam questions; with a part (a) of identiying the vectors and (b) of doing angles. THis involved having to remove the explanation of why it was BA (not AB) that is used.
* add in additional vector pathway question based on components
* adjust formatting throughout vector section to make the arrows above vectors much clearer.
* synthetic division, Example 2, first grid had '-5' as the input rather than '-2'. Rest of working was correct.
* in synthetic division/factorising section add in more detail about difference between factor and root; and how to phrase conclusion
* in factorising Example 1, the question asked to show that x = 1 is a root whereas the conclusion stated that (x-1) is a factor. Now corrected. Same issue in Example 1 of the solving equations chapter.
* in solving cubic equation section, remove part (b) from the example.
* in solving cubic equation section, remove Example 2 (where no root is given) as it is effectively a duplicate of the example from the previous section (the 'solving the equation' bit is a relatively minor addition which is covered by Example 1 anyway)
* add in paragraphs explaining the meaning of repeated roots and how to recognise them from a diagram
* remove first example in discriminant chapter (rational roots) as this is no longer in course; although text has been retained. All other examples renumbered accordingly
* remove final example in trig equations with squared terms (one that contains both multiple angle and phase angle) as it doesn't really add anything new that wasn't in the previous two examples; other than mixing it all together.
* add a second stationary point example to illustrate the example of a nature table that cannot contain all x values due to a restricted domain
* add in an extra example of differentiating sin/cos of the form sin(px+q)
* remove the formal method in the chain rule section; and the formal integration by substitution from the integrating brackets section; and from the "more difficult integrals using the link between differentiation and integration" section
* for example 3 in 'equation of a circle' section, change the numbers so that the radius is no longer the same (sqrt13) as in example 2
* for example 2 in 'equation of a circle without brackets' section, change numbers so that decimals are not involved in solution
* improve the explanation about why a circle exists if g^2+f^2-c>0
* in intersection of a line/circle section, delete example 1 as it just duplications example 2.
* adapt Example 3 to also find the coordinates of the point of contact, in line with recent SQA exam and unit assessments.
* move the section on equation of tangents in front of the section on intersections of lines/circles; move Example 2 of the equations section into the intersection section and re-renumber
* add in second example about circle intersections
* remove final example of areas and curves as it was A/B and needed more explanation than was ideal.
* page 81, Example 3, change "point" to "points" as there are two points of intersection in the answer
* Wave Function chapter: Example 2 (radians) had somehow moved to be at the end of the entire chapter, whereas it should have been earlier. Moved back to correct place.
* for trigonometric equations and wave functions, some minor issues with degree signs in questions tightened up to ensure accuracy
* in all nature tables, a label for 'slope' added for bottom row consistent with current SQA marking policy
* page 29 Example 5, remove "where a > 0" as this was irrelevant to the question
between Version 1.3 and 1.4
[version 1.4 NOW COMPLETE AND PUBLISHED]
* p7: "show that" explanation - added in sentence saying "(in exactly the same form as it was stated in the question)"
* p9: changed the easiest fraction simplification example (6/8) to say that sqrt(9/10) should be simplified to 3/sqrt(10) in line with SQA advice as this needs spelling out more
* p25/6 (inverse functions), added in a note that a inverse function MUST begin with f^{-1}(x)=
* in all wave function examples, after kcosa=.. and ksina=.. a note is added to the effect " (these must be stated explicitly)"; and also same note added once in first example after tana=ksina/kcosa
* brackets added between integral sign and dx for all expressions containing + or -
* p12 example 2: "to convert degrees into radians" changed to "to convert radians into degrees"
* p10 typing mistake amended to change "theses" to "these"
* various full stops added
* various minor formatting changes e.g. indents, size of fractions
* vectors example 3: underlines added for vectors
* vector pathways - "example 4" renamed to "example" as it is the only example in that section
* p66 - typing error "known cubics" changed to "known as cubics"
* p114 example of 7cos3x changed to 7cos(3x+1) to include an answer than has (px+q) in
* p114 typing mistake changed: "numerical clue" to "numerical value"
* p146 "find the limit" changed to "find the limits" in example 2
between Version 1.2 and 1.3
[version 1.3 NOW COMPLETE AND PUBLISHED]
* optimisation example 1 (on closed interval). Second sentence of question was missing
* decimal points replaced with throughout to match SQA formatting; some minor page break changes; a few very minor layout or wording changes
* p52: ksin(x+alpha) formula was incorrect. now changed
* p41 end of sketching derived function example, "sketch on right" changed to "sketch on bottom left of previous page" to match layout
* rephrased "radians have no units" to "no symbol is required to represent Radians"
between Version 1.1 and 1.2
[version 1.2 NOW COMPLETE AND PUBLISHED]
* synthetic division moved from Expressions and Formulae to Relationships and Calculus as per SQA syllabus change May 2014
* logarithmic/exponential equations moved from R&C to E&F as per SQA syllabus change May 2014
* page 142 '3, 11, 26, 57' corrected to '3, 11, 27, 59'
* layout issue on p40 corrected
* layout issue involving vector notation corrected
* p65 Example 3, "two perpendicular vector" changed to "two perpendicular vectors"
between Version 1.0 and 1.1
[version 1.1 NOW COMPLETE AND PUBLISHED]
* p72: incorrect factorising: should be (2k-3) instead of (2k+3)
* p4, 8, 47, 99, 101, 106, 120, 132, 138, 144: minor amendments
* added in 'quicker' formulae for completing the square on p19 and in completing the square section (where method adapted to just use the 'quicker' version); also on formula sheet at start
* p123 "pair of gradients is" changed to "pair of gradients are"
* p149 "maximum" changed to "minimum"
* p157-158, added "units " to answer
NATIONAL 5 MATHEMATICS REVISION NOTES CORRECTIONS/UPDATES
between Version 4.0 and 4.1
between Version 3.1 and 4.0
[VERSION 4.0 NOW COMPLETE AND PUBLISHED]
* various minor formatting and wording changes
* adjust wording throughout to ensure methods of solving and rearranging equations always refer to doing the same to both sides
* move 'angles and similar shapes' chapter in front of 'Right-Angled Trigonometry' chapter so that the RAT chapter can be directly in front of the 'Trigonometric Graphs and Equations' chapter.
* remove section on #2.1
* rewrite section on #2.2 to better reflect exam rather than units
* Surds section: add in example of expanding a (double) bracket containing a surd as Example 2. Delete old example 4 (division). Renumber old examples 2/3 accordingly.
* Negative powers: add in new example 1 that is numerical. Renumber others accordingly
* page 21 (scientific notation): add in missing word 'button'
* expanding single brackets: adjust first example to have a negative coefficient of second bracket
* completing the square: add an example with odd coefficient of x
* adding and subtracting fractions: remove explicit referenes to kiss and smile and adjust working to a more understanding-based method. Add in new Example 1 where one fraction already has the lowest common multiply in its denominator. Delete old Example 1. Adjust example 2 to be an addition. Renumber others accordingly.
* gradient example 2, change to a line with a negative gradient
* areas and sectors: add in two additional examples involving going backwards
* significant rewriting to straight line section.
* remove section 1 example 2 of straight line section as it duplicates the 'identify equation from graph' section
* rewrite example 3 and renumber to example 2. Remove parts (a) and (b), renumber (c) to (a), add new part (b) and change so that each subquestion only asks for either gradient or y-intercept and not both.
* remove section on drawing straight lines as this is not examinable at National 5 level
* adjust final straight line example to have a fractional gradient to practice rearranging
* add in a second example for Example 4 in the equations section to show the two different ways of treating it
* change Example 1 in equations with fractions section in order to better match the standard of exam questions
* change 'd' to '2cd' in Example 1 in changing the subject example to make it slightly more difficult
* in section on graphs of quadratic functions amend example 2 to have turning point in 2nd rather than third quadrant.
* in section on graphs of quadratic functions include part (b) in both examples on axis of symmetry (example 1) and y-intercept (example 2) to strengthen the coverage of coordinate geometry
* add new example 6 in quadratics by factorising section covering quadratic solving in a geometric (area of rectangle) context.
* in quadratic formula section, split method up to create an extra step 3 where b² – 4ac is calculated before the rest of the substitution
* in discriminant section remove Example 2 as constraints on coefficients are not actually on National 5 maths syllabus as far as I can tell.
* converse of Pythagoras: be more explicit about the criteria for getting the conclusion mark. Add in a note that the two square calculations must be separate. Adjust Example to ask whether G is due North of F rather than just asking whether it's right angled. Correct error in solution where 106.09² had been written instead of 10.3²
* right-angled trigonometry. Reduce level of detail in examples 1/2/3 because this is supposed to be revision of prior learning. Remove example 4 (in a circle diagram).
* page 74: similar shapes Example 4, typing error: PT = 32 cm (previously wrongly said 28 cm) and in final line of answer "area" changed to "length"
* sin/cos/tan graphs: make the diagrams of the basic graph larger and clearer.
* Example 2: change amplitude from 2.4 to 2.5
* page 77: change 'period' to 'frequency' in table
* phase angle: change definition to how far graph moved to the LEFT and say angle is what it ADDED (not taken away)
* noncalculator sin, cos, tan: adjust diagram in Example 1 to better match the proportions shown and to include a note that the denominator could be rationalised.
* add in new Example 2 and Example 3 on non-calculator trigonometry to deepen understanding.
* improve quality of CAST diagram illustration
* add in new Example 4 in a real life situation
* trigonometric identities example 2. Change question so that answer is 'sin x' rather than '5'.
* A = ½absinC. Add in new Example 2 (non-calculator)
* sine rule. add new Example 3 (obtuse angle) and Example 4 (two triangles)
* vector pathways. Add in new diagram before example to further illustrate the key concept.
* adding/subtracting fractions. Merge examples 1a/1b to a single example 1 and remove reference to kiss and smile.
* multiplying/dividing fractions. Add in new Example 4 involving order of operations.
* scattergraph example 2. Change diagram/phrasing to better match style of SQA questions
* standard deviation: change numbers in example so that mean and 'n' are not the same
* comments about statistics: rewrite to be clearer and to better illustrate the range of reasons marks may be gained or lost
between Version 3.0 and 3.1
[VERSION 3.1 NOW COMPLETE AND PUBLISHED]
* adapted June 2021 to match change in SQA Course Specification so that all mentions of semi interquartile range are replaced with interquartile range
* various minor formatting changes
between Version 2.1 and 3.0
[VERSION 3.0 NOW COMPLETE AND PUBLISHED]
* adjust font to be sans-serif (Calibri) rather than Times New Roman
* make wording/examples more consistent between N5 Maths and N5 Applications of Maths, in sections where the content is the same
* all assessment-style questions rephrased to have a clear command word in line with SQA strategies. e.g. "how many..." changed to "Calculate how many..."; "make [a drawing]" changed to "construct..."; "is the..." changed to "determine whether the..."
* many minor layout/phrasing issues
* throughout (all explanation/justify examples): add in example where explanation includes a 'less than' sign
* surds: add in 4th example about dividing
* multiplying brackets: change letter in question to not be 'x' so that the letter is distinct to the multiply sign
* multiplying brackets: refer to the variety of methods and show grids for the grid method for each example
* difference of two squares: slightly rephrase explanations
* factorising trinomials: improve layout of section for greater clarity.
* completing the square: take out the q = c-p method and replace with a better but equivalent explanation that is more adaptable to Higher. Also remove the example with odd coefficients, as this is not really adding anything new.
* sketching straight lines: update diagrams
* equations with letters on both sides: change the examples to use different numbers/letters
* the section on inequalities (multiplying/dividing by a negative) moved to jojn the rest of the inequality section
* in cross-multiplying section, change Example 1: x/4 = 1/x to a/4 = 1/a
* graphical simultaneous equations: add in a second answer requiring an algebraic approach to find the intersection of two graphs
* re-write right-angled reigonometry (revision) section to better match National 4 Maths notes, including use of 'Hyp'/'Opp'/'Adj' instead of 'H'/'O'/'A'
* add in similar triangles question to section on similarity
* include instructions "express your answer in component form" where necessary in vectors section, to match SQA exam questions
* include instructions "give your answer in its simplest form" for 'equation of a straight line' questions, to match SQA exam questions.
* adapt scattergraph/line of best fit example to use y-b=m(x-a) rather than y=mx+c to better match SQA exam questions
* add in second example to 'functions' section that involves going backwards
* page 79 - typing mistake corrected "represente" to "represented"
* page 83 - typing mistake corrected "too add the vectors" to "to add the vectors"
* page 56 - updated the nature of roots section to match SQA expectations as per verification key messages March 2017: "two real and distinct", "one real and repeated", "no real roots"
between Version 2.0 and 2.1
[VERSION 2.1 NOW COMPLETE AND PUBLISHED]
* two-digit by two-digit multiplication: "238 is split into 200, 300 and 8" changed to "238 is split into 200, 30 and 8"
* converse of Pythagoras section added in
* add in reference to InterQuartile Range as well as Semi InterQuartile range
* add in extra completing square example where coefficient of x is odd
* in "writing comments on statistics" added in a note to use the word 'on average' in sentences about the mean and added in an extra example of a sentence that wouldn't get any marks
* p42, equation of straight line, add in an equation where gradient is a fraction
* p82, vector pathways, example changed from 3d to 2d, since SQA advice is that 3d vector pathways would only be at Higher
between Version 1.3 and 2.0
[VERSION 2.0 NOW COMPLETE AND PUBLISHED]
* decimal points replaced with throughout to match SQA formatting; some minor page break changes
* comparing statistics example re-edited to match the National 5 Lifeskills version
* non-calculator section added in
between Version 1.2 and 1.3
[VERSION 1.3 NOW COMPLETE AND PUBLISHED]
* Page 58: Example 4cos(2x-15) changed to be 4cos(x-15) to avoid any dispute over whether phase angle should be 15 or 7.5
* Page 40: added plusminus sign in front of square root
* Introduction: phrase "Schools or individuals who purchase a site licence before the first National 5 exam in May 2014 will be eligible to receive a free copy of any revised notes. To enquire further about this, email david@dynamicmaths.co.uk " removed now that May 2014 is here.
* Back page "maths" changed to "Mathematics"
* rules of powers section, Key Rule 1, minor typo "when you multiplying" changed to "when you multiply"
* Added in second "quick" method for completing the square, along with two corresponding formulae
* Increased font size in fractions on formula sheet and reordered formula sheet to match order of notes; also in the Volume section
* corrected mistake in which co-interior angles were incorrectly referred to as back bearings
* final section (comparing statistics) - more examples of comments that would/would not get the marks included
* adjustments to layout on page 52
* page 56: changed reference to "copying diagram onto exam paper" to "write on exam paper" since Nat5 is write on.
* layout issue involving vector notation corrected
between Version 1.1 and 1.2
[VERSION 1.2 NOW COMPLETE AND PUBLISHED]
* A few minor grammatical and/or layout errors corrected on pages 8, 9, 16, 35, 44, 46
* Added in new section "Exam Technique" covering communication marks, rounding, units etc
* Page on negative and fractional powers - minor rephrasing
* Additional notes about units and rounding at start of volumes topic
* (Old) Pages 15 and 16: added in sentences on the importance of units.
* (Old) Pages 23 and 24: Examples 1 and 2. Units in answer are given in cm. Should be m.
* (Old) Page 28: Example 3, solution (c): "moving 8x across to become -8x". "8x" and "-8x" are wrong way about.
* (Old) Page 44 (formula box) and Page 45: Example 1. "=0" was missed off the end of the quadratic equation.
* (Old) Page 46: Example 1. units of answer given in cm. Should be m.
* (New) Page 55: missing squared symbol for area in Example 1 (2500cm)
* (Old) Page 55: 5 lines down "repeats itself three times between 0 and 120". 120 should say 360.
* (Old) Page 55: table at end. Says period of 2cos(x-45) is 0. Should say 1.
* Added in 4th example to changing the subject section
NATIONAL 5 APPLICATIONS OF MATHEMATICS REVISION NOTES CORRECTIONS
between Version 4.1 and 4.2
* various minor formatting changes
* WRITE ON VERSION ONLY Page 78 of write on version, Basic Skill Example 3, remove (incorrect) first line of solution
between Version 4.0 and 4.1
[version 4.1 NOW COMPLETE AND PUBLISHED]
* various minor formatting changes
* p17: Assessment Style Example 3. Change to involve two different perccentages, including a depreciation.
* Scale Drawing: remove Basic Skill Example as it has no angles. Give scale in Assessment Style Example to match SQA exams.
* p49 time zone. change "1st March" and "25th December" to "1 March" and "25 December" to match SQA standard date formatting.
* p50 time zones. change Assessment Style Example 2 to involve days/hours and a shipping voyage to match the two past exam questions
* p54: Assessment Style Example 1. Completely rewritten as 3d Pythagoras does not appear to reflect the complexity of tasks being asked in exams. Replaced with a 2d example.
* p55: Assessment Style Example 2. Correct "sale" to "sail" in final sentence. Then change question so that part (a) is only about getting a length and part (b) is about perimeter not area. Previous question had a lot of steps.
* Gradient: add new Basic Skill Example 2 (noncalculator) and renumber existing Basic Skill Example to Basic Skill Example 1.
* Gradient Assessment style example 1: remove superfluous word 'in'.
* Gradient Assessment style example 2: remove part (b). Numerical comparisons have already been covered in this chapter.
* Circles: change order of questions so that all basic examples come first and then all assessment style examples
* add in new diagram summarising all key circle formulae.
* p70: adjust numbers in Basic Skill Example (overtime) to make hourly rate more realistic given the minimum wage
* National Insurance: remove previous Basic Skill Example 3 and renumber Basic Skill Example 4 accordingly. Add in new Basic Skill Example 4 to cover higher rate National Insurance.
* change layout in higher rate questions to a table format for clarity
* restructure Assessment Style Example 3 (NI/net pay/Michelle Hall) to have a part a and b to better match exam questions
* p80 Savings and Borrowing. Delete Assessment Style Example 1 (comparing three bank accounts). This matches a previous unit assessment question, but not any current exam questions. Renumber Assessment Style Example 2 to 'Assessment Style Example'
* p80 Basic Skill Example 3. Change numbers to be stated in the question and adjust names/currencies.
* p82 Basic Skill Example 3 (payment plan) bullet point 2 change "payment plan price" to "total payment plan price" to match wording in bullet point 1
* p83: remove superfluous word "loan"
* Boxplots assessment style example. Add in part a about calculating quartiles, in line with exam questions. Adjust diagram for 2014 so that the 2014 diagram is more obviously more consistent. Put diagrams side by side to make comparison easier. Change 2018 to 2024.
* p100: Basic Skill Example - adjust pie chart numbers so that degrees are all whole numbers
between Version 3.1 and 4.0
[version 4.0 NOW COMPLETE AND PUBLISHED]
* various minor formatting changes
* new section (part of numeracy unit) on sampling and bias to reflect that these topics are in the course arrangements
* standard deviation: change numbers in example so that mean and 'n' are different
* p69 Example: last two lines had errors in. Correct final answer is 262.05, not 261.75
* p3: adjust formula sheet not given in exam to include multiplication signs for the benefit of weaker candidates who are less likely to be able to interpret algebraic notation
* p9: change 'foreign exchange' to 'currency exchange'
* p14: replace BODMAS diagram with a better diagram
* p15: rephrase all questions to include a command word.
* pages 17-18: be slightly more explicit about the need to divide by 100 when finding the mutiplier
* p18: assessment style example 3: remove part a
* p19: remove reference to Kiss and Smile method (Example 7b) and replace with new assessment style example involving subtraction from 1
* p21: renumber Assessment Style Example 4 to Assessment Style Example 5
* p23: remove reference to Speed/Distance/Time formula triangle
* p23: expand km/h to include 'kilometres per hour' and 'kmph' as alternatives; same for others
* p23: basic skill example 2. Have both a cube and cuboid in the example
* p24/25: basic skill examples 1/2/3 (speed, distance, time) adjust numbers in each question
* p25: add in proportional circle diagrams to Basic Skill Example 1 as an alternative method
* p27: change layout of table in Basic Skill Example 3 to match that used earlier
* p27: integrate Basic Skill Examples 1a and 1b
* p28: Basic Skill Example 2 and Assessment Style Example (indirect proportion). Reword question to better match SQA examples, and rewrite solution to involve two 'steps' to make the method clearer.
* p28: reword page to be more consistent in use of word 'indirect' rather than 'inverse'.
* p29: (probability) change Basic Skill Example 1 so that the total is the total number of pupils, rather than the total number of girls; as restricting to girls is an unnecessary complication for a Basic Skill Example.
* p29: rephrase both questions to move away from implying a binary interpretation of gender.
* p32: stem and leaf. Basic Skill Example 3: change part (b) to mean, rather than lowest, given that mean is often asked in N5 Numeracy questions.
* p33: remove content on dot plots as these are not emphasised in any way in the course specification
* p36: remove word 'usually' from description of whether endpoints are acceptable
* p36: change Basic Skill example to have a part a and a part b; with part b involving a percentage tolerance
* p39: rewrite text to reflect that, whilst syllabus does require scale to be chosen, exam questions typically do not.
* p40: assessment style example (scale drawing). Split into part (a) and part (b). In write on notes (only) state the scale to be used as 1 cm : 50 m. Retain 'choosing' instruction in full notes.
* p41-42 (Scale Drawing). Split question into parts a and b. Include a North arrow in the write-on notes
* p43 (Container Packing). Remove all references to cylinders, including the Assessment Style Example. Cuboids only.
* p43 (Container Packing). Change basic skill example 1 so that it involves cuboids and not cylinders, and is 3d rather than 2d.
* p44. Change Basic Skill Example 2 to have slightly more realistic numbers and to adjust the way the method is explained.
* p47. Add sentence saying that tasks written above each other can be done at the same time
* p48. Adjiust the guidelines for filling out an activity diagram
* Gradient: remove assessment style example 3 (going backwards) as going backwards is not typically required for N5 Applications exam questions.
* p69/70 (budgeting). Remove 'what will an exam question look like' and add in a section about 'how many weeks to save up' in Basic Skill Example (Iain Asghar)
* p72: basic skill example 2; change part (b) to double-time
* p72: remove 'what should an exam question look like'
* p73: Assessment Style Example 2 (commission; Harvey/Hamish RObertson). Change to remove picture of wageslip and use text to state the salient features
* p74: Basic Skill Example 3 (Income tax/Alison McNeill). Clarify question to make it clear that all figures are annual, and to clearly distinguish between gross and net pay.
* p75: Assessment Style Example 3 (Michelle Hall). Change so that final answer is for monthly pay, and to make clearer that all other values are annual.
* p77: Basic Skill Examples 1&2: add in proportion diagram as an alternative visual representation
* p84. Switch order of Basic Skill Examples 3 (payment plan) and 4 (credit card) and delete Assessment Style Example about credit cards as the basic skill example covers the necessary content sufficiently
* Standard deviation: in write on notes (only) delete Example 1b so that there is only one blank space
* rewrite section on sentences for statistics questions to give clearer advice
between Version 3.0 and 3.1
[version 3.1 NOW COMPLETE AND PUBLISHED]
* various minor formatting changes
* remove sections on formulae and using equations to go backwards, as it is now very clear that these are not relevant to the course specification and will not be tested in an exam
* probability: add in new Basic Skill example 3 involving a two-way table, as these have now occurred a few times in exams. Also add in an Exam style example about expected frequencies, given that the section heading (and course arrangements) included the terms expected frequency but there had not previously been any content
* Appreciation/Depreciation section: delete Assessment Style example 3 (no start value) as this is not consistent with the syllabus or past exams. Renumber previous Assessment Style Example 2 (appreciation where you need to calculate the percentage first) to Assessment Style example 3. Add in new Assessment Style example 2 about percentage profit/loss and add in percentage formula/loss formula before it, and in formula sheet
* Remove all content on simple interest from Savings section
* Remove the two examples on calculating APR in the Loans section and replace with a basic example where APR is given.
* change diagram at start of "Task Planning" chapter (cook meat/carrots etc) to match SQA style (tasks in boxes not on arcs)
* change most instances of "weight" to read "mass/weight" to be consistent with SQA policy of only using word 'mass' in assessments
* correct formatting in credit card bill example, where bank account number was split over two lines
* p4: "very routine" changed to "of a routine nature"
* p4: "links with other parts of the course" changed to "interleaving of other parts of the course"
* p6: "there are often two marks for rounding" changed to "there may be two marks for rounding" to reflect decreased prominence of unit assessments
* p6: rephrase the answer to the assessment style example to avoid referring to a non-integer number of buses as a "decimal number of buses"
* p7: add in gradient as a second example of answers likely to be fractions (alongside probability) to reflect the prominence of fractions in gradient past exam questions
* p9: change "course notes" to "course syllabus"
* p11: add in word 'first' to blue note in both examples
* p13: change "write" to "express"
* p14: change title of assessment style example 2 from "division by a three-digit number" to "division by a more difficult number" as the number is not a three-digit number. Also add the words "in a company" to the question
* p14: mistype in BODMAS section: "calculator" changed to "calculation". Sentences reordered too.
* p14: change "calculate the percentage" to "express an amount as a percentage"
* p15: percentage profit and loss, change "you always have to work out" to "you must always calculate"
* p18: change "topheavy fractions" to "improper (topheavy) fractions" to promote better use of mathematical vocabulary, and add a second example 11/5
* p19: "addition" and "subtraction" instead of "add sum" and "take away sum"
* p20: Basic Skill Example 9; change "metal" to "electronics" to sound mkore true to real life
* p22 and Basic Skill Example 1 (and Formula Sheet at start): remove area of square as separate example; add perimeter in to formulae and to example
* p25: "ratios consist of numbers"; add in the words "two or more"
* p28: inverse proportion, change "highly unlikely" to "unlikely" as it cannot be ruled out that SQA may choose to do so at some point
* p36: reword 'real measurement' to 'target measurement' and make slight change to units used ( instead of p; % instead of mm)
* p37: add two other examples for what might be expected in an exam question (unit conversion, percentages)
* p37: units for degrees had been inadvertently stated as ' C'. The erroneous 'C' has now been removed.
* p38: change "10, 100 or 1000" to "multiples of 10, 100 or 1000"
* p39: Assessment Style example. Give some examples of other scale factors that might work. Change the example to use a scale factor of 50 rather than 20, to ensure the suggested diagram would fit on a typical A4 portrait page.
* p40: "remove words "For unit assessments"
* p42: rephrase "do a division sum with" to just "divide"
* p42: change question mark in Basic Skill Example 1 to a full stop
* p42: use "aligned" instead of "turned" to be consistent with typical exam questions (also in Solution to Basic Skills example on p43)
* p43: slightly rephrase "the larger and smaller containers will always be the same size" to "Each larger container will be the same size; and each smaller container will be the same size."
* p43: move "comparing different alignments" from the "might" to the "will" category for past exam questions
* p44: Assessment Style Example. Slightly rephrase questions to be more consistent with past exam questions.
* p45: change "on each arrow" to "in each box" as there are no arrows in the diagram
* p45: rephrase definition of critical path from "longest path" to "longest route from the start to end"
* p46: delete Basic Skills Example 2, as the skill of creating a precedence table is unlikely to be tested, and there is no 'one right answer' which limits the usefulness of the example. Add identifying critical path to the list of what 'might' be in an exam question
* p49: Basic Skill Examples 1 and 2. Rephrase to be more consistent with use of phrases such as local time and to better match past exam questions (e.g "is 8 hours behind UK time" rather than "GMT-8".
* p50: add " Require you to read the information in the question to decide whether to add or subtract the time difference."
* p49: rephrase Assessment Style Example 1 to better reflect past exam questions e.g. use of phrases "local time". Main gist of question remains unchanged.
* p52: change "usually" to "often"
* p53: rephrase bullet point about two-step calculations to focus more on the need to work out lengths first. Add new bullet point (in 'might' section) about two triangles
* p53: Assessment Style Example 1: state explicitly that box is a cuboid
* p55: remove paragraph on negative gradients as not appropriate to N5AoM course. Replacec with brief mention of steeper/less steep positive gradients.
* p55: insert brief reference to the term "average gradient" and adapt Basic Skill Example 1 to be set in a real-life context and to use the term average gradient.
* p56: split Assessment Style Example 1 into part (a) and part (b)
* p59: correct typing mistake saying diameter was 9.8cm (should be 9.6cm). Rest of question already used 9.6.
* p59: Basic Skill Example 2. Correct error where question text said 35cm and diagram said 25cm. 25cm is correct.
* p62: Assessment Style Example 2: explicitly state in question that the triangle is right-angled
* p69: Assessment Style Example. Underline the words per year and per month in the question for emphasis
* p70: Basic Skill Example 1: change question from "calculate his pay" to "calculate his commission" a this is what question is requiring.
* p71: correct "get paid" to "gets paid"
* p73&74: Move National Insurance basic skill example to be before the assessment style example. Rephrase to include the standard line from exams "NI is calculated before deductions such as..."
* p74: add a note that NI is usually the focus of exam questions rather than tax
* p74: Assessment Style Example 3. Change question to (a) include a pension calculation, (b) focus on NI not tax, in line with recent exam questions
* p75: move special offers/discounts into the "will always" section rather than "might" and give more examples of the types of special offer that might be used.
* p76: Basic Skill example 2. Tweak example to be for 10 people rather than 5 people
* p77: add brief note of other ways of expressing exchange rates.
* p77: Basic Skill Example 2. Correct minor mistake where the word dollars was placed after words "base currency" rather than "other currency"
* p77 onwards: change any occurence of "Euros" to "Euro". Change "Pounds" to "Pounds Sterling" on a number of occasions (though not all)
* p78 add in explicit note that Pounds Sterling is the official name; and also add in a note that candidates should expect to come across unfamiliar currencies in the exam
* p78 Assessment Style Examples 1 and 2. Change "Euros" to "Euro" and minor other wording changes that do not change the nature of the question e.g. removing the three-letter codes and using words "pounds sterling" where appropriate
* p80: new Basic Skill example 3 involving converting between two currencies where the base isn't known
* p80: rename section from "Savings" to "Savings and Interest"
* p80: delete Basic Skill Example 1 about simple interest. Renumber Basic Skill Example 2 to Basic Skill Example 1.
* p83: remove reference to simple interest and rephrase Basic Skill Example 2 so that the interest is calculated as a single lump sum rather than as simple interest
* p84: Basic Skill Examples 3 and 4 (calculating APR): remove both, and replace with a simple example where APR is given.
* p84: remove entire section on what an exam question might look like for loans, as past exam questions are not consistent enough to draw conclusions
* p84: remove Style Example 1 (Liu family) as this was designed to be relevant to a specific unit assessment question which is no longer compulsory. Replace with new Basic Skill example with same figures but using hire purchase. Renumber Assessment Style Example 2 to just "Assessment Style Example"
* p89: small changes to the "what an exam question looks like" box to reflect that a nonstandard scale may be required
* p91: Basic Skill Example 2. Add basic context (shoe sizes) and label on axis.
between Version 2.2 and 3.0
[version 3.0 NOW COMPLETE AND PUBLISHED]
* adjust font to be sans-serif (Calibri) rather than Times New Roman
* make wording/examples more consistent between N5 Maths and N5 Applications of Maths, in sections where the content is the same
* all assessment-style questions rephrased to have a clear command word in line with SQA strategies. e.g. "how many..." changed to "Calculate how many..."; "make [a drawing]" changed to "construct..."; "is the..." changed to "determine whether the..."
* many minor layout/phrasing issues
* remove formulae and all references to semi-interquartile range; and only remain InterQuartile range (formula sheet at start and statistics chapter)
* throughout (all explanation/justify examples): add in example where explanation includes a 'less than' sign
* pages 11/12: use term 'grid method' rather than 'box method'
* in Numeracy chapter, new section on BODMAS added following 2018 exam question
* in the Numeracy chapter, all Percentages and Fractions content integrated into one section
* add in extra example for adding/taking away to include the 'standard' method as well as 'kiss and smile'
* add in second (assessment-style) example about indirect proportion
* tolerances for all lengths adjusted from +-2mm to +-1mm and for angles from +-2 to +-1 (pages 36, 38, 39, 40...
* page 41, basic skills example. Changed all words to be 'tins' (sometimse 'cans' was used, which could be confusing)
* pages 42-43. Adjust wording of container packing examples to match SQA phrasing ("orient", "must be aligned in same direction")
* remove one of the container packing examples (the one with six orientations) as it appears to be more difficult than the exam standard that the SQA is setting.
* remove the container packing example that relates to first fit as this is N4 not N5
* task planning: change "prerequisite task" to "preceding task" to match vocabulary used in SQA exams
* task planning: add in section with advice on filling out activity networks
* Task Planning Assessment Style Example: adjust example to better reflect recent exam questions
* remove the two examples of Pythagoras in circles as it appears unlikely to form part of the content of future exam questions
* Gradient: add in additional assessment-style example of comparing fractional gradients without a calculator.
* Net pay: adapt assessment style example 1 (Rachel/radiographer) so that it's net pay being calculated rather than gross pay
* National Insurance: Basic Skills Example. Adapt table to have third row, and adapt wording to better reflect 2018 exam question.
* adjust Best Deal example to better reflect SQA exam questions
* in Foreign Exchange sentence, add in sentence clarifying meaning of commission
* adapt interest comparison question to take into account fact that first 1000 of savings interest is now tax-free
* exchange rates updated to be more relevant to the 2018/9 markets
* years in the boxplot question updated to 2018/2014 rather than 2014/2010
between Version 2.1 and 2.2
[version 2.2 NOW COMPLETE AND PUBLISHED]
* changed all occurrences of "Lifeskills Mathematics" to "Applications of Mathematics" to reflect SQA course name change
* page 31, typing mistake "757" for action film changed to "75"
* in "writing comments on statistics" added in a note to use the word 'on average' in sentences about the mean and added in an extra example of a sentence that wouldn't get any marks
between Version 2.0 and 2.1
* Basic Skill Example 2 - container packing - in step three, it said "shoe boxes", now changed to "tissue boxes"
* minor changes to layout; and to line spacing in container packing section
* changed container packing question to reflect fact that smaller containers will not necessarily be of the same size. Added in extra Assessment Style Example 3.
between Version 1.1 and 2.0
[version 2.0 NOW COMPLETE AND PUBLISHED]
* various other examples added in throughout, including:
* multiplying two two-digit numbers (one basic plus one assessment example); dividing by two-digit numbers (one basic plus one assessment)
* finding percentage without a calculator
* rewriting section on container packing to include two new examples plus revised layout/phrasing of the existing example
* rewriting entire section on scale drawing in an attempt to make examples and diagrams clearer
* adding question on comparing fractions
* adding extra example on converting time to/from decimal; and rewrote existing one to make it more relevant to way course is phrased
* comparing time differences question (Jen/Jo/Phone call)
* add in another APR example
* cone slant height
* Changed Basic Skills Example 1 in Time Zones from May to March so that Daylight Savings Time doesn't make a difference
* page 47: should say 348m instead of 448m and rest of example corrected to match
between Version 1.0 and 1.1
[version 1.1 NOW COMPLETE AND PUBLISHED]
* Tax examples changed to match real-life thresholds
* Pythagoras in circles diagrams changed to make them less faint
* p5 "if a mark requires" changed to "if a question requires"
* p7 "units is split" changed to "units are split"
* p8 style of explanation required for a comparison is often ... word "different" had been missed out
* p9 "you will lost" changed to "you will lose" and bookmark error at base fixed
* p11 9.428 changed to 9.42
* p12 Basic Skill Example: number 446.586 written again by mistake; should have been 0.00567
* p13 "In this questions" changed to "in these questions"
* p22 Ratio written the wrong way around should be 17:19 not 19:17
* p23 "kept at the a temperature" changed to "kept at a temperature"
* p24 faint table rewritten to be easier to read
* p29 Assessment style example, 3rd bullet point, "No" changed to "Yes"
* p33 "if the diagram had been drawn" changed to "if the diagram has been drawn"
* p35 "with A being the most efficient" changed to "with C being the most efficient"
* p60 "pay tax on your income you" changed to "pay tax on the income you"
* p63 "you get 1.27 dollars" changed to "you get 1.27 euros"
* p65 "above" changed to "on the previous page"
* p66 "six years" changed to "three years"
* p75/78 "ask your to" changed to "ask you to" on three occasions
NATIONAL 4 APPLICATIONS OF MATHEMATICS REVISION NOTES CORRECTIONS/UPDATES
between Version 3.0 and 3.1
* various minor formatting changes
*
between Version 2.1 and 3.0
[version 3.0 NOW COMPLETE AND PUBLISHED]
* adjust font to be sans-serif (Calibri) rather than Times New Roman
* make wording/examples more consistent between N4 Maths and N4 Applications of Maths, in sections where the content is the same
* all assessment-style questions rephrased to have a clear command word in line with SQA strategies. e.g. "how many..." changed to "Calculate how many..."; "make [a drawing]" changed to "construct..."; "is the..." changed to "determine whether the..."
* many minor layout/phrasing issues
* throughout (all explanation/justify examples): add in example where explanation includes a 'less than' sign
* add brief section on bar charts, line graphs and trend
* in probability section, give all answers as either a percentage or a fraction rather than always fractions
* add in more detail of explanations that would/wouldn't get marks in relevant questions.
* loan example 3: adjust the question to ask how much was paid each month rather than in total (the solution didn't match the question)
* remove section on bias/sampling. This is not in the course.
* update all diagrams in the scatter graph section to make them clearer
* update pie chart drawing example to include the drawing of the pie chart, not just calculating the angles
* scale drawing: Rewrite solution in Example 1 and Example 2 for increased clarity
* container packing: remove the example of crates being packed into a lorry
* area: remove entire section on surface area of a prism as this is not in the course
between Version 2.0 and 2.1
* p39 Example 3 (loan repayments) final line had incorrect totals ( 795.42 and 795.38). These should have been 1193.13 and 1193.09.
between Version 1.1 and 2.0
[version 2.0 NOW COMPLETE AND PUBLISHED]
* changed all occurrences of "Lifeskills Mathematics" to "Applications of Mathematics" to reflect SQA course name change
* all references indicating that a specific question would be in the Added Value Unit removed, to reflect the fact that schools can now make their own AVUs.
* Example 3 - loans. Previously whole year's interest was added on. Question corrected (and starting value changed) in order to reflect fact that only 8 months interest should be added
between Version 1.0 and 1.1
[version 1.1 NOW COMPLETE AND PUBLISHED]
* decimal points replaced with throughout to match SQA formatting
* reformatted the negative number section so that explanations are clearer and examples are aligned in columns
* added in section on First Fit Algorithm
NATIONAL 4 MATHEMATICS CORRECTIONS
between Version 2.0 and 2.1
* various minor formatting changes
* moved the copyright statements and the record of corrections from back page to after contents
* factorising Example 1, "Write 3 in front of the bracket" becomes "Write 3 in front of the brackets"
* area of a circle example 3, incorrect "continued on next page" removed from middle of answer
* changing subject of a formula examples 1 and 2, minor change to sentence before each example
* adjust fonts in diagrams in right-angled trigonometry section and adjust wording of Example 3 to better match a 'do the same to both sides' strategy
between Version 1.6 and 2.0
[version 2.0 NOW COMPLETE AND PUBLISHED]
* adjust font to be sans-serif (Calibri) rather than Times New Roman
* make wording/examples more consistent between N4 Maths and N4 Applications of Maths, in sections where the content is the same
* all assessment-style questions rephrased to have a clear command word in line with SQA strategies. e.g. "how many..." changed to "Calculate how many..."; "make [a drawing]" changed to "construct..."; "is the..." changed to "determine whether the..."
* many minor layout/phrasing issues
* throughout (all explanation/justify examples): add in example where explanation includes a 'less than' sign
* add in more detail of explanations that would/wouldn't get marks in relevant questions.
* in probability section, give all answers as either a percentage or a fraction rather than always fractions
* update pie chart drawing example to include the drawing of the pie chart, not just calculating the angles
* change example 1 in 'equations with letters on both sides' to have different coefficients of each letter to minimise confusion. Tidy up working/layout in the entire equations section.
* update all diagrams in the scatter graph section to make them clearer
between Version 1.5 and 1.6
* decimal points replaced with throughout to match SQA formatting
* reference to 2sf in cylinder volume question changed to 1dp
* reformatted the negative number section so that explanations are clearer and examples are aligned in columns
between Version 1.4 and 1.5
[VERSION 1.5 NOW COMPLETE AND PUBLISHED]
* references to (fixed) content of old Added Value Unit removed since all content is now examinable in AVU
between Version 1.3 and 1.4
[VERSION 1.4 NOW COMPLETE AND PUBLISHED]
* changed grouped frequency table example to match style of unit assessment
* Introduction: phrase "Schools or individuals who purchase a site licence before the first National 5 exam in May 2014 will be eligible to receive a free copy of any revised notes. To enquire further about this, email david@dynamicmaths.co.uk " removed now that May 2014 is here.
* Back page "maths" changed to "Mathematics"
* Font size changed in section 1 to match the rest of the notes
* Various minor punctutation and wording changes throughout.
* update table of percentages to make fractions easier to read
* added in part (b) to gradient example
* Added in example of area of composite shape involving taking away
* grey background for definitions to make them stand out
* method in pie chart changed
* 'O', 'A' and 'H' in trigonometry section changed to be 'Opp', 'Adj' and 'Hyp' to avoid confusion with any potential confusion with letters such as 'h' for height
between Version 1.2 and 1.3
[VERSION 1.3 NOW COMPLETE AND PUBLISHED]
* Added in new section "Exam Technique" covering communication marks, rounding, units etc
* extra example 4 added in to non calculator percentage section as a multiple of 1%. Also units changed in example 1 so not all money.
* Explained meanings of "denominator" in Fraction/Percentage section; and replaced numerator with "number on top"
between Version 1.1 and 1.2
[VERSION 1.2 NOW COMPLETE AND PUBLISHED]
* An example added on ratio
* A few minor grammatical and/or layout errors corrected on pages 8, 20, 23, 29, 33, 43, 53, 55, 58, 59
* Page 40 "when discrete table is" should read "when discrete data is"
* Page 41 Example 2. "the list of number above" changed to reflect the fact that the list is actually on the previous page in Example 1.
* Page 46. " of the form y=b where a can be...". 'a' should be 'b'
* Page 57. In step two it says "we have the opposite". Should say "adjacent".
* Page 58. In the quadrilateral solution it says "x = 360-90-65-50". 'x' should read 'y'
* Page 78. Diagram added to Example 1