Corrections appear in this file in this order:
* ADVANCED HIGHER MATHEMATICS CORRECTIONS
* NEW HIGHER MATHEMATICS CORRECTIONS
* NATIONAL 5 MATHEMATICS CORRECTIONS
* NATIONAL 5 APPLICATIONS OF MATHEMATICS (LIFESKILLS MATHEMATICS) CORRECTIONS
* NATIONAL 4 APPLICATIONS OF MATHEMATICS (LIFESKILLS MATHEMATICS) CORRECTIONS
* NATIONAL 4 MATHEMATICS CORRECTIONS
ADVANCED HIGHER MATHEMATICS CfE CORRECTIONS
between Version 1.1 and 1.2
* removed "which will be examined in May 2016"
* 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
NEW HIGHER MATHEMATICS CORRECTIONS
between Version 1.4 and 1.5
* change title on front page from "New (CfE) Higher Mathematics Course Notes" to "Higher Mathematics Course Notes"
* change numerator in Example 1 on page 23 to '5 + x' rather than '3 + x' as previously the fraction inadvertently could be cancelled
* 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 CORRECTIONS
between Version 2.1 and 2.2
* 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 (LIFESKILLS MATHEMATICS) CORRECTIONS
between Version 2.2 and 2.3
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 (LIFESKILLS MATHEMATICS) CORRECTIONS
between Version 2.0 and 2.1
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 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
* 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