Advanced Higher Mathematics

This page contains free Dynamic Worksheets relating to the Advanced Higher Mathematics course. If you want resources for other levels of course, go to our Free Resources homepage.

Free Resources:

SQA Exam Question Bank: Advanced Higher Maths (a database of all past exam questions, including questions from the old Advanced Higher and Sixth Year Studies (CSYS) syllabi going back to the 1990s)
Formula Sheet: a colour coded list of formulae relevant to the course

Resources that can be purchased in our Online Store:

These are the only resources on this site that require payment. Every other resource listed is entirely free.

Advanced Higher Maths Revision Notes (cost: £45 for schools/colleges/tutors, £10 for individual learners, parents or carers. Bulk discount available if purchasing more than one level.)

Free Solver Spreadsheets (easy ways for teachers to check answers to questions):

Dot (scalar) product and cross (vector) product SOLVER - input two or three vectors a, b, c and automatically get a.b and a × b and b.c etc... Saves repeated determinant calculation. sAlso now updated to calculate scalar triple product as well.
Gaussian elimination SOLVER - enter a system of three equations with three unknowns in augmented matrix form, the system solves to obtain the lower triangular form and the reduced echelon form
Matrices SOLVER - enter up to two 2×2 or 3×3 matrices, and the solver automatically calculate the determinant, the product, the inverse (of 2×2 matrices only), the square and the cube
Inverse of a 3×3 matrix SOLVER - enter a 3×3 matrix into an augmented matrix, and the solver automatically calculate the inverse matrix using elementary row operations
Euclidean Algorithm SOLVER - enter two numbers and find their greatest common divisor
Changing Number Bases SOLVER - enter a base 10 number and a base (between 2 and 64) and the number will be converted into that base.
Angles between vectors:
- Angle between vectors from coordinates SOLVER - input three 3d coordinates A, B and C and automatically get the angles ABC, ACB and BAC.
- Angle between vectors SOLVER - input two or three vectors and get the angle(s) between them.

Free Dynamic Worksheets covering specific topics at this level:

Outcome	Topic(s)	Worksheet(s)
Methods in Algebra and Calculus Unit: Assessment Standard 1.1	Long division, Partial fractions	No content yet
Methods in Algebra and Calculus Unit: Assessment Standard 1.2	Differentiation	No content yet
Methods in Algebra and Calculus Unit: Assessment Standard 1.3	Integration	No content yet
Methods in Algebra and Calculus Unit: Assessment Standard 1.4	Differential Equations	No content yet
Applications in Algebra and Calculus Unit: Assessment Standard 1.1	Binomial Theorem, Complex Numbers	Complex-01: modulus and argument of complex numbers
Applications in Algebra and Calculus Unit: Assessment Standard 1.2	Sequences and Series	No content yet
Applications in Algebra and Calculus Unit: Assessment Standard 1.3	Summation, Proof by Induction	No content yet
Applications in Algebra and Calculus Unit: Assessment Standard 1.4	Functions, Graphs, Stationary Points	No content yet
Applications in Algebra and Calculus Unit: Assessment Standard 1.5	Motion, Optimisation	No content yet
Geometry, Proof and Systems of Equations Unit: Assessment Standard 1.1	Matrices, Gaussian Elimination	Matrices SOLVER - enter up to two 2×2 or 3×3 matrices, and the solver automatically calculate the determinant, the product, the inverse and the square Gaussian elimination SOLVER - enter a system of three equations with three unknowns in augmented matrix form, the system solves to obtain the lower triangular form and the reduced echelon form Inverse of a 3×3 matrix SOLVER - enter a 3×3 matrix into an augmented matrix, and the solver automatically calculate the inverse matrix using elementary row operations
Geometry, Proof and Systems of Equations Unit: Assessment Standard 1.2	Vectors, Lines, Planes	Dot (scalar) product and cross (vector) product SOLVER - input two or three vectors a, b, c and automatically get a.b and a × b and b.c etc... Saves repeated determinant calculations Angles between vectors: Angle between vectors from coordinates SOLVER - input three 3d coordinates A, B and C and automatically get the angles ABC, ACB and BAC. Angle between vectors SOLVER - input two or three vectors and get the angle(s) between them.
Geometry, Proof and Systems of Equations Unit: Assessment Standard 1.3	Polar Form, de Moivre, Argand Diagrams	No content yet
Geometry, Proof and Systems of Equations Unit: Assessment Standard 1.4	Euclidean Algorithm, Number Bases	Euclidean Algorithm SOLVER - enter two numbers and find their greatest common divisor Changing Number Bases SOLVER - enter a base 10 number and a base (between 2 and 64) and the number will be converted into that base.
Geometry, Proof and Systems of Equations Unit: Assessment Standard 1.5	Proof	No content yet

Looking for maths tutoring? Saturday School Scotland offer tutoring for National 5 and Higher Mathematics and use Dynamic Maths revision notes