Higher Maths SQA Past paper booklets

Welcome to our Higher Mathematics SQA Past paper topic by topic booklet section! These booklets are designed to be downloaded and viewed electronically but feel free to print them off if you wish. Just simply click on the links below to download them.

Most questions are linked to a full video solution. Just click on each link if viewing them electronically. We will also keep updating any missing links over time.

These topic by topic booklets should give you an indepth understanding of the types of questions that could appear in your final examination. Try and answer each question more than once throughout the year. If you manage this, you will instantly recognise (and therefore should know how to answer!) at least 90% of your final exam.

Good luck!

Topic 1 - Straight Line

1.1 - Gradient of a straight line (no stand alone questions have been asked)

1.2 - Equation of a straight line (no stand alone questions have been asked)

1.3 - Calculating the gradient when given the angle

1.4 - The distance between two points (no stand alone questions have been asked)

1.5 - Calculating the Midpoint (no stand alone questions have been asked)

1.6 - Parallel and perpendicular gradients

1.7 - Collinearity

1.8 - Medians, altitudes and perpendicular bisectors

1.9 - Points of intersection 1

Topic 2 - Recurrence Relations

2.1 - Calculating missing terms

2.2 - Finding the limit

2.3 - Calculating the values of 'a' and 'b'

2.4 - Recurrence relations in context

Topic 3 - Functions

3.1 - Domain and range

3.2 - Composite functions

3.3 - Inverse functions

Topic 4 - Graphs of related functions

4.1 - Graphs of related functions

4.2 - Logarithmic and exponential graphs

Topic 5 - Trigonometric functions and graphs

5.1 - Working with radians (no stand alone questions have been asked)

5.2 - Graphs of trigonometric functions

Topic 6 - Differentiation

6.1 - Learning to differentiate

6.2 - Rates of change

6.3 - Tangent to curve

6.4 - Increasing and decreasing functions

6.5 - Stationary points and curve sketching

6.6 - Maximum and minimum values in closed intervals

6.7 - Optimisation

Topic 7 - Polynomials

7.1 - Factorising polynomials

7.2 - Finding missing terms

7.3 - Points of intersection 2

Topic 8 - Quadratics

8.1 - Writing the equation of a quadratic/cubic

8.2 - Completing the square

8.3 - Quadratic inequalities

8.4 - The discriminant

8.5 - Points of intersection 3

Topic 9 - Integration

9.1 - Indefinite integrals

9.2 - Definite integrals

9.3 - Differential equations

9.4 - Shaded area

Topic 10 - Trigonometry

10.1 - Trigonometric formulae

10.2 - Trig equations

10.3 - Trig identities

Topic 11 - The circle

11.1 - The equations of a circle

11.2 - Tangent to a circle

11.3 - Points of intersection 4

11.4 - Intersecting circles

Topic 12 - Vectors

12.1 - Vector calculations

12.2 - Vector journeys

12.3 - Collinearity and ratio

12.4 - Scalar product

12.5 - The angle between 2 vectors

Topic 13 - Further calculus

13.1 - Further differentiation

13.2 - Further integration

Topic 14 - Logs and exponentials

14.1 - Simplifying a numerical expression

14.2 - Solving log equations

14.3 - Exponential equations

14.4 - Experimental data

Topic 15 - The Wave Function

15.1 - The Wave Function part (a)'s

15.2 - The Wave Function part (b)'s