Higher Mathematics Online Textbook

Welcome to our Higher Mathematics Differentiated Online Textbook!

To download an exercise please click on the links below. Print back to back if you want to include the answers. If you just want the questions, be sure to just print page 1.

If students require a lesson before hand to access the outcomes covered in the textbook exercises you will find around 200 of them here. Simply copy and paste the video lessons into your desired platform to share with your students, e.g. Show my Homework, GLOW, Edmodo, etc.

**THIS IS VERY MUCH A WORK IN PROGRESS AND CONTENT WILL BE ADDED OVER THE COURSE OF THE YEAR. KEEP CHECKING THIS PAGE FOR REGULAR UPDATES**

Underlined exercises have a textbook exercise uploaded.

Topic 1 - The Straight Line

1.1 - The gradient of a straight line

1.2 - The equation of a straight line

1.3 - Calculating the gradient/angle when given the angle/gradient

1.4 - The distance between 2 points

1.5 - Calculating the Midpoint

1.6 - Parallel and perpendicular gradients

1.7 - Collinearity

1.8 - Medians, altitudes and perpendicular bisectors

1.9 - Points of intersection 1

Straight Line Cheat Sheet

Topic 2 - Recurrence Relations

2.1 - Calculating missing terms in recurrence relations 

2.2 - Calculating the limit  in a recurrence relation

2.3 - Finding the values of a and b in a recurrence relation

2.4 - Recurrence relations in context

Recurrence Relations Cheat Sheet

Topic 3 - Functions

3.1 - Domain and range 

3.2 - Composite functions

3.3 - Calculating the inverse function

Functions Cheat Sheet

Topic 4 - Graphs of functions

4.1 - Graphs of related functions 

4.2 - Graphs of exponential and logarithmic functions

Graphs of Functions Cheat Sheet

Topic 5 - Graphs of trigonometric functions

5.1 - Changing between degrees and radians

5.2 - Trigonometric graphs

Graphs of trigonometric functions Cheat Sheet

Topic 6- Differentiation

6.1 - Learning to differentiate

6.2 - Rates of change

6.3 - The tangent to a curve

6.4 - Increasing/decreasing functions

6.5 - Stationary points and curve sketching

6.6 - Maximum and minimum values within a closed interval

6.7 - Optimisation

Differentiation Cheat Sheet

Topic 7 - Polynomials

7.1 - Factorising polynomials

7.2 - Finding unknown values in polynomials

7.3 - Points of intersection 2

Polynomials Cheat Sheet

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

Quadratics Cheat Sheet

Topic 9 - Integration

9.1 - Indefinite integrals

9.2 - Definite integrals

9.3 - Solving differential equations

9.4 - Shaded area

Integration Cheat Sheet

Topic 10 - Trigonometry

10.1 - Double angle and addition formulae

10.2 - Solving trig equations

10.3 - Trig identities

Trigonometry Cheat Sheet

Topic 11 - The Circle

11.1 - The equation of a circle

11.2 - The tangent to a circle

11.3 - Points of intersection 4

11.4 - Intersecting circles

The Circle Cheat Sheet

Topic 12 - Vectors

12.1 - Vector calculations

12.2 - Vector journeys

12.3 - Collinearity

12.4 - Perpendicular vectors

12.5 - The angle between 2 vectors

Vectors Cheat Sheet

Topic 13 - Further Calculus

13.1 - Further differentiation

13.2 - Further integration

Further Calculus Cheat Sheet

Topic 14 - Logs and Exponentials

14.1 - Simplifying logarithmic expressions

14.2 - Solving log equations

14.3 - Solving exponential equations

14.4 - Experimental data

Logs and Exponentials Cheat Sheet

Topic 15 - The Wave Function

15.1 - Finding the wave function

15.2 - Part (b) type questions

The Wave Function Cheat Sheet