MATHEMATICS

Learner’s Study and

Revision Guide for

Grade 12

Identifying formulae on the Information Sheet

Revision Notes by

Roseinnes Phahle

Information Sheet (or Formula Sheet) by the Department of Basic Education

Preparation for the Mathematics examination brought to you by Kagiso Trust

INFORMATION SHEET

This is a formula sheet that will be given to you in the examination. Always refer to it as you are preparing for the examination so you become familiar with what is on it and what is not.

Identifying and writing down formulae

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IDENTIFYING FORMULAE AND EQUATIONS GIVEN ON THE FORMULA SHEET

TOPIC DESCRIPTION OF FORMULA WRITE DOWN FORMULA or EQUATION Analytical Geometry Gradient of a line given two points.

Equation of a line given the slope and the y - intercept.

Equation of a line given the slope and a point on the line.

The relationship between the slope of a line and the angle θ made by the line with the positive direction of the x -axis.

The distance formula.

The midpoint formula.

The equation of a circle with centre ( )ba; and radius r .

Calculus Definition of ( )xf ' in terms of the formula you use to differentiate from first principles.

Algebra Solution of a quadratic equation.

Preparation for the Mathematics examination brought to you by Kagiso Trust

TOPIC DESCRIPTION OF FORMULA WRITE DOWN FORMULA or EQUATION Financial Mathematics

Simple Interest – Growth Simple Interest – Decay

Compound Interest – Growth Compound Interest – Decay

Future Value

Present Value

Series & Sequences The sum of n 1’s.

The sum of 1+2+3+ . . . . . + n

The sum of the first n terms of an arithmetic series.

The sum of the first n terms of a geometric series.

The sum to infinity of a geometric series and the condition for its convergence.

Identifying and writing down formulae

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TOPIC DESCRIPTION OF FORMULA WRITE DOWN FORMULA or EQUATION Trigonometry The sine rule

The cosine rule

Area rule

The sine of the sum of two angles.

The cosine of the sum of two angles.

The sine of the difference of two angles.

The cosine of the difference of two angles.

The sine of a double angle.

The cosine of a double angle 1. 2. 3.

Data Handling The mean.

Variance.

Preparation for the Mathematics examination brought to you by Kagiso Trust

FORMULAE THAT DO NOT APPEAR ON THE FORMULA SHEET

Certain formulae do not appear on the formula sheet that is given to you in the examination. Complete the table below by writing them in. Learn to derive them and memorise them as they will not be on the formula sheet.

TOPIC DESCRIPTION OF FORMULA WRITE DOWN FORMULA Analytical Geometry The product of the gradients of lines

perpendicular to each other.

Calculus The differentiation rule

The average gradient between two points at ax = and bx = on a curve ( )xf .

Financial Mathematics

Converting a nominal rate of interest to an effective rate of interest

Series & Sequences The last or thn term of an arithmetic series or sequence.

The last or thn term of a geometric series or sequence.

The last or thn term of a quadratic series or sequence. There are two formulae. Write both down.

Transformation Geometry

The coordinates of the image point( )yxA ′′′ ; of a point ( )yxA ; rotated

about the origin through an angle of θ .

Trigonometry General solutions if

1. k=θsin 2. k=θcos 3. k=θtan

Other formulae or rules that do not appear on the formula sheet you will be given in the examination are covered under appropriate sections in the Revision Units. For example, not all transformation rules are listed above.