KT Classroom Information Sheet

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

IDENTIFYING FORMULAE AND EQUATIONS GIVEN ON THE FORMULA SHEET TOPIC Analytical Geometry

DESCRIPTION OF FORMULA 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 (a; b ) and radius r .

Calculus

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

Algebra

Solution of a quadratic equation.

3

WRITE DOWN FORMULA or EQUATION

Preparation for the Mathematics examination brought to you by Kagiso Trust

TOPIC Financial Mathematics

DESCRIPTION OF FORMULA 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.

WRITE DOWN FORMULA or EQUATION

Identifying and writing down formulae

TOPIC Trigonometry

DESCRIPTION OF FORMULA The sine rule

WRITE DOWN FORMULA or EQUATION

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.

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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 Analytical Geometry

DESCRIPTION OF FORMULA The product of the gradients of lines perpendicular to each other.

Calculus

The differentiation rule

Financial Mathematics

The average gradient between two points at x = a and x = b on a curve f (x ) .

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

Series & Sequences

WRITE DOWN FORMULA

The last or n th term of an arithmetic series or sequence.

The last or n th term of a geometric series or sequence.

The last or n th term of a quadratic series or sequence.

There are two formulae. Write both down.

Transformation Geometry

The coordinates of the image point A′(x ′; y ′) of a point A(x; y ) rotated about the origin through an angle of θ.

Trigonometry

General solutions if 1.

2.

3.

sin θ = k cosθ = k tan θ = k

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.