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.
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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.