Targeting that Grade C in Mathematics

A Simplified Revision Guide

St Edmund Campion Mathematics Department

2 + 3 = 8 + 217 4 28

= 29 = 1 1

28 28

Adding Fractions: SMILEY FACE

Fraction of an Amount

1. Divide amount by denominator (bottom)2. Multiply by the numerator (top)

Find ⅚ of £42

Answer: 42 6 × 5 = £35

Percentage Increase/Decrease with a Calculator

1. Divide amount by 100 using your calculator2. Multiply by the percentage3. Add or subtract to the original amount depending

whether it is an increase or decrease

Increase £342 by 19%

Answer: 342 100 × 19 = £64.98

£342 + £64.98 = £406.98

Pythagoras’ Theorem

13cm

17cm

17² + 13² = 458

√458 = 21.4cm (3sf)

9cm

14cm

14² - 9² = 115

√115 = 10.7cm (3sf)

Solving Equations

Solve Equations with Unknown on Both Sides

Trial & ImprovementThe question will tell you what 2 values the solution lies between. Always start halfway between the two numbers

Estimating

Always round the numbers as much as possible so that you make the calculation the easiest it can be.

By first rounding each number to 1 significant figure find estimates to the following calculation: 2.8 x 61.59 ≈ 3 x 60 = 180 = 18 12.9 10 10

It is easier to round 12.9 to 10 instead of 13

Straight Line Graphs

Percentages without a Calculator

1. Find 10% first by dividing by 10 (take off 0)2. Then halve to get 5%3. And halve again to get 2½ % if needed4. Add answers together to get required percentage

Find 15% of £210

Answer: 10% = £21 5% = £10.50

15% = 21 + 10.50 = £31.50

Ratios

Make sure you read the

question carefully first

Divide £120 in the ratio of 5:1

1) 5 + 1 = 6 2) 120 6 = £20

3) 5 x 20 = £100 1 x 20 = £20

Planes of Symmetry

The Circle Parts

The Circle: Area and Circumference

A = πr²

= 3.14 x 5.8 ²

= 105.6cm² (1dp)

C = πd

= 3.14 x 11.2

= 35.2cm (1dp)

Angle Types

Area of Triangle

Area = 12 x 8 2

= 48cm²Multiply BUT remember to halve your answer

Area of Composite Shape

Split into a triangle and a rectangle

Area = 6 x 8 2

= 24cm²

Area = 6 x 10 = 60cm²

Total Area = 24 + 60 = 84cm²

Volume of Cuboid

Volume of Triangular Prism

Multiply the base, height and length together BUT remember to halve as it is triangular

Volume = 1.7 x 2.3 x 13 2

= 25.4cm³(1dp)

Quadrilaterals: 4 Sides

Measuring Angles

Drawing Angles

Long Multiplication of Decimals

Forget about decimal point first, but remember to put it back in the right place at the end.

Perpendicular and Angle Bisectors

Put compass points at A and B and draw to arcs that cross (zulu shield)

3D Coordinates

Always (x, y, z) and start from (0, 0, 0)The questions usually involve a cuboid and you need to identify coordinates

U = (4, 7, 0)Q = (4, 0, 0)R = (4, 0, 3)V = (0, 0, 3)T = (0, 7, 0)S = (0, 7, 3)O = (0, 0, 0)

Metric and Imperial UnitsMetric Imperial

Metres Yards, Feet

Centimetres Inches

Kilometres Miles

Grams Ounces

Kilograms Stone/pounds

Litres Gallons

Prime Factors: Factor Trees

+, + ―> ++, - ―> --, + ―> --, - ―> +

5 12 19 26 33Difference

= 7

0th Term = -2 (this would be the number before the first term

So nth term formula is: T(n) = 7n - 2

nth Term of Sequence

Averages

Mean: Add up the numbers and divide by how many there are

Mode: Most common number

Median: The middle number

Range: The highest value subtract the lowest

Pie Charts

360 20 = 18

Multiply all frequencies by 18

Estimated Mean

1. Find mid points2. Multiply frequency

and midpoints to get fx

3. Add up frequency and fx columns

4. Divide sum of fx column by frequency column to get answerMean = 4320 120 = 36

A correlation shows a relationship between the two pieces of data

being graphed. There are three types of

correlation. x x x

x x

x x x

x x x

POSITIVE NEGATIVE NO Correlation

Scattergraphs and Correlation

Stem and Leaf Diagrams

B I D M A S

6 + 4 x 3 = 6 + 12 = 18

20 ― 6 x 3 = 20 – 18 = 2

Tesselations

A shape tessellates if it fits together without leaving any gaps like a jigsaw.

Rotating a Shape

1. Use tracing paper and trace the shape

2. Put pencil at the coordinate

3. Rotate (turn) the shape the number of degrees anticlockwise

Translations

Factorising

Number Factors

Look for the largest number that goes into both numbers

Factorise 12a + 15

3 is the largest number that goes into 12 and 15

12a + 15 = 3(4a + 5)

Letter Factors

Look for the common letters

Factorise 4a² + 7a

= 4aa + 7a

= a(4a + 7)

Indices

3x7 × 4x² = 12x9

x2 × x4 = x6

x5 x = x4

Substitution

Multiplying Fractions

1. Multiply the Numerators (Top numbers)2. Multiply the denominators (bottom numbers)3. Simplify your answer

3 x 6 = 3 x 6 = 18 = 94 7 4 x 7 28 14

Area, Perimeter and Volume by Counting

Perimeter

Count the outside of the shape

Area

Count the squares inside the shape

Perimeter = 10cm

Area = 5cm²

Volume

Count the cubes that make up the

shape

Volume = 10cm³

Frequency Polygons

Need to plot the frequency against the mid group value.

Can draw the bars in first