Targeting that Grade C in Mathematics A Simplified Revision Guide St Edmund Campion Mathematics Department

2 + 3 = = 29 = 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 Find ⅚ of £42 Answer: 42  6 × 5 = £35

Percentage Increase/Decrease with a Calculator 1.Divide amount by 100 using your calculator 2.Multiply by the percentage 3.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 = £ 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 & Improvement The 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 ≈ 3 x 60 = 180 = 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 needed 4.Add answers together to get required percentage Find 15% of £210 Answer: 10% = £21 5% = £ % = = £31.50 Find 15% of £210 Answer: 10% = £21 5% = £ % = = £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 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 = 48cm² Multiply 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 = = 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) 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 Units MetricImperial MetresYards, Feet CentimetresInches KilometresMiles GramsOunces KilogramsStone/pounds LitresGallons

Prime Factors: Factor Trees

+, + ―> + +, - ―> - -, + ―> - -, - ―> +

Difference = 7 0 th Term = -2 (this would be the number before the first term So nth term formula is: T(n) = 7n - 2 nth Term of Sequence

AveragesAverages 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 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 points 2.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 answer 1.Find mid points 2.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 answer Mean = 4320  120 = 36

A correlation shows a relationship between the two pieces of data being graphed. There are three types of correlation. x xx x x x x x POSITIVE NEGATIVE NO Correlation Scattergraphs and Correlation

Stem and Leaf Diagrams

B I D M A S x 3 = = ― 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 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 3x 7 × 4x² = 12x 9 x 2 × x 4 = x 6 x 5  x = x 4

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 = x

Area, Perimeter and Volume by Counting Perimeter Count the outside of the shape Perimeter Count the outside of the shape Area Count the squares inside the shape Area Count the squares inside the shape Perimeter = 10cm Area = 5cm² Volume Count the cubes that make up the shape 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 Need to plot the frequency against the mid group value. Can draw the bars in first