targeting that grade c in mathematics a simplified revision guide st edmund campion mathematics...
DESCRIPTION
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 = £35TRANSCRIPT
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Targeting that Grade C in Mathematics
A Simplified Revision Guide
St Edmund Campion Mathematics Department
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2 + 3 = 8 + 217 4 28
= 29 = 1 1
28 28
Adding Fractions: SMILEY FACE
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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
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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
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Pythagoras’ Theorem
13cm
17cm
17² + 13² = 458
√458 = 21.4cm (3sf)
9cm
14cm
14² - 9² = 115
√115 = 10.7cm (3sf)
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Solving Equations
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Solve Equations with Unknown on Both Sides
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Trial & ImprovementThe question will tell you what 2 values the solution lies between. Always start halfway between the two numbers
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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
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Straight Line Graphs
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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
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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
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Planes of Symmetry
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The Circle Parts
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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)
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Angle Types
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Area of Triangle
Area = 12 x 8 2
= 48cm²Multiply BUT remember to halve your answer
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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
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Volume of Cuboid
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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)
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Quadrilaterals: 4 Sides
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Measuring Angles
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Drawing Angles
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Long Multiplication of Decimals
Forget about decimal point first, but remember to put it back in the right place at the end.
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Perpendicular and Angle Bisectors
Put compass points at A and B and draw to arcs that cross (zulu shield)
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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)
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Metric and Imperial UnitsMetric Imperial
Metres Yards, Feet
Centimetres Inches
Kilometres Miles
Grams Ounces
Kilograms Stone/pounds
Litres Gallons
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Prime Factors: Factor Trees
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+, + ―> ++, - ―> --, + ―> --, - ―> +
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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
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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
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Pie Charts
360 20 = 18
Multiply all frequencies by 18
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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
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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
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Stem and Leaf Diagrams
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B I D M A S
6 + 4 x 3 = 6 + 12 = 18
20 ― 6 x 3 = 20 – 18 = 2
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Tesselations
A shape tessellates if it fits together without leaving any gaps like a jigsaw.
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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
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Translations
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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)
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Indices
3x7 × 4x² = 12x9
x2 × x4 = x6
x5 x = x4
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Substitution
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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
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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
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Frequency Polygons
Need to plot the frequency against the mid group value.
Can draw the bars in first