Transcript Adding Fractions: SMILEY FACE

Targeting that Grade C in Mathematics
A Simplified Revision Guide
St Edmund Campion Mathematics Department
Adding Fractions: SMILEY FACE
2
7
+
3
4
=
8 + 21
28
=
29 = 1 1
28
28
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 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
=
£406.98
Pythagoras’ Theorem
14cm
13cm
17cm
17² + 13² = 458
9cm
14² - 9² = 115
√458 = 21.4cm (3sf)
√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 61.59
12.9
≈ 3 x 60
=
10
It is easier to round 12.9
to 10 instead of 13
180
10
=
18
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
15% = 21 + 10.50 = £31.50
5% = £10.50
Ratios
Make sure
you read the
question
carefully first
Divide £120 in the ratio of 5:1
1) 5 + 1 = 6
3) 5 x 20 = £100
2) 120  6 = £20
1 x 20 = £20
Planes of Symmetry
The Circle Parts
The Circle: Area and Circumference
C = πd
= 3.14 x 11.2
= 35.2cm (1dp)
A = πr²
= 3.14 x 5.8 ²
= 105.6cm² (1dp)
Angle Types
Area of Triangle
Area = 12 x 8
2
Multiply BUT remember
to halve your answer
= 48cm²
Area of Composite Shape
Split into a triangle and a rectangle
Area = 6 x 8
2
= 24cm²
Total Area = 24 + 60
Area = 6 x 10
= 60cm²
= 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 Units
Metric
Imperial
Metres
Yards, Feet
Centimetres
Inches
Kilometres
Miles
Grams
Ounces
Kilograms
Stone/pounds
Litres
Gallons
Prime Factors: Factor Trees
+, + ―> +
+, - ―> -, + ―> -, - ―> +
nth Term of Sequence
5
12
19
26 33
Difference = 7
0th Term =
-2
(this would be the
number before the first term
So nth term formula is:
T(n) = 7n - 2
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
Mean = 4320  120 = 36
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
Scattergraphs and Correlation
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
POSITIVE
NEGATIVE
x
x
x
x
NO Correlation
Stem and Leaf Diagrams
BIDMAS
6
+
4
x
3
20
―
6 x 3
=
=
6 + 12 = 18
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
Letter Factors
Look for the largest number
that goes into both numbers
Look for the common letters
Factorise 4a² + 7a
Factorise 12a + 15
= 4aa + 7a
3 is the largest number that
goes into 12 and 15
12a + 15
=
3(4a + 5)
= a(4a + 7)
Indices
x2 × x4 = x 6
7
3x
5
x
 x =
× 4x² =
9
12x
4
x
Substitution
Multiplying Fractions
1. Multiply the Numerators (Top numbers)
2. Multiply the denominators (bottom numbers)
3. Simplify your answer
3 x
4
6
7
=
3 x 6
4 x 7
=
18
28
=
9
14
Area, Perimeter and Volume by
Counting
Perimeter
Count the outside
of the shape
Area
Count the squares
inside the shape
Perimeter = 10cm
Volume = 10cm³
Area = 5cm²
Volume
Count the cubes
that make up the
shape
Frequency Polygons
Need to plot the frequency against the
mid group value.
Can draw the bars in first