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GCSE Maths - Foundation revision cards

A set of revision cards for GCSE Foundation
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What are the multiples of 20?
20, 40, 60, 80, 100, 120 ...
What are the factors of 20?
1, 2, 4, 5, 10, 20
How do you find 50% of a number?
÷ 2
How do you find 25% of a number?
÷ 4 (or half it and half again)
How do you find 10% of a number?
÷ 10
How do you find 1% of a number?
÷ 100
How do you find 5% of a number?
Find 10%, then half it.
How do you find 20% of a number?
Find 10%, then double it.
How do you find 75% of a number?
Add 50% and 25%
How do you 'square' a number?
Multiply it by itself.
e.g. 5² = 5 x 5 = 25
How do you 'cube' a number?
Multiply it by itself and by itself again.
e.g. 2³ = 2 x 2 x 2 = 8
What is the sum of the angles in a triangle?
180⁰
What is the sum of the angles in a quadrilateral?
360⁰
What is the sum of the angles in a pentagon?
540⁰
What is the sum of the angles in a hexagon?
720⁰
How do you find the area of a triangle?
½base times height
How do you find the area of a rectangle?
Length times width
How do you find the circumference of a circle?
π x diameter (or 2πr)
How do you find the area of a circle?
π x r² (πr²)
How do you find a fraction of an amount? (e.g. ¾ of 20)
Divide by the bottom, times by the top.
(e.g. 20 ÷ 4 = 5 5 x 3 = 15)
What does a cylinder look like?
What does a cone look like?
What does a sphere look like?
What does a parallelogram look like?
What does a trapezium look like?
How many sides does a pentagon have?
5
How many sides does an octagon have?
8
How many sides does a hexagon have?
6
How many sides does a decagon have?
10
How many sides does a heptagon have?
7
How many sides does a nonagon have?
9
What are the first 10 square numbers?
1, 4, 9, 16, 25, 36, 49, 64, 81, 100
What are the first 10 prime numbers?
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
What are the first 5 cube numbers?
1, 8, 27, 64, 125
What is a prime number?
A number divisible only by 1 and itself.

e.g. 7 is a prime number as it's factors are 1 and 7. 9 is not a prime number as it's factors are 1, 3 and 9.
How do you calculate the mean?
Add up all the values and divide by how many values there are.
How do you calculate the range?
Highest value subtract smallest value.
How do you find the median?
Arrange all the numbers in order, then find the middle value.
How do you find the mode?
It is the most common value (or item)
What does the speed, distance, time triangle look like?
How do you 'square root' a number? e.g. √36
Find what number multiplies by itself to give the number you are square rooting.

e.g. √36 is 6
How do you 'cube root' a number? e.g. ³√125
Find what number multiplies by itself and by itself again to give the number you are cube rooting.

e.g. ³√125 = 5
How do you find the estimated mean from a frequency table?
1) Find midpoints
2) Find 'fx column' by multiplying midpoints by frequency.
3) Add up the 'fx column' and divide by total frequency
What is a radius?
A line from the centre of the circle to the circumference
What is a diameter?
A line from one side of the circle to the other, passing through the centre.
What is an arc?
An arc is part of the circumference.
What is a tangent?
A straight line that touches a circle.
What is a chord?
A line joining two points on the circle, but not passing through the centre (that is the diameter).
What is a sector?
The region bound between two radii and the arc.
Some people call it a 'pizza slice.'
What is a segment?
The region between a chord and an arc.
What is ½ as a decimal?
0.5
What is ¼ as a decimal?
0.25
What is ¾ as a decimal?
0.75
What is ¹/₅ as a decimal?
0.2
What is ¹/₁₀ as a decimal?
0.1
What is ³/₁₀ as a decimal?
0.3
What is ⁴/₅ as a decimal?
0.8
What is ¼ as a percentage?
25%
What is ¾ as a percentage?
75%
What is ½ as a percentage?
50%
What is ¹/₅ as a percentage?
20%
What is 0.7 as a fraction?
⁷/₁₀
What is 0.13 as a fraction?
¹³/₁₀₀
How do you convert decimals to percentages?
Multiply the decimal number by 100 and add the % symbol.
How do you convert percentages to decimals?
Divide the percentage by 100.
How do you convert percentages to fractions?
Write the percentage over 100 and simplify.
How do you convert fractions to decimals?
Divide the numerator by denominator
How do you convert decimals to fractions?
Remember 0.1 is one-tenth, 0.01 is one-hundredth etc.

e.g. Write 0.7 as a fraction. As this is seven-tenths, it would be ⁷/₁₀
How do you convert fractions to percentages?
Method 1) Find an equivalent fraction with 100 on the demoninator. The numerator is the percentage.

Method 2) Divide numerator by denominator to find the decimal. Then multiply by 100.
How do you multiply fractions?
Multiply numerators and multiply denominators. Simplify if you can.
How do you divide by a fraction?
Multiply by the reciprocal of the second fraction.
How do you add fractions?
Make both fractions have a common denominator, then add.
What is a reciprocal?
You find a reciprocal by "flipping" over a fraction.

A number multiplied by it's reciprocal is 1.
What is a negative X a negative?
Positive.
e.g. -4 x -2 = 8
What is a positive X a negative?
Negative.
e.g. 5 x -3 = -15
What is a negative X a positive?
Negative.
e.g. -10 x 2 = -20
What is a positive ÷ a negative?
Negative.
e.g. 20 ÷ -2 = -10
What is a negative ÷ a positive?
Negative.
e.g. -15 ÷ 3 = -5
What is a negative ÷ a negative?
Positive.
e.g. -40 ÷ -8 = 5
When drawing a Stem-and-Leaf diagram, what should you always include?
A key
How do you find the angles when drawing a pie chart?
1. Add up the frequencies.
2. Divide 360 by the total frequency
3. Multiply each frequency by that number.
What does the net of a cube look like?
What does the net of a cylinder look like?
What does the net of a square-based pyramid look like?
What does the net of a triangular prism look like?
What are edges, faces and vertices?
Give some examples of metric units for length.
metre, millimetre, kilometre, centimetre
Give some example of imperial units for length.
foot, yard, inch, mile
Give some examples of metric units for weight.
gram, kilogram, tonne
Give some examples of imperial units for weight.
pound, stone, ton
Give some examples of metric units for volume/capacity.
litre, centilitre, millilitre
Give some examples of imperial units for volume/capacity.
pint, gallon
How many centimetres are in 1 metre?
100
How many millimetres are in 1 centimetre?
10
How many metres are in 1 kilometre?
1000
How many grams are in 1 kilogram?
1000
How many kilograms are in 1 tonne?
1000
How many millilitres are in 1 litre?
1000
How many cm³ are in 1 litre?
1000
How many inches are in 1 foot?
12
How many feet are in a yard?
3
How many pounds are in 1 stone?
16
Approximately how many centimetres are in 1 foot?
30
Approximately how many kilometres are in 1 mile?
1.6
Approximately how many pounds are in 1 kilogram?
2.2
Approximately how many litres are in 1 gallon?
4.5
Approximately how many kilometres are in 5 miles?
8
What does positive correlation look like?
What does negative correlation look like?
What does no correlation look like?
How do you plot the coordinate (3, 5)?
Go 3 along the x-axis and then 5 up.
"Along the corridor, up the stairs."
What does the graph x=2 look like?
What does the graph y=2 look like?
How do you draw the graph y=2x + 1?
1) Draw a xy table, with values of x, 0, 1 and 2.
2) Multiply the values of x by 2 and then add 1.
3) Plot the coordinates on the graph
4) Draw a straight line that passes through the points .... and continues.
How is the gradient of a line worked out?
Method 1 - Use rise ÷ run like in the picture.
Method 2 - go across 1 square and see how many the line goes up.
What does an acute angle look like?
An acute angle is an angle less than 90 degrees.
What does an obtuse angle look like?
An obtuse angle is greater than 90 but less than 180 degrees.
What does a reflex angle look like?
A reflex is greater than 180 degrees
What do the angles add up to in a right angle?
90 degrees
What do the angles on a straight line add up to?
180 degrees
What do the angles at a point (full circle) at up to?
360 degrees
What are vertically opposite angles?
When two lines cross, the opposite angles are equal. They are called vertically opposite angles.
What is an isosceles triangle?
A triangle with two equal angles and two equal length sides.
What is a right-angled triangle?
A triangle with a 90 degree angle.
What is a scalene triangle?
A triangle where all angles are of different size and all sides are of different length.
What do all exterior angles of a polygon add up to?
360 degrees
What does each interior and exterior angle add up to?
180 degrees
What is the size of each interior angle for a regular pentagon?
108 degrees
If a polygon is "regular," what does that mean?
All angles are the same size and all sides are the same length.
What are corresponding angles?
What are alternate angles?
What are co-interior angles?
These will always add to 180 degrees.
Bearings should usually have how many figures?
3.
If a bearing is less than 100°, it has a zero in front. e.g. 050°
What is the bearing if travelling North?
000°
What is the bearing if travelling East?
090°
What is the bearing if travelling South?
180°
What is the bearing if travelling West?
270°
What is the bearing if travelling North-East?
045°
How is the bearing of A from B found?
1. Join A and B with a straight line.
2. Draw a North line at B.
3. Measure the clockwise angle from the North line to the line that joins A and B.
There are 5 blue counters and 3 green counters in a bag. What is the probability of a green?
³/₈
The probability of rain is 0.7. What is the probability of no rain?
1 - 0.7 = 0.3
How do you find how many times an outcome is "expected"?
Multiply the probability by the number of trials.

e.g. A dice is rolled 30 times. How many 2's are expected? ¹/₆ x 30 = 5 times.
Two shapes are congruent. What does that mean?
They are the same shape and size.
Two shapes are similar. What does that mean?
One is an enlargement of the other. The same shape, but different size.
What does tessellate mean?
Identical shapes fit together with no gaps.
How do you construct a 'perpendicular bisector?'
1. Set your compass to OVER half the length of the line.
2. Place the compass point on one end of the line and draw an arc.
3. Repeat for the other end of the line.
4. Draw a line joining where the arcs cross.
How do you construct an 'angle bisector?'
1. Put the point of the compass where the lines meet and draw an arc on each line.
2. Put the point of the compass on where the arc meets the line and draw an arc towards the middle of the angle.
3. Repeat
4. Join where the arcs cross to where the lines meet.
How do you order decimals? e.g. 0.4, 0.13 and 0.312 (from smallest to largest)
1. Make all numbers the same length by adding zeros.
2. Order the decimals.
e.g.
0.130, 0.312, 0.400
How do you estimate a calculation?
Round each number to 1 significant figure and then work out.
When asked to 'criticise' a question, what are the typical mistakes?
1. No timescale in the question.
2. The question is leading.
3. The catagories overlap.
4. No 'other' or 'more than' option.
How do you write a number as a product of primes? e.g. 20
Use a prime factor tree.
What is the LCM (Lowest Common Multiple)? e.g. LCM of 7 and 4.
The LCM is the first common multiple of both numbers.
e.g. The LCM of 7 and 4 is 28.
What is the HCF (Highest Common Factor)? e.g. HCF of 15 and 20.
The HCF is the largest factor of both numbers.
e.g. The HCF of 15 and 20 is 5.
What is y³ x y⁵
y⁸ (add the powers)
What is y⁸ ÷ y²
y⁶ (subtract the powers)
What is (y²)⁴
y⁸ (multiply the powers)
How do you calculate 'percentage change?'
change ÷ original x 100
How do you expand brackets?
Multiply the terms inside, by the term outside.
How do you expand two brackets?
Use FOIL
What does factorise mean?
Putting the brackets back in.
a + a + a
3a
a x a x a
a x a
5w + 3w - w
7w
Expand and simplify 3(w + 2) + 5(w + 3)
3w + 6 + 5w + 15 = 8w + 21
How do you find the perimeter?
Add up all the lengths of the sides.
How do you find the area of a parallelogram?
Base times height
How do you find the area of a trapezium?
It is on the formula sheet and is ½(a+b)h
A car travels 60 miles in 3 hours. What is it's average speed?
S = D ÷ T
60 ÷ 3 = 20mph
How do you share £40 in the ratio 2:3
1) Add 2 + 3 = 5
2) £40 ÷ 5 = £8 in one part
3) 2 x £8 = £16
4) 3 x £8 = £24
Solve 3y = 21
Solve w - 8 = 3
Solve 2w + 3 = 17
Solve 6w + 1 = 4w + 13
When solving using trial and improvement to 1 decimal place, if 4.5 is too low and 4.6 is too high, what would you do next?
Try 4.55.
If it is too low, 4.6 is the answer.
If it is too high, 4.5 is the answer.
Make w the subject of w - 3 = c
w = c + 3
Show x < 4 on a number line
Show x > 2 on a number line
Show x ≥ 1 on a number line
Show x ≤ 3 on a number line
Find the nth term for 8, 11, 14, 17 ...
1. Find out what the size is increasing/decreasing by. (in this case 3)
2. Write the times tables for that number below the sequence and also 3n
3. See what you would have to do to 3 times tables to get to the sequence... +5
4. Then the nth term is 3n + 5
If the nth term is 4n + 1, what is the 100th term?
401.
4 x 100 + 1 = 401
How do you find the volume of a cuboid?
length x width x height
How do you find the surface area of a 3D shape?
Find the area of all faces and add them up.
How do you find the volume of a Triangular Prism?
Find the area of the triangle, then multiply by how long the shape is.
How do you find the volume of a cylinder?
Find the area of the circle using π r²
Multiply by how long the cylinder is.
What is the translation vector, for the translation of 2 squares to the right and 3 squares upwards?
What is the translation vector, for the translation of 1 square to the left and 3 squares upwards?
When asked to rotate a shape on a grid, what are the steps?
1. Ask for tracing paper.
2. Place the tracing paper on the grid and trace over the shape AND the centre of rotation.
3. Rotate the shape, the degrees and direction you are asked to - Make sure the centre of rotation stays in the correct place.
4. Draw the shape on the grid.
What is Pythagoras' Theorem?
a² + b² = c²
where c is the longest side (hypotenuse) and a&b are the shorter sides.
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