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GCSE Maths > Foundation > Flashcards

Foundation Flashcards

1
Q

What are the multiples of 20?

A

20, 40, 60, 80, 100, 120 …

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2
Q

What are the factors of 20?

A

1, 2, 4, 5, 10, 20

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3
Q

How do you find 50% of a number?

A

÷ 2

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4
Q

How do you find 25% of a number?

A

÷ 4 (or half it and half again)

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5
Q

How do you find 10% of a number?

A

÷ 10

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6
Q

How do you find 1% of a number?

A

÷ 100

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7
Q

How do you find 5% of a number?

A

Find 10% then half it

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8
Q

How do you find 20% of a number?

A

Find 10% then double it

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9
Q

How do you find 75% of a number?

A

Add 50% and 25%

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10
Q

How do you ‘square’ a number?

A

Multiply it by itself. e.g. 5² = 5 x 5 = 25

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11
Q

How do you ‘cube’ a number?

A

Multiply it by itself and by itself again. e.g. 2³ = 2 x 2 x 2 = 8

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12
Q

What is the sum of the angles in a triangle?

A

180°

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13
Q

What is the sum of the angles in a quadrilateral?

A

360°

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14
Q

What is the sum of the angles in a pentagon?

A

540°

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15
Q

What is the sum of the angles in a hexagon?

A

720°

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16
Q

How do you find the area of a triangle?

A

½base times height

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17
Q

How do you find the area of a rectangle?

A

Length times width

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18
Q

How do you find the circumference of a circle?

A

Pi x diameter (or 2?r)

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19
Q

How do you find the area of a circle?

A

Pi x r² (?r²)

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20
Q

How do you find a fraction of an amount? (e.g. ¾ of 20?)

A

Divide by the bottom times by the top. (e.g. 20 ÷ 4 = 5, 5 x 3 = 15)

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21
Q

What does a cylinder look like?

A

tin of soup, can of pop…

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22
Q

What does a cone look like?

A

traffic cone, ice cream cone

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23
Q

What does a sphere look like?

A

ball

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24
Q

What does a parallelogram look like?

A

pushed over rectrangle

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25
Q

How many sides does a pentagon have?

A

5

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26
Q

How many sides does an octagon have?

A

8

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27
Q

How many sides does a hexagon have?

A

6

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28
Q

How many sides does a decagon have?

A

10

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29
Q

How many sides does a heptagon have?

A

7

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30
Q

How many sides does a nonagon have?

A

9

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31
Q

What are the first 10 square numbers?

A

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

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32
Q

What are the first 10 prime numbers?

A

2, 3, 5, 7, 11, 13, 17, 19, 23, 29 (remember, 1 is not prime!!!)

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33
Q

What are the first 5 cube numbers?

A

1, 8, 27, 64, 125

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34
Q

What is a prime number?

A

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

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35
Q

How do you calculate the mean?

A

Add up all the values and divide by how many values there are

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36
Q

How do you calculate the range?

A

Highest value subtract smallest value

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37
Q

How do you find the median?

A

Arrange all the numbers in order then find the middle value

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38
Q

How do you find the mode?

A

It is the most common value (or item)

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39
Q

How do you ‘square root’ a number?

A

Find what number multiplies by itself to give the number you are square rooting. e.g. square root 25 is 5

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40
Q

How do you ‘cube root’ a number? e.g. cube root of 8?

A

Find what number multiplies by itself and by itself again to give the number you are cube rooting. e.g. cube root of 8 is 2

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41
Q

How do you find the estimated mean from a frequency table?

A

1) Find midpoints 2) Find ‘fx column’ by multiplying midpoints by frequency. 3) Add up the ‘fx column’ and divide by total frequency

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42
Q

What is a radius?

A

A line from the centre of the circle to the circumference

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43
Q

What is a diameter?

A

A line from one side of the circle to the other passing through the centre

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44
Q

What is an arc?

A

An arc is part of the circumference

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45
Q

What is a tangent?

A

A straight line that touches a circle

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46
Q

What is a chord?

A

A line joining two points on the circle but not passing through the centre (that is the diameter)

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47
Q

What is a sector?

A

The region bound between two radii and the arc. Some people call it a ‘pizza slice.

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48
Q

What is a segment?

A

The region between a chord and an arc

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49
Q

What is ½ as a decimal?

A

0.5

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50
Q

What is ¼ as a decimal?

A

0.25

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51
Q

What is ¾ as a decimal?

A

0.75

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52
Q

What is 9/10 as a decimal?

A

0.9

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53
Q

What is 6/100 as a decimal?

A

0.06

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54
Q

What is 7/25 as a decimal?

A

0.28

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55
Q

What is 1/3 as a decimal?

A

0.33333333…..

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56
Q

What is ¼ as a percentage?

A

25%

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57
Q

What is ¾ as a percentage?

A

75%

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58
Q

What is ½ as a percentage?

A

50%

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59
Q

What is \u00b9\/\u2085 as a percentage?

A

20%

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60
Q

What is 0.7 as a fraction?

A

7/10

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61
Q

What is 0.13 as a fraction?

A

13/100

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62
Q

How do you convert decimals to percentages?

A

Multiply the decimal number by 100 and add the % symbol

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63
Q

How do you convert percentages to decimals?

A

Divide the percentage by 100

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64
Q

How do you convert percentages to fractions?

A

Write the percentage over 100 and simplify

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65
Q

How do you convert fractions to decimals?

A

Divide the numerator by denominato?

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66
Q

How do you convert decimals to fractions?

A

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?

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67
Q

How do you convert fractions to percentages?

A

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

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68
Q

How do you multiply fractions?

A

Multiply numerators and multiply denominators. Simplify if you can

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69
Q

How do you divide by a fraction?

A

Multiply by the reciprocal of the second fraction, i.e : flip the second fraction, change the divide into a times

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70
Q

How do you add fractions?

A

Make both fractions have a common denominator then add

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71
Q

What is a reciprocal?

A

You find a reciprocal by flipping over a fraction. A number multiplied by it’s reciprocal is 1

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72
Q

What is a negative X a negative?

A

Positive. e.g. -4 x -2 = 8

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73
Q

What is a positive X a negative?

A

Negative. e.g. 5 x -3 = -15

74
Q

What is a negative X a positive?

A

Negative. e.g. -10 x 2 = -20

75
Q

What is a positive ÷ a negative?

A

Negative. e.g. 20 ÷ -2 = -10

76
Q

What is a negative ÷ a positive?

A

Negative. e.g. -15 ÷ 3 = -5

77
Q

What is a negative ÷ a negative?

A

Positive. e.g. -40 ÷ -8 = 5

78
Q

When drawing a Stem-and-Leaf diagram what should you always include?

A

A key

79
Q

How do you find the angles when drawing a pie chart?

A
  1. Add up the frequencies. 2. Divide 360 by the total frequency 3. Multiply each frequency by that number
80
Q

Give some examples of metric units for length?

A

metre millimetre kilometre centimetre

81
Q

Give some example of imperial units for length?

A

foot yard inch mile

82
Q

Give some examples of metric units for weight?

A

gram kilogram tonne

83
Q

Give some examples of imperial units for weight?

A

pound stone ton

84
Q

Give some examples of metric units for volume\/capacity?

A

litre centilitre millilitre

85
Q

Give some examples of imperial units for volume/capacity?

A

pint gallon

86
Q

How many centimetres are in 1 metre?

A

100

87
Q

How many millimetres are in 1 centimetre?

A

10

88
Q

How many metres are in 1 kilometre?

A

1000

89
Q

How many grams are in 1 kilogram?

A

1000

90
Q

How many kilograms are in 1 tonne?

A

1000

91
Q

How many millilitres are in 1 litre?

A

1000

92
Q

How many cm³ are in 1 litre?

A

1000

93
Q

How many inches are in 1 foot?

A

10

94
Q

How many feet are in a yard?

A

1/3

95
Q

How many pounds are in 1 stone?

A

14

96
Q

Approximately how many centimetres are in 1 foot?

A

30

97
Q

Approximately how many kilometres are in 1 mile?

A

1.6

98
Q

Approximately how many pounds are in 1 kilogram?

A

2.2

99
Q

Approximately how many litres are in 1 gallon?

A

4.5

100
Q

Approximately how many kilometres are in 5 miles?

A

8

101
Q

What does positive correlation look like?

A

points form a line going up

102
Q

What does negative correlation look like?

A

points form a line going down

103
Q

What does no correlation look like?

A

points scattered all over the graph

104
Q

How do you plot the coordinate (3,5)?

A

Go 3 along the x-axis and then 5 up. (Along the corridor up the stairs)

105
Q

What does the graph x=2 look like?

A

vertical line, crosses the x-axis at 2

106
Q

What does the graph y=2 look like?

A

Horrizontal line, crosses the y-axis at 2

107
Q

How do you draw the graph y=2x + 1?

A

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

108
Q

How is the gradient of a line worked out?

A

Method 1 - Use rise ÷ run . Method 2 - go across 1 square and see how many the line goes up

109
Q

What does an acute angle look like?

A

An acute angle is an angle less than 90 degrees

110
Q

What does an obtuse angle look like?

A

An obtuse angle is greater than 90 but less than 180 degrees

111
Q

What does a reflex angle look like?

A

A reflex is greater than 180 degree

112
Q

What do the angles add up to in a right angle?

A

90 degrees

113
Q

What do the angles on a straight line add up to?

A

180 degrees

114
Q

What do the angles at a point (full circle) at up to?

A

360 degrees

115
Q

What are vertically opposite angles?

A

When two lines cross the opposite angles are equal. They are called vertically opposite angles

116
Q

What is an isosceles triangle?

A

A triangle with two equal angles and two equal length sides

117
Q

What is a right-angled triangle?

A

A triangle with a 90 degree angle

118
Q

What is a scalene triangle?

A

A triangle where all angles are of different size and all sides are of different length

119
Q

What do all exterior angles of a polygon add up to?

A

360 degrees

120
Q

What does each interior and exterior angle add up to?

A

180 degrees

121
Q

What is the size of each interior angle for a regular pentagon?

A

108 degrees

122
Q

If a polygon is regular, what does it mean ?

A

All angles are the same size and all sides are the same length

123
Q

What are corresponding angles?

A

make a F shape in parallel lines

124
Q

What are alternate angles?

A

make a Z shape in parallel lines

125
Q

What are allied (supplementary) angles?

A

These will always add to 180 degrees (C shape)

126
Q

Bearings should usually have how many figures?

A
  1. If a bearing is less than 100 degrees it has a zero in front. e.g. 050°
127
Q

What is the bearing if travelling North?

A

000°

128
Q

What is the bearing if travelling East?

A

90°

129
Q

What is the bearing if travelling South?

A

180°

130
Q

What is the bearing if travelling West?

A

270°

131
Q

What is the bearing if travelling North-East?

A

045°

132
Q

How is the bearing of A from B found?

A
  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
133
Q

There are 5 blue counters and 3 green counters in a bag. What is the probability of a green?

A

03-Aug

134
Q

The probability of rain is 0.7. What is the probability of no rain?

A

1 - 0.7 = 0.3

135
Q

How do you find how many times an outcome is expected?

A

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

136
Q

Two shapes are congruent. What does that mean?

A

They are the same shape and size

137
Q

Two shapes are similar. What does that mean?

A

One is an enlargement of the other. The same shape but different size

138
Q

What does tessellate mean?

A

Identical shapes fit together with no gaps

139
Q

How do you construct a ‘perpendicular bisector??

A
  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
140
Q

How do you construct an ‘angle bisector??

A
  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
141
Q

How do you order decimals? e.g. 0.4 0.13 and 0.312 (from smallest to largest)

A
  1. Make all numbers the same length by adding zeros. 2. Order the decimals. e.g. 0.130 0.312 0.400
142
Q

How do you estimate a calculation?

A

Round each number to 1 significant figure and then work out with BIDMAS

143
Q

When asked to ‘criticise’ a question what are the typical mistakes?

A
  1. No timescale in the question. 2. The question is leading. 3. The catagories overlap. 4. No ‘other’ or ‘more than’ option
144
Q

How do you write a number as a product of primes?

A

Use a prime factor tree

145
Q

What is the LCM (Lowest Common Multiple)? e.g. LCM of 7 and 4?

A

The LCM is the first common multiple of both numbers. e.g. The LCM of 7 and 4 is 28

146
Q

What is the HCF (Highest Common Factor)? e.g. HCF of 15 and 20?

A

The HCF is the largest factor of both numbers. e.g. The HCF of 15 and 20 is 5

147
Q

What is y³ x y°

A

y³(add the powers)

148
Q

What is y³ ÷ y²?

A

y (subtract the powers)

149
Q

What is (y²)°

A

y° (multiply the powers)

150
Q

How do you calculate ‘percentage change??

A

change ÷ original x 100

151
Q

How do you expand brackets?

A

Multiply the terms inside by the term outside

152
Q

How do you expand two brackets?

A

Use FOIL

153
Q

What does factorise mean?

A

Putting the brackets back in

154
Q

a + a +a ?

A

3a

155
Q

a x a x a

A

a³

156
Q

a x a x a

A

a²

157
Q

5w + 3w - w

A

7w

158
Q

Expand and simplify 3(w + 2) + 5(w + 3)

A

3w + 6 + 5w + 15 = 8w + 21

159
Q

How do you find the perimeter?

A

Add up all the lengths of the sides?

160
Q

How do you find the area of a parallelogram?

A

Base times height

161
Q

How do you find the area of a trapezium?

A

It is on the formula sheet and is ½(a+b)?

162
Q

A car travels 60 miles in 3 hours. What is it’s average speed?

A

S = D ÷ T 60 ÷ 3 = 20mph

163
Q

How do you share £40 in the ratio 2:3?

A

1) Add 2 + 3 = 5 2) £40 ÷ 5 = £8 in one part 3) 2 x£8 = £16 4) 3 x £8 = £24

164
Q

Solve 3y = 24

A

y = 24/3 = 8

165
Q

Solve w - 8 = 7

A

w = 7 + 8 = 15

166
Q

Solve 2w + 3 = 11

A

2w = 11-3 = 8 , w = 8/2 = 4

167
Q

Solve 6w + 1 = 4w + 13

A

4w + 1 - 6w = 13 , 2w + 1 =13 , 2w = 13 -1 , 2w = 12, w = 12/2 = 6

168
Q

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?

A

Try 4.55. If it is too low 4.6 is the answer. If it is too high 4.5 is the answer

169
Q

Make w the subject of w - 3 = c

A

w = c + 3

170
Q

What does x

A

x is stricly less than 4 (cannot be 4)

171
Q

What does x > 2 mean ?

A

x is stricly more than 2 (cannot be 4)

172
Q

Find the nth term for 8 11 14 17 ..?

A
  1. Find out what the size is increasing/decreasing by. (in this case +3 , means it is 3n ) 2. Find what number would come before, here 5, which is positive , so the nth term is 3n + 5
173
Q

If the nth term is 4n + 1 what is the 100th term?

A
  1. 4 x 100 + 1 = 401
174
Q

How do you find the volume of a cuboid?

A

length x width x height

175
Q

How do you find the surface area of a 3D shape?

A

Find the area of all faces and add them up

176
Q

How do you find the volume of a Triangular Prism?

A

Find the area of the triangle then multiply by how long the shape is

177
Q

How do you find the volume of a cylinder?

A

Find the area of the circle using Pi x r², then multiply by how long the cylinder is

178
Q

What is the translation vector for the translation of 2 squares to the right and 3 squares upwards?

A

(2,3)

179
Q

What is the translation vector for the translation of 1 square to the left and 3 squares upwards?

A

(-1,3)

180
Q

When asked to rotate a shape on a grid what are the steps?

A
  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
181
Q

What is Pythagoras’ Theorem?

A

a² + b² = c² where c is the longest side (hypotenuse) and a&b are the shorter sides

GCSE Maths (12 decks)

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