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SHHS - GCSE Maths > Foundation > Flashcards

Flashcards in Foundation Deck (181)
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1

What are the multiples of 20?

20, 40, 60, 80, 100, 120 …

2

What are the factors of 20?

1, 2, 4, 5, 10, 20

3

How do you find 50% of a number?

÷ 2

4

How do you find 25% of a number?

÷ 4 (or half it and half again)

5

How do you find 10% of a number?

÷ 10

6

How do you find 1% of a number?

÷ 100

7

How do you find 5% of a number?

Find 10% then half it

8

How do you find 20% of a number?

Find 10% then double it

9

How do you find 75% of a number?

Add 50% and 25%

10

How do you 'square' a number?

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

11

How do you 'cube' a number?

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

12

What is the sum of the angles in a triangle?

180°

13

What is the sum of the angles in a quadrilateral?

360°

14

What is the sum of the angles in a pentagon?

540°

15

What is the sum of the angles in a hexagon?

720°

16

How do you find the area of a triangle?

½base times height

17

How do you find the area of a rectangle?

Length times width

18

How do you find the circumference of a circle?

Pi x diameter (or 2?r)

19

How do you find the area of a circle?

Pi x r² (?r²)

20

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)

21

What does a cylinder look like?

tin of soup, can of pop…

22

What does a cone look like?

traffic cone, ice cream cone

23

What does a sphere look like?

ball

24

What does a parallelogram look like?

pushed over rectrangle

25

How many sides does a pentagon have?

5

26

How many sides does an octagon have?

8

27

How many sides does a hexagon have?

6

28

How many sides does a decagon have?

10

29

How many sides does a heptagon have?

7

30

How many sides does a nonagon have?

9

31

What are the first 10 square numbers?

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

32

What are the first 10 prime numbers?

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

33

What are the first 5 cube numbers?

1, 8, 27, 64, 125

34

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

35

How do you calculate the mean?

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

36

How do you calculate the range?

Highest value subtract smallest value

37

How do you find the median?

Arrange all the numbers in order then find the middle value

38

How do you find the mode?

It is the most common value (or item)

39

How do you 'square root' a number?

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

40

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

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

41

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

42

What is a radius?

A line from the centre of the circle to the circumference

43

What is a diameter?

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

44

What is an arc?

An arc is part of the circumference

45

What is a tangent?

A straight line that touches a circle

46

What is a chord?

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

47

What is a sector?

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

48

What is a segment?

The region between a chord and an arc

49

What is ½ as a decimal?

0.5

50

What is ¼ as a decimal?

0.25

51

What is ¾ as a decimal?

0.75

52

What is 9/10 as a decimal?

0.9

53

What is 6/100 as a decimal?

0.06

54

What is 7/25 as a decimal?

0.28

55

What is 1/3 as a decimal?

0.33333333…..

56

What is ¼ as a percentage?

25%

57

What is ¾ as a percentage?

75%

58

What is ½ as a percentage?

50%

59

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

20%

60

What is 0.7 as a fraction?

7/10

61

What is 0.13 as a fraction?

13/100

62

How do you convert decimals to percentages?

Multiply the decimal number by 100 and add the % symbol

63

How do you convert percentages to decimals?

Divide the percentage by 100

64

How do you convert percentages to fractions?

Write the percentage over 100 and simplify

65

How do you convert fractions to decimals?

Divide the numerator by denominato?

66

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?

67

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

68

How do you multiply fractions?

Multiply numerators and multiply denominators. Simplify if you can

69

How do you divide by a fraction?

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

70

How do you add fractions?

Make both fractions have a common denominator then add

71

What is a reciprocal?

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

72

What is a negative X a negative?

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

73

What is a positive X a negative?

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

74

What is a negative X a positive?

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

75

What is a positive ÷ a negative?

Negative. e.g. 20 ÷ -2 = -10

76

What is a negative ÷ a positive?

Negative. e.g. -15 ÷ 3 = -5

77

What is a negative ÷ a negative?

Positive. e.g. -40 ÷ -8 = 5

78

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

A key

79

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

80

Give some examples of metric units for length?

metre millimetre kilometre centimetre

81

Give some example of imperial units for length?

foot yard inch mile

82

Give some examples of metric units for weight?

gram kilogram tonne

83

Give some examples of imperial units for weight?

pound stone ton

84

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

litre centilitre millilitre

85

Give some examples of imperial units for volume/capacity?

pint gallon

86

How many centimetres are in 1 metre?

100

87

How many millimetres are in 1 centimetre?

10

88

How many metres are in 1 kilometre?

1000

89

How many grams are in 1 kilogram?

1000

90

How many kilograms are in 1 tonne?

1000

91

How many millilitres are in 1 litre?

1000

92

How many cm³ are in 1 litre?

1000

93

How many inches are in 1 foot?

10

94

How many feet are in a yard?

1/3

95

How many pounds are in 1 stone?

14

96

Approximately how many centimetres are in 1 foot?

30

97

Approximately how many kilometres are in 1 mile?

1.6

98

Approximately how many pounds are in 1 kilogram?

2.2

99

Approximately how many litres are in 1 gallon?

4.5

100

Approximately how many kilometres are in 5 miles?

8

101

What does positive correlation look like?

points form a line going up

102

What does negative correlation look like?

points form a line going down

103

What does no correlation look like?

points scattered all over the graph

104

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

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

105

What does the graph x=2 look like?

vertical line, crosses the x-axis at 2

106

What does the graph y=2 look like?

Horrizontal line, crosses the y-axis at 2

107

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

108

How is the gradient of a line worked out?

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

109

What does an acute angle look like?

An acute angle is an angle less than 90 degrees

110

What does an obtuse angle look like?

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

111

What does a reflex angle look like?

A reflex is greater than 180 degree

112

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

90 degrees

113

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

180 degrees

114

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

360 degrees

115

What are vertically opposite angles?

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

116

What is an isosceles triangle?

A triangle with two equal angles and two equal length sides

117

What is a right-angled triangle?

A triangle with a 90 degree angle

118

What is a scalene triangle?

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

119

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

360 degrees

120

What does each interior and exterior angle add up to?

180 degrees

121

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

108 degrees

122

If a polygon is regular, what does it mean ?

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

123

What are corresponding angles?

make a F shape in parallel lines

124

What are alternate angles?

make a Z shape in parallel lines

125

What are allied (supplementary) angles?

These will always add to 180 degrees (C shape)

126

Bearings should usually have how many figures?

3. If a bearing is less than 100 degrees it has a zero in front. e.g. 050°

127

What is the bearing if travelling North?

000°

128

What is the bearing if travelling East?

90°

129

What is the bearing if travelling South?

180°

130

What is the bearing if travelling West?

270°

131

What is the bearing if travelling North-East?

045°

132

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

133

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

03-Aug

134

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

1 - 0.7 = 0.3

135

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

136

Two shapes are congruent. What does that mean?

They are the same shape and size

137

Two shapes are similar. What does that mean?

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

138

What does tessellate mean?

Identical shapes fit together with no gaps

139

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

140

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

141

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

142

How do you estimate a calculation?

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

143

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

144

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

Use a prime factor tree

145

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

146

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

147

What is y³ x y°

y³(add the powers)

148

What is y³ ÷ y²?

y (subtract the powers)

149

What is (y²)°

y° (multiply the powers)

150

How do you calculate 'percentage change??

change ÷ original x 100

151

How do you expand brackets?

Multiply the terms inside by the term outside

152

How do you expand two brackets?

Use FOIL

153

What does factorise mean?

Putting the brackets back in

154

a + a +a ?

3a

155

a x a x a

156

a x a x a

157

5w + 3w - w

7w

158

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

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

159

How do you find the perimeter?

Add up all the lengths of the sides?

160

How do you find the area of a parallelogram?

Base times height

161

How do you find the area of a trapezium?

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

162

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

S = D ÷ T 60 ÷ 3 = 20mph

163

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

164

Solve 3y = 24

y = 24/3 = 8

165

Solve w - 8 = 7

w = 7 + 8 = 15

166

Solve 2w + 3 = 11

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

167

Solve 6w + 1 = 4w + 13

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

168

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

169

Make w the subject of w - 3 = c

w = c + 3

170

What does x

x is stricly less than 4 (cannot be 4)

171

What does x > 2 mean ?

x is stricly more than 2 (cannot be 4)

172

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

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

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

401. 4 x 100 + 1 = 401

174

How do you find the volume of a cuboid?

length x width x height

175

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

Find the area of all faces and add them up

176

How do you find the volume of a Triangular Prism?

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

177

How do you find the volume of a cylinder?

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

178

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

(2,3)

179

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

(-1,3)

180

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

181

What is Pythagoras' Theorem?

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