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Help Your Kids: Maths
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Please see below for the answers to the practice questions on the Help Your Kids: Maths Revision cards (2nd Edition). If you are still unsure about a certain question or topic, why not look at the Maths Clinic videos to help you?
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ANSWERS 2nd Ed
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A♣ - 1) a) 20 b) 24 c) 23 d) 27 2) 84 3) 18
2♣ - 1) 8000, 200, 70, 3, 6/10 (6 tenths), 9/100 (9 hundredths). You can write these in words or figures but decimals are not acceptable (eg 0.6 and 0.09)
2) a) 130 b) 36 c) 34 d) 5.6 e) 2260 f) 0.06
h) 47 x 0.26 = 1222 so 4.7 x 0.26 = 12.22 (÷ 100) i) 4100000 h) 0.00062 h) 7.9 x 10⁵
3♣ - 1) a) 2:3 b) 2:3 c) 2:3
2) a) 1:2.5 b) 1:1.5
3) a) Ali has £16, Beth has £24, Cal has £24 and Dan has £36
b) £21 and £35
c) 240ml of red, 320ml of white
4♣ - 1) a) 16 b) 48 c) 6.9 d) 13.5
2) Bag A: 80 - 16 = £64
Bag B: 80% = £52, 40% = £26, 20% = £13, 100% = 52+13 = £65 (original price)
5♣ - 1) a) 17 b) 48 c) 18 d) 36 e) 24 f) 20/4 = 5
2) a) (4 + 3) x 5 = 35 b) 24 - (2 + 4 x 3) = 10
6♣ - 1) a) -5 b) -7 c) 9 d) 4 e) 42 f) -4 g) 25 h) -120
7♣ - 1) a) 4000 b) 3780 c) 3782.5
2) a) 3440 b) 0.62
3) a) 300 x 50 = 15000 = 7500
2 2
b) 8 x 30 = 240 = 2400 = 480
0.5 0.5 5
8♣ - 1) a) 49 b) 64 c) 25 d) -1000 e) 8 f) 1 f) 40
2) a) 3 b) 8 c) 3
9♣ - 1) £5.60 2) Choc A: 500g = £9.50, Choc B: 500g = £9, so Choc B is better value
3) 200g of flour, 5 eggs, 300ml of milk
10♣ - 1) a) 4 b) 24 2) 36 3) a) 144.75 b) 470
J♣ - 1) 5/6 2) 9/20 3) 46/35 = 1 and 11/35 4) 4 and 5/12
Q♣ - 1) a) 12/20 = 3/5 b) 7/2 x 5/3 = 35/6 = 5 and 5/6
2) a) 16/15 = 1 and 1/15 b) 20/9 x 4/5 = 80/45 = 16/9 = 1 and 7/9
K♣ - 1) a) £3374.59 b) £3230.67 (don't worry if your answers are out by a few pence)
A♥ - 1) v = 45°, w = 55°, x = 28°, y = 81°, z = 108°
2♥ - 1) a) x = 127° (alternate angles)
b) y = 81° (corresponding & opposite angles)
c) z = 113° (alternate or corresponding angles & angles on a straight line = 180°)
3♥ - 1) a) a = 45° b) b = 135° c) c = 135° d) d = 17°
4♥ - 1) a) reflection using the y axis (or x = 0) as the mirror line
b) Rotation, 180° (either direction), (centre 0,2)
c) Rotation, 90° clockwise (or 270° anti-clockwise), centre (4,1)
d) Reflection using the mirror line x = 2
5♥ -
6♥ - Check the shapes you have drawn look like the ones on the card. They do not need to be anywhere near perfect!
7♥ - 1) Check your circle part names:
2) a) Set your compass to a gap of 6cm and draw the circle. Note that this will give a diameter of 10cm which is how big your circle should be.
b) Set your compass to a gap of 5cm (half the 10cm diameter). Note that this will give a diameter of 12cm which is how big your circle should be.
8♥ - 1) Rectangle: 28cm², Triangle: 14cm². Parallelogram: 28cm², Trapezium: 24cm²
2) a) 44cm b) 100cm²
9♥ - 1) a) Circumference = 25.1cm or 8ℼ, Area = 50.3cm² or 16ℼ cm²
b) Circumference = 28.3cm or 9ℼ cm, Area = 63.6cm² or 20.25ℼ cm²
2) a) Area = 78.5/2 = 39.3cm² or 12.5ℼ,
b) Perimeter = 31.4/2 + 10 = 25.7cm or 5ℼ + 10 cm
10♥ - 1) a) 20 x 12 = 240cm³ b) 50.3 x 15 = 753.8cm³ or 240ℼ cm³
2) Find the area of each face: 6 x 4 = 24, 3 x 4 = 12, 6 x 3 = 18. Then add them together and double for the other three faces: 54 x 2 = 108cm²
J♥ - 1) a) 5.29cm
2) Height of triangle = 4cm. Volume = (3x4)/2 x 8 = 48cm³
Q♥ - 1) a) 24.6° b) 41.8°
K♥ - 1) a) 7.56cm b) 8.00cm
2) a) y = 18cm b) z = 7.5cm
clubsA
diamondsA
spadesA
heartsA
A♦ - 1) a) Mode = 10 b) Mean = 75/10 = 7.5
c) Median = 8, d) Range = 12 - 3 = 9
1) Class A: Mean=75%, Median=79%, Range=51%
Class B: Mean=69.4%, Median=70%, Range=23%
Conclusion: Class A has a higher mean and median than Class B which shows that Class A scored higher on average. However, Class B has smaller range which shows that its scores were more consistent.
2♦ - 1) a) Mode = 1 pet b) Mean = 1.2 pets
c) Range = 3 - 0 = 3 pets
b) y = 81° (corresponding & opposite angles)
c) z = 113° (alternate or corresponding angles & angles on a straight line = 180°)
3♦ - 1)
2) Mean = 725/17 = 42.6 years old
4♦ - 1) a) Median = 29 mph b) Mode = 30 mph
c) Range = 41-18 = 23 mph d) 30 mph
2)
5♦ - 1) a) 1/4 b) 80° = 240 people, 40° = 120 people, 120° = 360 people
2)
6♦ - 1) Around 84kg 2) Around 192cm
7♦ - 1) 30 miles 2) 16 miles per hour
3) Tom's speed = 12 600 metres/hour
Jia's speed = 12 500 metre/hour
Therefore, Tom is going faster (if he can keep up the same pace!)
8♦ - 1) 20km/h 2) 30 min 3) 40km/h
9♦ - 1) 40cm²
2) Volume = (6x4)/2 x 10 = 120cm³
Mass = 120x0.8 = 96g
10♦ - 1) a) 4/8 (or 1/2) b) 1/8 c) 2/8 (or 1/4) d) 4/8 (or 1/2)
2) Place your events on the scale as shown below:
J♦ - 1) a) i) 0.64 ii) 0.76
b) 1 - 0.64 = 0.36 (left for pink and grey) so 3x=0.36 and x = 0.12
c) 0.4 x 240 = 96 times
Q♦ - 1)
2) 0.3 x 0.44 = 0.132
K♦ - 1) a) 60mm b) 7.5km c) 340cm d) 8700g
e) 0.675 litres f) 5 x 100² = 50000cm²
2) 3500m + 720m - 1250m = 2970m or 2.97km
3) 1:15PM or 13:15
A♠ - 1) a) 8 b) 1 c) 13 d) 69 e) 27 (square a and then times by the 3) f) 81 g) 25 - - 9 = 25+ 9 = 34 h) 5 + 4 = 9
2) 5/9(68 - 32) = 5/9 of 36 = 20°C
2♠ - 1) a) 5a + 11b b) 3c - d (3c - 1d is fine) c) 7e + 1 d) 11f - 12g e) 3h f) 10k² + 2k g) 5 + 4 = 9
3♠ - 1) a) 12a - 21 b) 12x + 18y c) 2t² - 5t
2) 7c + 28 - 4c + 10 = 3c + 38
3) a) 5(2f + 5) b) 8(m + 3) c) 4x(3x + 2)
4♠ - 1) a) a³ b) 12b² c) c⁸ d) d⁴ e) 8e⁻² f) f⁸ g) g¹⁵ h) 4h¹⁸ ((4h⁶)³ would be equal to 64h¹⁸ - be careful with where the brackets are in these questions!) i) 12st
5♠ - 1) a) x = 3 b) x = 6 c) x = -3 d) x = 9 e) x = 2.4 f) x = 6
6♠ - 1) a) x = 4 b) x = 7 c) x = -3 d) x = 4 e) x = 6 f) x = 6
7♠ - 1) 10x + 9 = 24 so x = 1.5. Then substitute this into the expressions for each side. Area = (8 x 6)/2 = 24cm² (Just a coincidence for this particular triangle that the area is the same as the perimeter)
2) a) Rio's age is x + 3 b) Eva's age is 2(x + 3) or 2x + 6 c) Total age is x + x + 3 + 3x + 6 = 5x + 9
8♠ - 1)
2) -4 ≤ x < 1
9♠ - 1) a) 0,1,2,3,4 b) -2,-1,0,12) a) x ≤ 8 b) x >2 c) -3 ≤ x or x ≥ -3 d) -x < 1.5 e) x < 7
10♠ - 1)
J♠ - 1)
Q♠ - 1) a) 3,9,15,21,27 b) 1,6,11,16,21 c) 4,2,0,-2,-4
2) a) 4n+5 b) 3n - 2 c) -2n + 11 or 11 - 2n
3) List the sequence out to check... 7,11,15,19,23,27,31,35,39,43,47,51,55,59 - No, 57 is NOT in the sequence as you skip past it.
Or you can form an equation: 4n + 3 = 57. When you solve this you get 54/4 which is not a whole number which also means 57 is NOT a term in the sequence.
K♠ - 1) a) x = y - d
3
9
c) x = f - st d) x = yp - 6
2) a) 7 x 4 + 2 x 6 = £40 b) 74 - 56 = 28, 28/2 = 14 miles
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