1 Year 7, 2014 Exam revision ANSWERS. 2 Number : 3.3 Rounding Numbers3.3 Rounding Numbers 1.3...

1

Year 7, 2014 Exam

revision ANSWERS

2

What’s in your Exam:Number:3.3 Rounding Numbers 1.3 Arithmetic 1.2 Averages and Range 1.6 Long Multiplication and Division1.5 Decimals 1 2.2 Fractions 4.1 Ratio & Proportion 2.5 Percentages 3.2 Orders of Operation 3.1 Properties of Number 3.4 Negative Numbers 4.6 Metric and Imperial Units 4.2 Decimals 2 4.5 Solving Problems

Tick off, when you

have revised!

Shape and space:1.4 Area and Perimeter 3.6 Calculating Angles 5.2 Reflection 5.1 Rotation 5.3 Translation 5.4 Construction 3.5 3D Objects and Nets

Algebra:2.1 Number Machines 1.1 Sequences 2.4 Rules of Algebra 4.3 Solving Equations 2.3 Coordinates 4.4 Straight Line Graphs

3

Round these numbers to the nearest 10:1) 152) 343) 574) 1215) 299

Round these numbers to the nearest 1 dp:1) 15.212) 34.373) 57.594) 121.355) 205.99

Rounding

4

Round these numbers to the nearest 10:1) 152) 343) 574) 1215) 299

Round these numbers to the nearest 1 dp:1) 15.212) 34.373) 57.594) 121.355) 205.99

203060120300

15.234.457.6121.4206.0

5

1)234 + 252)532 + 173)699 + 194)999+1275)19+356)55-117)39-128)126-179)319-2110)678-99

Arithmetic 1

6

1)234 + 252)532 + 173)699 + 194)999+1275)19+356)55-117)39-128)126-179)319-2110)678-99

2595497181126544427109298579

7

Averages and Range

8

7216mBluecar

67.8182810.5

131.58cm5m2

9

1)12 x 132)62 x 93)199 x 94) 505 x 55) 31 x 306)715 ÷ 47)235 ÷ 58)48 ÷ 49)558 ÷ 910)14032 ÷ 8

Multiplication and division:

10

1)12 x 132)62 x 93)199 x 94) 505 x 55) 31 x 306)715 ÷ 47)235 ÷ 58)48 ÷ 49)558 ÷ 910)14032 ÷ 8

15655817912525930178.754712621754

11

Arrange these in order smallest to biggest1)0.21, 0.31, 0.122)0.15, 0.143, 0.23) 1.2, 0.12, 0.21, 1.124) 2.3, 2.03, 0.75, 0.85) £1.20, 75p, £0.8

Work out:1) 5+0.262) 0.078+2.053) 13.47+27.0844) 59.2-34.85) 12-3.74

Decimals 1:

12

Arrange these in order smallest to biggest1)0.21, 0.31, 0.122)0.15, 0.143, 0.23) 1.2, 0.12, 0.21, 1.124) 2.3, 2.03, 0.75, 0.85) £1.20, 75p, £0.8

Work out:1) 5+0.262) 0.078+2.053) 13.47+27.0844) 59.2-34.85) 12-3.74

0.12, 0.21, 0.310.143, 0.15, 0.20.12, 0.21, 1.12, 1.20.75, 0.8, 2.03, 2.375p, £0.8, £1.20

5.262.12840.55424.48.26

13

1)5.1 x 22)9 x 0.0743)0.3 x 44)4.23 x 105)0.427 x 1006)8.42 ÷ 27)205.2 ÷ 68)89.2 ÷ 109)7 ÷ 100010)890.4 ÷ 10

Decimals 2:

14

1)5.1 x 22)9 x 0.0743)0.3 x 44)4.23 x 105)0.427 x 1006)8.42 ÷ 27)205.2 ÷ 68)89.2 ÷ 109)7 ÷ 100010)890.4 ÷ 10

10.20.6661.242.342.74.2134.28.920.00789.04

15

Harder (level 6 ) decimal questions

1) 51 x 0.02

2) 912 ÷ 0.12

3) 5791 × 21.3

4)69.2 ÷ 13 (3dp)

1.02

7600

123348.3

5.323

16

Harder (level 6 ) decimal questions

1) 51 x 0.02

2) 912 ÷ 0.12

3) 5791 × 21.3

4)69.2 ÷ 13 (3dp)

17

Work out what the “?” represents:1)15 = ? 20 4

2) 8 = ? = ? 12 6 3

3) ? = 3 = 15 21 7 ?

4) ? = 3 = ? 10 5 25

5) 21 = ? = 7 ? 30 15

Fractions 1:

18

Work out what the “?” represents:1)15 = ? 20 4

2) 8 = ? = ? 12 6 3

3) ? = 3 = 15 21 7 ?

4) ? = 3 = ? 10 5 25

5) 21 = ? = 7 ? 30 15

3

4, 2

9, 35

6, 15

45, 14

19

Change the following to mixed numbers:1)7/22)10/73)9/44)150/1005)19/5

Change the following to improper fractions:

6)1 ¼ 7)1 ⅓8) 2⅟5

9)8 3/7

10)3 1/10

Fractions 2:

20

Change the following to mixed numbers:1)7/22)10/73)9/44)150/1005)19/5

Change the following to improper fractions:

6)1 ¼ 7)1 ⅓8) 2⅟5

9)8 3/7

10)3 1/10

5/44/311/559/731/10

3 ½ 1 3/7

2 ¼ 1 ½ 3 4/5

21

Find the given fractions of the numbers:1)3/8 of £242)¾ of £363)5/8 of 480cm4)7/10 of 30g5)5/9 of £1086)5/8 of 64p7)2/3 of 120cm8)8/9 of 72litres9)2/5 of 30p10)2/3 of 30kg

Fractions 3:

22

Find the given fractions of the numbers:1)3/8 of £242)¾ of £363)5/8 of 480cm4)7/10 of 30g5)5/9 of £1086)5/8 of 64p7)2/3 of 120cm8)8/9 of 72litres9)2/5 of 30p10)2/3 of 30kg

£9£27300cm21g£6040p80cm64litres12p20kg

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1) 1/5 + 2/52) 1/6 + 4/63) 9/10 – 3/104) 12/15 – 5/155) ¼+ ½ 6) 3/8 + ½7) 5/8 – ½8) 2/3 – 1/69) 1/10 – 1/2010)7/8 – 1/2

Fractions 4:

24

1) 1/5 + 2/52) 1/6 + 4/63) 9/10 – 3/104) 12/15 – 5/155) ¼+ ½ 6) 3/8 + ½7) 5/8 – ½8) 2/3 – 1/69) 1/10 – 1/2010)7/8 – 1/2

3/55/63/57/15¾7/81/8½1/203/8

25

Change these fractions to decimals and percentages

1) ¼2) ½3) 1/34) 1/1005) 1/106) 2/107) 9/108) 27/1009) 11/2010)2/25

Fractions 5:

26

Change these fractions to decimals and percentages

1) ¼2) ½3) 1/34) 1/1005) 1/106) 2/107) 9/108) 27/1009) 11/2010)2/25

0.25, 25%0.5, 50%0.333333....., 33.3333...%0.01, 1%0.1, 10%0.2, 20%0.9, 90%0.27, 27%0.55, 55%0.08, 8%

27

Write these ratios in the simplest form:1)8:122)5:253)9:154)12:305)21:356)24:327)36:548)44:779)36:8410)65:39

Ratios

28

Write these ratios in the simplest form:1)8:122)5:253)9:154)12:305)21:356)24:327)36:548)44:779)36:8410)66:39

2:31:53:52:53:53:42:34:73:722:13

29

Divide the numbers into the ratios

1) £18 into 1:2

2) £27 into 2:7

3) £35 into 2:3

4) £42 into 3:4

5) £100 into 3:7

Ratios2:

30

Divide the numbers into the ratios

1) £18 into 1:2

2) £27 into 2:7

3) £35 into 2:3

4) £42 into 3:4

5) £100 into 3:7

£6 and £12

£6 and £21

£14 and £21

£18 and £24

£30 and £70

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1)20% of £502)10% of £903)50% of £454)90% of £1005)1% of £3006)5% of $1007)60% 0f 608)30% of $409)40% OFF £3010) 10% OFF $40

Percentages1

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1)20% of £502)10% of £903)50% of £454)90% of £1005)1% of £3006)5% of $1007)60% 0f 608)30% of $409)40% OFF £3010) 10% OFF $40

£10£9£27.50£90£3$536$12£18$36

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Use a calculator to work out:1) 24% of £322) 97% of 40003) 35% of 400m4) 37% of £9.655) 8% of £11.646) 11% of 710km7) 6% of £4068) 18% of 28km9) 19% of £112010)12% of £24.52

Percentages 2:

34

Use a calculator to work out:1) 24% of £322) 97% of 40003) 35% of 400m4) 37% of £9.655) 8% of £11.646) 11% of 710km7) 6% of £4068) 18% of 28km9) 19% of £112010)12% of £24.52

£7.683880140m£3.57£0.9378.1km£24.365.04km£212.80£2.94

35

Pg15 Questions

1) 96 ÷ 4 – 42) 9 + 26 ÷ 133) 1 x 2 + 34) 4 x 11 – 28 ÷ 75) 13 x 11 – 4 x 86) 30 – 9 x 2 + 407) (20-12) x (17 – 9)8) 1001 + (57 x 3)9) (16 – 7) x 610)(2 x 5 x 3) ÷ (11-5)

Order of operations:

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1) 96 ÷ 4 – 42) 9 + 26 ÷ 133) 1 x 2 + 34) 4 x 11 – 28 ÷ 75) 13 x 11 – 4 x 86) 30 – 9 x 2 + 407) (20-12) x (17 – 9)8) 1001 + (57 x 3)9) (16 – 7) x 610)(2 x 5 x 3) ÷ (11-5)

101154011152641172545

37

Write all the factors of:1) 122) 243) 364) 155) 18Write the first 5 multiples of:6) 47) 78) 99) 1210) 15

Number properties1:

38

Write all the factors of:1) 122) 243) 364) 155) 18Write the first 5 multiples of:6) 47) 78) 99) 1210) 15

1,2,3,4,6,121,2,3,4,6,8,12,241,2,3,4,6,9,12,18,361,3,5,151,2,3,6,9,184,8,12,16,207,14,21,28,359,18,27,36,4512,24,36,48,6015,30,45,60,75

39

Choose the numbers that fall into the group written above the table. Unravel them to find the name of a county cricket team.

1 15 2 37 21 5 29 81 53 39 27T L E S D S X H E C O

1: Prime Numbers

24 27 6 1 125

8 18 150

64 216

36

A E S S R Y S X R U T

2: Cube Numbers

3 9 10 1 16 18 25 15 21 12 6D L H R L S X U M E A

3: Triangular Numbers

6 1 20 100

8 12 64 27 30 62 256

P E L X N E K A S H T

4: Powers of 2

40

1) 6 + - 42) -3 + - 63) -4 – 14) 8 – 135) -2 + 46) -3 - - 27) 7 - + 108) 7 + - 99) - 6 - - 610)-8 + - 2

Negative numbers1:

41

1) 6 + - 42) -3 + - 63) -4 – 14) 8 – 135) -2 + 46) -3 - - 27) 7 - + 108) 7 + - 99) - 6 - - 610)-8 + - 2

2-9-5-52-1-3-20-10

42

× -4 -3 -2 -1 0 1 2 3 4-4 4 0 -4 -8 -16-3 0 -3 -6 -9-2 0 -2 -6 -8-1 0 -1 -2 -3 -40 0 0 0 0 012 -6

3 9

4

Complete the table

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1. 4 x 1 = _4_2. 4 x 2 = ___3. 4 x 3 = ___4. 4 x 4 = ___5. Positive × Positive =

_________6. 4 ÷ 4 = 17. 8 ÷ 4 = ___8. 12 ÷ 4 = ___9. 16 ÷ 4 = ___10.Positive ÷ Positive =

___________

11.– 4 x 1 = ___12.– 4 x 2 = ___13.– 4 x 3 = ___14.– 4 x 4 = ___15.Negative x Positive

= _________16.– 4 ÷ – 4 = 117.– 8 ÷ – 4 = ___18.– 12 ÷ – 4 = ___19.– 16 ÷ – 4 = ___20.Negative ÷ Negative

= ___________ 

44

Unit conversions:1) Convert 12.5cm to inches. 2) The longest nose on a living person is 8.8cm.

Convert this measurement to inches.3) The largest bubble gum bubble blown has a

diameter of 20.3 inches. Convert this measurement to centimetres.

4) Convert 51cm into feet. 5) The longest snake ever is 7.3m. Convert to feet.

(Hint: convert 7.3m to centimetres first, then into feet)

6) Convert 6.5 feet into (i) cm (ii) m.7) Convert the following into litres: 4 pints and 3

gallons8) Convert the following into pints: 855 ml and 7 l9) Convert the following into kilograms:4.4 pounds

& 1 stone10)Convert the following into kilometres:9 miles

& 16.5 miles11)Extension question I run a 10km race in 56

minutes. What is my average speed for the race in:

a) kilometres per minute b) miles per minute c) miles per hour

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1) 12.5cm / 2.5 = 5 inches2) 8.8cm / 2.5 = 3.52 = 3.5 inches (1 dp)3) 20.3 inches x 2.5 = 50.75 = 50.8cm (1 dp)4) 51cm / 30 = 1.7 feet5) 7.3m = 730cm. 730 / 30 = 24.33333…. = 24.3 feet (1 dp)6) (i) 6.5 feet x 30 = 195cm (ii)195 / 100 = 1.95m7) 4 pints / 1.75 = 2.285714…. = 2.3 litres (1 dp) b) 3

gallons x 4.5 = 13.5 litres8) 855ml / 570 = 1.5 pints b) 7l x 1.75 = 12.25 pints9) 4.4 pounds / 2.2 = 2 kg b) 1 stone = 14 pounds. 14 /

2.2 = 6.36363636… = 6.4 kg (1 dp)10)9miles x 1.6 = 14.4 km b) 16.5 miles x 1.6 = 26.4 km11)a) 10km / 56 minutes = 0.1785714… = 0.2 km per

minuteb) 10 km / 1.6 = 6.25 miles. 6.25 miles / 56 minutes = 0.11160714… = 0.1 miles per minutec) 60 mins in 1 hour. 0.11160714… x 60 = 6.69642857…. = 6.7 miles per hour

46

Number machines

47

6

11

2

5

2540

6

15

11

1827

712

79

17

25

660

8222

418

25

48

Copy and complete the sequences:1)1,3,5,?,9,?2)2,4,?,8,10,?3)3,?,9?,15,18,?4)33,30,?,24,?5)66,?,?,33,?,116)2?,8,?,14,17,?7)8,?,18,?,28,?

Work out the next two terms and the term to term rule:8)4,8,12,169)27,24,21,1810)100,200,400,80011)1,10,100,100012)0,250,500,75013)812,712,612,51214)318,338,358,378

Sequences

49

Copy and complete the sequences:1)1,3,5,?,9,?2)2,4,?,8,10,?3)3,?,9?,15,18,?4)33,30,?,24,?5)66,?,?,33,?,116)2?,8,?,14,17,?7)8,?,18,?,28,?

Work out the next two terms and the term to term rule:8)4,8,12,169)27,24,21,1810)100,200,400,80011)1,10,100,100012)0,250,500,75013)812,712,612,51214)318,338,358,378

7,116,126,12,2127,2155,44,225,11,2013,23,33

20,24 +415,12 -31600,3200 x210000,100000, x101000,1250 +250412,312 -100398,418 +20

50

51

52

53

Rules of Algebra

54

2x 4x 4x 10x 10x 13x

3x + 1

x+4 2x+25x+

53x+1

4x+78x+

3 11x+7

9x+5

x+2y 5x+y 4x+2y2x+

2y2x+9y

10x+y

18x+5y+4

5x+6y+2

5x+8y+7

x+y+8 2x+3y

+33x+5y+5

55

Rules of algebra

56

B = 12B = 7B = 5.5

s=4

s=7s=6

d=220

F=30

F=48F=6.5

m=6

57

Rules of Algebra

58

37.650.28

207.

5

1.221.250.83

59

Solving algebra

60

(x-11)÷52(x+7)

(3x+5) ÷43(10-x)

x÷3 + 5

x=70 x=6 x=67

x=65 x=40 x=5x=40 x=30 x=12

x=64 x=36 x=100

61

Solving algebra

62

x+7

x+y

p-q

n-5

k-2

t+2

0 1 2 3 4 5 6-6 -5 -4 -3 -2-101

23

4

5

6

-6-5

-4-3

-2

x

y

78

9

-7

-8

-9

7 8-1-7-8

x 5

y -6 -3 0 3 6

x -3 -2 -1 0 1

Y

x -6 -3 0 3 6

y 4 4 4 4 4

x -6 -3 0 3 6

y -4 2

x -6 -3 0 3 6

y -9 0

x = -4

x = 5

These lines are v_________ and p_________

They pass through the x-axis at _____________________

X -4 -4 -4 -4 -5

y -6 -3 0 3 6Complete each table or equation, plot the line on the graph and label it, then complete the missing words

Graphs of Algebraic Equations

y = -8

y = __

These lines are h____________ and p____________ They pass through the y-axis at _________________

y = x + 2

y = x - __

Adding a value to x moves the graph _____________ Subtracting a value from x moves it ______________

Linear Graphing

63

0 1 2 3 4 5 6-6 -5 -4 -3 -2-101

23

4

5

6

-6-5

-4-3

-2

x

y

78

9

-7

-8

-9

7 8-1-7-8

x -2 -1 0 1 2

y

x -2 -1 0 1 2

y

x 0 1 2 3 4

y

x -2 -1 0 1 2

y

Complete each table, then plot the points on the graph, complete the line and label it

Graphs of Algebraic Equations

y = 3x + 1

y = 2x - 1

y = 5 – x

y = ½x - 3

64

65

Work out the perimeter of:Area and perimeter

66

Work out the perimeter of:

38cm46cm

42cm 38cm

36cm 45cm

67

Area and perimeter

68

117m2

100m2

27cm2

22cm2

72cm2

69

Calculating Angles1:

70

Reflex Obtuse

Right AngleObtus

eObtuse

158o 356o 115o 211o

71

Calculate the angles marked with lettersCalculating Angles2:

72

Calculate the angles marked with letters

339o 115

o

85o

47o

115o

225o

169o

65o

72o 26o50o

46o

73

74

Identify two pairs of corresponding angles and two pairs of alternate angles in each diagram:

Find the missing angles:

75

1 4 5 °

7 4 °

9 2 °

y

P

Q

RS

N o t d raw n accu ra te ly

y

3 x 2 x4 x

N o t d raw n accu ra te ly1: Find x and y

2: Find y:

Sum of angles in a polygon = (number of sides – 2) x 180

76

Copy and complete:Calculating Angles3:

77

Copy and complete:two two

no nothree three

90four four90 two

twoequal

parallelfour four

twotwoequal four four

oneone

equalfour four

twotwo

equal

perpendicular

78

Calculating Angles4:

79

Reflection

80

A B

C ED

81

Rotation:

82

90o A/C (1,5)180o (3.5,4)

180o (1.5,3)90o A/C (3,3)

83

Symmetry

84

2 1 4

2 1 6

85

Translation

86

a) 2 right and 3 upb) 6 rightc) 2 left and 3 downd) 6 lefte) 4 right and 2 upf) 2 left and 7 upg) 4 left and 2 downh)2 right and 7 down

87

3D Objects and Nets

88

8 6 12

89

3D shapes and nets

90

91

3D shapes and nets

92

13cm3

11cm3

15cm3 13c

m3

10220

16348

8324

20240

93

1. The number FIVE as written using block capitals contains exactly 10 strokes or segments of a straight line. Find a number which when written out in words (using no tricks) contains as many strokes as the number says.

2. There are two clocks. One of them gains 6 seconds in every hour, while the other loses 9 seconds in every hour. If they are both set to show the same time, and then set going, how long will it be before they are exactly 1 hour different?

3. How many days is it from Wednesday the 1st August to the first Saturday in September?

4. Find four consecutive odd numbers which add up to to a total of 80.

5. What is the opposite of "NOT OUT"?

6. When one particular number, written in figures, is turned upside down it increases in value by 21. Which number is that?

7. A car has travelled 24,000 km and, in that distance, has worn out 6 tyres. Each tyre travelled the same distance. How far did each separate tyre travel?

8. A man bought 50 metres of rope in a shop. He did not know it, but the metre-rule used to measure the rope was 1cm short. What length of rope did he actually get?

9. Find two whole numbers which, when multiplied together give an answer of 41.

10.

If 6 cats can catch 6 rats in 6 minutes, how many cats are needed to catch 10 rats in 10 minutes?

Problem solving:

94

Answers:1.TWENTY NINE 2.240 hours3.32 inclusive of both dates. 4.17 + 19 + 21 + 23 = 805.OUT!6.68 (changes to 89)7.4-wheeler 16,000 km each. 3-

wheeler 12,000 km each.8.49.5 metres9.1 x 4110.6 cats.

95

On this diagram you may start at any square and move up or down or across (but NOT diagonally) into the next square. No square may be used twice. The digits in each square are written down in the order they are used. What is the largest number that can be made?

96

How many acute angles can be found in this drawing?

The French Flag (known as the tricolour) is coloured  Red , White ,and Blue in the way shown. Using the same three colours, how many different flags would it be possible to make?

97

 Draw out a 3 by 3 grid like that shown. Place the numbers -2 2 2 3 3 3 4 4 4 in it so that, when any line of three numbers is added up in any direction (including diagonally), the total is always 9

Arrange the numbers 1 to 9, using each one only once, placing only one number in each cell so that the totals in both directions ( up and down and across) are the same. How may different ways are there of doing this?

98

The diagram shows an equilateral triangle and an isosceles triangle. Work out the size of the angle marked x.

99

Answer: