Download - Year 7, 2014
1
Year 7, 2014 Exam
revision ANSWERS
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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
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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
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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
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1)234 + 252)532 + 173)699 + 194)999+1275)19+356)55-117)39-128)126-179)319-2110)678-99
Arithmetic 1
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1)234 + 252)532 + 173)699 + 194)999+1275)19+356)55-117)39-128)126-179)319-2110)678-99
2595497181126544427109298579
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Averages and Range
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7216mBluecar
67.8182810.5
131.58cm5m2
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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:
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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
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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
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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
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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
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Harder (level 6 ) decimal questions
1) 51 x 0.02
2) 912 ÷ 0.12
3) 5791 × 21.3
4)69.2 ÷ 13 (3dp)
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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
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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
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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:
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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:
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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
3/55/63/57/15¾7/81/8½1/203/8
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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%
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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
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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
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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:
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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
£7.683880140m£3.57£0.9378.1km£24.365.04km£212.80£2.94
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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
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Write all the factors of:1) 122) 243) 364) 155) 18Write the first 5 multiples of:6) 47) 78) 99) 1210) 15
Number properties1:
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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
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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
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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
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1) 6 + - 42) -3 + - 63) -4 – 14) 8 – 135) -2 + 46) -3 - - 27) 7 - + 108) 7 + - 99) - 6 - - 610)-8 + - 2
Negative numbers1:
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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
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× -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
= ___________
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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
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Number machines
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6
11
2
5
2540
6
15
11
1827
712
79
17
25
660
8222
418
25
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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
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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
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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
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Rules of algebra
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B = 12B = 7B = 5.5
s=4
s=7s=6
d=220
F=30
F=48F=6.5
m=6
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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
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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
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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
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Calculating Angles1:
70
Reflex Obtuse
Right AngleObtus
eObtuse
158o 356o 115o 211o
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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
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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: