Year 7, 2014 Exam revision ANSWERS

Tick off, when you have revised! What’s in your Exam: Number: 3.3 Rounding Numbers  1.3 Arithmetic  1.2 Averages and Range  1.6 Long Multiplication and Division 1.5 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  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  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  4.5 Solving Problems 

Rounding Round these numbers to the nearest 10: 1) 15 2) 34 3) 57 4) 121 5) 299 Round these numbers to the nearest 1 dp: 1) 15.21 2) 34.37 3) 57.59 4) 121.35 5) 205.99

Round these numbers to the nearest 10: 1) 15 2) 34 3) 57 4) 121 5) 299 20 30 60 120 300 Round these numbers to the nearest 1 dp: 1) 15.21 2) 34.37 3) 57.59 4) 121.35 5) 205.99 15.2 34.4 57.6 121.4 206.0

Arithmetic 1 234 + 25 532 + 17 699 + 19 999+127 19+35 55-11 39-12 126-17 319-21 678-99

234 + 25 532 + 17 699 + 19 999+127 19+35 55-11 39-12 126-17 319-21 678-99 259 549 718 1126 54 44 27 109 298 579

Averages and Range

7 21 6m Blue car 6 7.8 18 28 10.5 13 1.5 8cm 5m2

Multiplication and division: 12 x 13 62 x 9 199 x 9 505 x 5 31 x 30 715 ÷ 4 235 ÷ 5 48 ÷ 4 558 ÷ 9 14032 ÷ 8

12 x 13 62 x 9 199 x 9 505 x 5 31 x 30 715 ÷ 4 235 ÷ 5 48 ÷ 4 558 ÷ 9 14032 ÷ 8 156 558 1791 2525 930 178.75 47 12 62 1754

Decimals 1: Arrange these in order smallest to biggest 1)0.21, 0.31, 0.12 2)0.15, 0.143, 0.2 3) 1.2, 0.12, 0.21, 1.12 4) 2.3, 2.03, 0.75, 0.8 5) £1.20, 75p, £0.8 Work out: 5+0.26 0.078+2.05 13.47+27.084 59.2-34.8 12-3.74

Arrange these in order smallest to biggest 1)0.21, 0.31, 0.12 2)0.15, 0.143, 0.2 3) 1.2, 0.12, 0.21, 1.12 4) 2.3, 2.03, 0.75, 0.8 5) £1.20, 75p, £0.8 0.12, 0.21, 0.31 0.143, 0.15, 0.2 0.12, 0.21, 1.12, 1.2 0.75, 0.8, 2.03, 2.3 75p, £0.8, £1.20 Work out: 5+0.26 0.078+2.05 13.47+27.084 59.2-34.8 12-3.74 5.26 2.128 40.554 24.4 8.26

Decimals 2: 5.1 x 2 9 x 0.074 0.3 x 4 4.23 x 10 0.427 x 100 8.42 ÷ 2 205.2 ÷ 6 89.2 ÷ 10 7 ÷ 1000 890.4 ÷ 10

5.1 x 2 9 x 0.074 0.3 x 4 4.23 x 10 0.427 x 100 8.42 ÷ 2 205.2 ÷ 6 89.2 ÷ 10 7 ÷ 1000 890.4 ÷ 10 10.2 0.666 1.2 42.3 42.7 4.21 34.2 8.92 0.007 89.04

Harder (level 6 ) decimal questions 51 x 0.02 912 ÷ 0.12 5791 × 21.3 69.2 ÷ 13 (3dp) 1.02 7600 123348.3 5.323

Harder (level 6 ) decimal questions 51 x 0.02 912 ÷ 0.12 5791 × 21.3 69.2 ÷ 13 (3dp)

Fractions 1: Work out what the “?” represents: 15 = ? 20 4 15 = ? 20 4 2) 8 = ? = ? 12 6 3 3) ? = 3 = 15 21 7 ? 4) ? = 3 = ? 10 5 25 5) 21 = ? = 7 ? 30 15

Work out what the “?” represents: 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

Fractions 2: Change the following to mixed numbers: 7/2 10/7 9/4 150/100 19/5 Change the following to improper fractions: 1 ¼ 1 ⅓ 2⅟5 8 3/7 3 1/10

Change the following to mixed numbers: 7/2 10/7 9/4 150/100 19/5 Change the following to improper fractions: 1 ¼ 1 ⅓ 2⅟5 8 3/7 3 1/10 3 ½ 1 3/7 2 ¼ 1 ½ 3 4/5 5/4 4/3 11/5 59/7 31/10

Fractions 3: Find the given fractions of the numbers: 3/8 of £24 5/8 of 480cm 7/10 of 30g 5/9 of £108 5/8 of 64p 2/3 of 120cm 8/9 of 72litres 2/5 of 30p 2/3 of 30kg

Find the given fractions of the numbers: 5/8 of 480cm 7/10 of 30g 5/9 of £108 5/8 of 64p 2/3 of 120cm 8/9 of 72litres 2/5 of 30p 2/3 of 30kg £9 £27 300cm 21g £60 40p 80cm 64litres 12p 20kg

Fractions 4: 1/5 + 2/5 1/6 + 4/6 9/10 – 3/10 12/15 – 5/15 ¼+ ½ 3/8 + ½ 5/8 – ½ 2/3 – 1/6 1/10 – 1/20 7/8 – 1/2

1/5 + 2/5 1/6 + 4/6 9/10 – 3/10 12/15 – 5/15 ¼+ ½ 3/8 + ½ 5/8 – ½ 2/3 – 1/6 1/10 – 1/20 7/8 – 1/2 3/5 5/6 7/15 ¾ 7/8 1/8 ½ 1/20 3/8

Fractions 5: Change these fractions to decimals and percentages ¼ ½ 1/3 1/100 1/10 2/10 9/10 27/100 11/20 2/25

Change these fractions to decimals and percentages ¼ ½ 1/3 1/100 1/10 2/10 9/10 27/100 11/20 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%

Ratios Write these ratios in the simplest form: 8:12 5:25 9:15 12:30 21:35 24:32 36:54 44:77 36:84 65:39

Write these ratios in the simplest form: 8:12 5:25 9:15 12:30 21:35 24:32 36:54 44:77 36:84 66:39 2:3 1:5 3:5 2:5 3:4 4:7 3:7 22:13

Ratios2: Divide the numbers into the ratios £18 into 1:2 £27 into 2:7

Divide the numbers into the ratios £6 and £12 £6 and £21 £14 and £21 £18 and £24 £30 and £70

Percentages1 20% of £50 10% of £90 50% of £45 90% of £100 1% of £300 40% OFF £30 10% OFF $40

20% of £50 10% of £90 50% of £45 90% of £100 1% of £300 5% of $100 60% 0f 60 30% of $40 40% OFF £30 10% OFF $40 £10 £9 £27.50 £90 £3 $5 36 $12 £18 $36

Percentages 2: Use a calculator to work out: 24% of £32 97% of 4000 35% of 400m 37% of £9.65 8% of £11.64 11% of 710km 6% of £406 18% of 28km 19% of £1120 12% of £24.52

Use a calculator to work out: 24% of £32 97% of 4000 35% of 400m 37% of £9.65 8% of £11.64 11% of 710km 6% of £406 18% of 28km 19% of £1120 12% of £24.52 £7.68 3880 140m £3.57 £0.93 78.1km £24.36 5.04km £212.80 £2.94

Order of operations: 96 ÷ 4 – 4 9 + 26 ÷ 13 1 x 2 + 3 4 x 11 – 28 ÷ 7 Pg15 Questions Order of operations: 96 ÷ 4 – 4 9 + 26 ÷ 13 1 x 2 + 3 4 x 11 – 28 ÷ 7 13 x 11 – 4 x 8 30 – 9 x 2 + 40 (20-12) x (17 – 9) 1001 + (57 x 3) (16 – 7) x 6 (2 x 5 x 3) ÷ (11-5)

96 ÷ 4 – 4 9 + 26 ÷ 13 1 x 2 + 3 4 x 11 – 28 ÷ 7 13 x 11 – 4 x 8 30 – 9 x 2 + 40 (20-12) x (17 – 9) 1001 + (57 x 3) (16 – 7) x 6 (2 x 5 x 3) ÷ (11-5) 10 11 5 40 111 52 64 1172 54

Number properties1: Write all the factors of: 12 24 36 15 18 Write the first 5 multiples of: 4 7 9

Write all the factors of: 12 24 36 15 18 Write the first 5 multiples of: 4 7 9 1,2,3,4,6,12 1,2,3,4,6,8,12,24 1,2,3,4,6,9,12,18,36 1,3,5,15 1,2,3,6,9,18 4,8,12,16,20 7,14,21,28,35 9,18,27,36,45 12,24,36,48,60 15,30,45,60,75

Choose the numbers that fall into the group written above the table Choose the numbers that fall into the group written above the table. Unravel them to find the name of a county cricket team. 1: Prime Numbers 1 15 2 37 21 5 29 81 53 39 27 T L E S D X H C O 2: Cube Numbers 24 27 6 1 125 8 18 150 64 216 36 A E S R Y X U T 3: Triangular Numbers 3 9 10 1 16 18 25 15 21 12 6 D L H R S X U M E A 4: Powers of 2 6 1 20 100 8 12 64 27 30 62 256 P E L X N K A S H T

Negative numbers1: 6 + - 4 -3 + - 6 -4 – 1 8 – 13 -2 + 4 -3 - - 2 7 - + 10 7 + - 9 - 6 - - 6 -8 + - 2

6 + - 4 -3 + - 6 -4 – 1 8 – 13 -2 + 4 -3 - - 2 7 - + 10 7 + - 9 - 6 - - 6 -8 + - 2 2 -9 -5 -1 -3 -2 -10

Complete the table × -4 -3 -2 -1 1 2 3 4 -8 -16 -6 -9 9

– 4 x 1 = ___ – 4 x 2 = ___ – 4 x 3 = ___ – 4 x 4 = ___ Negative x Positive = _________ – 4 ÷ – 4 = 1 – 8 ÷ – 4 = ___ – 12 ÷ – 4 = ___ – 16 ÷ – 4 = ___ Negative ÷ Negative = ___________   4 x 1 = _4_ 4 x 2 = ___ 4 x 3 = ___ 4 x 4 = ___ Positive × Positive = _________ 4 ÷ 4 = 1 8 ÷ 4 = ___ 12 ÷ 4 = ___ 16 ÷ 4 = ___ Positive ÷ Positive = ___________

Unit conversions: Convert 12.5cm to inches. The longest nose on a living person is 8.8cm. Convert this measurement to inches. The largest bubble gum bubble blown has a diameter of 20.3 inches. Convert this measurement to centimetres. Convert 51cm into feet. The longest snake ever is 7.3m. Convert to feet. (Hint: convert 7.3m to centimetres first, then into feet) Convert 6.5 feet into (i) cm (ii) m. Convert the following into litres: 4 pints and 3 gallons Convert the following into pints: 855 ml and 7 l Convert the following into kilograms:4.4 pounds & 1 stone Convert the following into kilometres:9 miles & 16.5 miles 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

12.5cm / 2.5 = 5 inches 8.8cm / 2.5 = 3.52 = 3.5 inches (1 dp) 20.3 inches x 2.5 = 50.75 = 50.8cm (1 dp) 51cm / 30 = 1.7 feet 7.3m = 730cm. 730 / 30 = 24.33333…. = 24.3 feet (1 dp) (i) 6.5 feet x 30 = 195cm (ii)195 / 100 = 1.95m 4 pints / 1.75 = 2.285714…. = 2.3 litres (1 dp) b) 3 gallons x 4.5 = 13.5 litres 855ml / 570 = 1.5 pints b) 7l x 1.75 = 12.25 pints 4.4 pounds / 2.2 = 2 kg b) 1 stone = 14 pounds. 14 / 2.2 = 6.36363636… = 6.4 kg (1 dp) 9miles x 1.6 = 14.4 km b) 16.5 miles x 1.6 = 26.4 km a) 10km / 56 minutes = 0.1785714… = 0.2 km per minute b) 10 km / 1.6 = 6.25 miles. 6.25 miles / 56 minutes = 0.11160714… = 0.1 miles per minute c) 60 mins in 1 hour. 0.11160714… x 60 = 6.69642857…. = 6.7 miles per hour

Number machines

6 25 11 40 2 6 5 15 25 11 18 6 27 60 1 2 7 2 8 22 9 18 7 4 17 25

Sequences Copy and complete the sequences: 1,3,5,?,9,? 2,4,?,8,10,? 3,?,9?,15,18,? 33,30,?,24,? 66,?,?,33,?,11 2?,8,?,14,17,? 8,?,18,?,28,? Work out the next two terms and the term to term rule: 4,8,12,16 27,24,21,18 100,200,400,800 1,10,100,1000 0,250,500,750 812,712,612,512 318,338,358,378

Copy and complete the sequences: 1,3,5,?,9,? 2,4,?,8,10,? 3,?,9?,15,18,? 33,30,?,24,? 66,?,?,33,?,11 2?,8,?,14,17,? 8,?,18,?,28,? Work out the next two terms and the term to term rule: 4,8,12,16 27,24,21,18 100,200,400,800 1,10,100,1000 0,250,500,750 812,712,612,512 318,338,358,378 7,11 6,12 6,12,21 27,21 55,44,22 5,11,20 13,23,33 20,24 +4 15,12 -3 1600,3200 x2 10000,100000, x10 1000,1250 +250 412,312 -100 398,418 +20

Rules of Algebra

4x 2x 4x 10x 10x 13x x+4 2x+2 3x + 1 4x+7 5x+5 3x+1 9x+5 8x+3 11x+7 4x+2y x+2y 5x+y 10x+y 2x+2y 2x+9y 18x+5y+4 5x+6y+2 5x+8y+7 x+y+8 2x+3y+3 3x+5y+5

Rules of algebra

B = 12 B = 7 B = 5.5 s=4 s=7 s=6 d=220 F=30 F=48 F=6.5 m=6

Rules of Algebra

37.6 50.2 8 20 7.5 1.22 1.25 0.83

Solving algebra

(x-11)÷5 2(x+7) (3x+5) ÷4 3(10-x) x÷3 + 5 x=70 x=6 x=67 x=65 x=40 x=5 x=40 x=30 x=12 x=64 x=36 x=100

Solving algebra

x+7 x+y n-5 p-q k-2 t+2

Graphs of Algebraic Equations Linear Graphing X -4 -5 y -6 -3 3 6 These lines are v_________ and p_________ They pass through the x-axis at _____________________ x = -4 Complete each table or equation, plot the line on the graph and label it, then complete the missing words x 5 y -6 -3 3 6 x = 5 y 9 8 x -3 -2 -1 1 Y y = -8 7 6 5 x -6 -3 3 6 y 4 y = __ 4 3 These lines are h____________ and p____________ They pass through the y-axis at _________________ 2 1 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 x -1 x -6 -3 3 6 y -4 2 -2 y = x + 2 -3 -4 x -6 -3 3 6 y -9 y = x - __ -5 -6 Adding a value to x moves the graph _____________ Subtracting a value from x moves it ______________ -7 -8 -9

Graphs of Algebraic Equations Complete each table, then plot the points on the graph, complete the line and label it y = 3x + 1 y x -2 -1 1 2 y 9 8 7 y = 2x - 1 6 5 x -2 -1 1 2 y 4 3 2 y = 5 – x 1 x 1 2 3 4 y -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 x -1 -2 -3 y = ½x - 3 -4 -5 x -2 -1 1 2 y -6 -7 -8 -9

Area and perimeter Work out the perimeter of:

Work out the perimeter of: 38cm 46cm 38cm 42cm 45cm 36cm

Area and perimeter

117m2 100m2 27cm2 72cm2 22cm2

Calculating Angles1:

Reflex Obtuse Right Angle Obtuse Obtuse 158o 356o 115o 211o

Calculating Angles2: Calculate the angles marked with letters

Calculate the angles marked with letters 339o 85o 115o 115o 169o 47o 225o 65o 46o 50o 72o 26o

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

Sum of angles in a polygon = (number of sides – 2) x 180 1: Find x and y 2: Find y: Sum of angles in a polygon = (number of sides – 2) x 180

Calculating Angles3: Copy and complete:

Copy and complete: two two no no three three 90 four four 90 two two equal parallel four four two two equal four four one one equal four four two two perpendicular equal

Calculating Angles4:

Reflection

B A D E C

Rotation:

180o (1.5,3) 90o A/C (1,5) 90o A/C (3,3) 180o (3.5,4)

Symmetry

1 2 4 6 2 1

Translation

2 right and 3 up 6 right 2 left and 3 down 6 left 4 right and 2 up 2 left and 7 up 4 left and 2 down 2 right and 7 down

3D Objects and Nets

8 6 12

3D shapes and nets

3D shapes and nets

15cm3 13cm3 11cm3 13cm3 10 2 20 20 2 40 8 3 24 16 3 48

Problem solving: 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?

Answers: TWENTY NINE 240 hours 32 inclusive of both dates. 17 + 19 + 21 + 23 = 80 OUT! 68 (changes to 89) 4-wheeler 16,000 km each. 3-wheeler 12,000 km each. 49.5 metres 1 x 41 6 cats.

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? 594836271

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? 6 acute angles, 6 flags (including one given)

Draw out a 3 by 3 grid like that shown  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?

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

Answer: