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Cambridge Lower Secondary Mathematics Workbook 8 2nd Edition Lynn Byrd, Greg Byrd, Chris Pearce - Solutions
8 Draw the plan view, the front elevation and the side elevation of this isosceles triangular prism. Use a scale of 1:20 120 cm 100 cm 80 cm
7 Draw the plan view, the front elevation and the side elevation of this right-angled triangular prism. Use a scale of 1:5 20 cm 25 cm 15 cm 35 cm
6 Draw the plan view, the front elevation and the side elevation of this 3D shape. Use a scale of 1:4 8 cm 12 cm 32 cm 8 cm 16 cm 20 cm
5 The diagram shows the dimensions of a shipping container. Abbie makes a house from three shipping containers. The containers are arranged as shown in the diagram. Draw the plan view, the front elevation and the side elevation of her house. Use a scale of 1:120 6 m 2.4 m 2.4 m
4 The diagram shows a 3D shape.The plan view, front elevation and side elevations are drawn on centimetre squared paper. Write if A, B or C is the correct scale drawing for each view. The scale used is 1:1. 2 cm 4 cm 2 cm 2 cm 3 cm 1 cm
3 Copy and complete the workings and scale drawings for this question. Draw the top view, front view and side view of each shape. Use a scale of 1:2 a cube Dimensions for the drawing: 8+2= cm 8 cm Top view Front view Tip Tip Draw a square of side length 4 cm. Draw a square of side length 4 cm. Side
2 The diagram shows a cuboid. The top view, front view and side view of the cuboid are drawn on centimetre squared paper. The scale used is 1:6.a Copy and complete the workings to find the dimensions of the scale drawing. 30+6=5cm 24+6= cm 12+6= cm b Match each drawing with the correct view.A Top
1 a The diagram shows a pentagonal prism. Write the number of faces, vertices and edges for this prism.b The formula linking the number of faces (F), vertices (V) and edges (E) for a 3D shape with no curved surfaces is E=F + V-2 Substitute your values for F and V (from parta) into the formula to
13 The diagram shows an athletics track. The radius of the inner semicircle at each end is 36.8 m. The length of the straight section is 84.39 m.a Work out the length of the inner perimeter of the track.b Give your answer correct to the nearest metre. The width of each lane is 1.22m. There are
12 Work out the perimeter of each compound shape.Give your answers correct to two decimal places (2 d.p.). a 20 12.6 cm 8.4 cm b 6 cm
11 The diagram shows a semicircle and three-quarters of a circle.I think the perimeter of the semicircle is less than the perimeter of the three- quarter circle shape.Is Marcus correct? Show working to support your answer. 8 cm 3 m
10 Work out the perimeter of this semicircle. Round your answer correct to 2 decimal places (2 d.p.). 24 cm
9 A circular pond has a circumference of 10.45 m.Show that the radius of the pond is 166 cm correct to the nearest centimetre.
8 The circumference of a circular coin is 56 mm.Work out the diameter of the coin.Give your answer correct to the nearest millimetre.
7 Work out the radius of a circle with circumference = 23 cm ab circumference = 17.8 m.Round each answer correct to 2 decimal places (2 d.p.).
6 Work out the diameter of a circle with circumference=35cm circumference =8.95m.a bRound each answer correct to 1 decimal place (1 d.p.).
5 Work out the circumference of each circle.Round each answer correct to 2 decimal places (2 d.p.).diameter= 16cm ab diameter =9.5m cradius=10cm dradius=2.8 m
4 Copy and complete the workings to find the circumference of each circle. Use = 3.14For the rest of the questions in this exercise, use the button on your calculator. a 5 cm b 1 cm radius, r=5cm diameter, d=2x5 = cm C = d = 3.14x10 = CI cm radius, r = 1 cm diameter, d=2x1 = cm C = d = 3.142 = cm
3 Copy and complete the workings to find the circumference of each circle. Use the button on your calculator. Round each answer correct to 2 decimal places (2 d.p.). a 9 cm d=9cm C = d b = 9 = cm 12 cm d = 12 cm C = d = X12 = cm
2 Copy and complete the workings to find the circumference of each circle. Use =3.142 Round each answer correct to 2 decimal places (2 d.p.). d=8cm a 8 cm C = d = 3.142x8 cm b 6 cm d=6cm C = d = 3.142x6 = = cm
1 Copy and complete the workings to find the circumference of each circle.Use pi=3.14 Round each answer correct to 1 decimal place (1 d.p.). a d = 4cm b 4 cm C = d = 3.14x4 5 cm = C cm d=5cm C = d = 3.14x5 cm
14 Make a copy of the coordinate grid shown.On the grid, plot the following points: (2, 2) (6, 2) (0, 4) (4, 4) (8,4) (2,6) (2,8) (6,8) (4,9) Which four points can you join to make each of these quadrilaterals? a rectangle C parallelogram e trapezium b d square kite y 10- 810 9- 7 6- 5 4- 3 2 1 0 0
13 This diagram shows the hierarchy of quadrilaterals. In the diagram, a quadrilateral below another is a special case of the one above it. For example, a square is a special rectangle but a rectangle is not a square. Use the diagram to decide if each statement is true (T) or false (F). A rhombus
12 Put each quadrilateral through this classification flow chart. Write the letter where each shape comes out. a b C d e rhombus trapezium kite rectangle square isosceles trapezium g parallelogram H START yes All angles are 90? yes Opposite angles are equal? no yes All sides the same length? All
11 Arun is describing an isosceles trapezium to Marcus.Has Arun given Marcus the correct information?Explain your answer. My quadrilateral has one pair of parallel sides and one pair of sides the same length. What is the name of my quadrilateral?
10 Match each quadrilateral with its correct properties.One pair of sides the -ii Two pairs of sides the ili One pair of parallel same length same length sides One pair of parallel sides One pair of equal angles Two pairs of equal angles A trapezium B isosceles trapezium C kite
9 Sofia is describing a rectangle to Zara.Has Sofia given Zara enough information for her to work out that the quadrilateral is a rectangle? Explain your answer. My quadrilateral has two pairs of parallel sides and two pairs of sides the same length. What is the name of my quadrilateral?
8 Match each quadrilateral with its correct side and angle properties. A square B rectangle C rhombus D parallelogram
7 Write true (T) or false (F) for each statement about regular polygons. a A hexagon has five lines of symmetry. b An octagon has order of rotation 8. C d e f A pentagon has order of rotation 10. A decagon has 10 lines of symmetry. A polygon with 15 lines of symmetry has 15 sides. A polygon with
6 Look at rhombus QRST. Copy and complete these sentences using the options in the box. sides are the same length. parallel TSR all QRS a b C Opposite sides are................... Angle TQR is equal to angle................. and angle QTS is equal to angle................ T S R
5 Look at parallelogram MNOP. Copy and complete these sentences using the options in the box. equal a b C MP opposite MN MPO .sides are the same length. NO is parallel to ....................nd PO is parallel to Angle PMN ................. to angle NOP and angle MNO is equal to angle....... P M N
4 Look at kite IJKL. Copy and complete these sentences using the options in the box. IL a equal not parallel LK IJ is the same length as ..................nd JK is the same length as.. b None of the sides are. Angle ILK. is............... to angle IJK but angle LIJ is.............. equal to angle
3 Look at rectangle EFGH. Copy and complete these sentences using the options in the box. HG opposite 90 FG a b C ...sides are the same length. EH is parallel to ................and.. EF is parallel to ........... All the angles are....... E F G H
2 Look at square ABCD. Copy and complete these sentences using the options in the box. BC length DC 90 a All sides are the same. b AB is parallel to ................. and AD is parallel to........ C All the angles are............. A B D C
1 For each regular polygon, give the correct name and number of sides. The first one is done for you.pentagon, 5 sides
14 Here are three formula cards.b= 18 a c-bx(2-1)-3(-11) a Work out the value of d when Explain the method you used. 23 =Work out the value of d when a= Explain the method you used.
13 Here are two calculation cards.Read what Sofia says.Is Sofia correct? Show all your working. A (1+1)x(2-3) B (31+2)+(+14)
12 Work out.do a calculation mentally, write down some If you cannot workings to help you. 2 10x(+-) 14 15 b 3+ (+) P 7 12-(+)
11 This is how Arun mentally works out 14+ (10-2)First, I work out which equals Then I work out 14+, which equals 14=2 a Explain the mistake Arun has made. Work out the correct answer. 3D
10 The diagram shows a rectangle. The area of the rectangle is 15 m. The width of the rectangle is m. 8 What is the length of the rectangle? length 58 m
9 a Work out. Some working has been shown to help you with the first two. i 6+=6x4+3=| ii iv 8+ 877 9+9x5+3= =9x5 5 V 12+ 5 i 7+ 1/1 vi 20+ 20+1 5
8 In a bag of mixed fruits, are lemons, are strawberries and the rest are bananas.
7 Work out these additions and subtractions. Work method as in Questions 3 and 4. Use the same a 915 + 12 + 13 - Gir e 18342/5 + + 132934 b f j C 1515 2/5 g k 291427 + 1435 79 d h -
6 Work out these additions and subtractions. Use the same method as in Questions 1 and 2. a 117218 + 121415 e i + 38 b f j 2519 3 45 23 79 1819 13 g k d 4918 3/5 13341 + -
5 In a tennis club, - of the members are women, 2 of the members are men and the rest are children.5 What fraction of the members are children?
4 Work out each subtraction. Some working has been shown to help you. 1 1 1x7-1x2 7-2, a 2 7 C 27 2x7 3x7-2x5 = b 14 14 35 d 5 7 5x7 35 35 2 23 1 2x5-1x3 5 = 3x5 5 3 5x5-3x6 65 6x5 15 15
3 Work out each addition. has been shown to Some working help you. 1 1 1x5+1x2_5+2 1 1x7+1x3 + a b 25 2x5 10 10 3 7 3x7 21 21 2 1 2x4+1x3 + C + = d 3 4 3x4 12 21 12 1 3 1x5+3x6 + 65 + = 6x5
2 Work out each subtraction. Some working has been shown to help you. a C 91 26 91 13 6 1 39 = 23 b d 88 7 10 10 8-8-8-* 14 70 10 - 18 1 5 =
1 Work out each addition. Some working has been shown to help you. a 1 1 + 5 10 = 2 1 b + == + 10 10 10 9 1 8 3. C + = + 84 8 B-M + == 1 + = 12 4 12 12 12 d -
15 The diagram shows a triangle.a b C Work out the value of y when x=30 Work out the value of y when x=43 Explain why it is not possible for x to be 65. 1.0 x+ 23 +15
14 A straight line graph has the equation y = = x Copy and complete this table of values.a 80 24 6b Draw a coordinate grid going from 0 to 8 on the x-axis and on the y-axis.Plot the points from the table above. Draw the line y = x from x=0tox=8.
13 The answers to these three calculation cards are the first three terms in a sequence.Work out a b the first term of the sequence the term-to-term rule of the sequence C the next three terms in the sequence d the 10th term in the sequence. 2+ 27 12 3+ 31 11 5+ 69 7
12 Which of these two calculation cards gives the smaller answer?Explain how you made your decision. 13 13 A 32+ B 35+ 15 15
12 Which of these two calculation cards gives the smaller answer?Explain how you made your decision. A 32+ 13 B 13 35+ 15 15
11 Which of these two calculation cards gives the greater answer?Explain how you made your decision. A 25+ B 7 25+3 38
10 Jaq uses this formula in a science lesson. s=uxt a Work out the value of s when u and 1= 12. b Work out the value of 1 when s=22 and u 9
9 The area of a rectangle is 18 m2.The width of the rectangle is - m. 5 What is the length of the rectangle?Give your answer as a mixed number in its lowest terms.
8 Work out the answer to each calculation. Give each answer as a mixed number in its lowest terms. a 4+ b 3+2 9 10 10+ d 814 15
7 Work out the answer to each calculation.Use the reciprocal method.been started first two have for you. The a C 35 5 40 =8x 8+2=8 9+ 47 3 = w3 = 7+ 7-7-8-08 e 6+ 79 b d 12+1
6 Work out the answer to each calculation. Use the diagrams to help you. 2+1 a 2+ b 2+ C 3+ 23 25 34
5 This is what Sofia says about dividing an integer by a unit fraction.Use Sofia's method to work out The quick way to divide an integer by a unit fraction is to multiply the integer by the denominator of the fraction.
4 Work out the answer to each calculation. Draw diagrams to help if you want to. a 1+ 15 b 3+1 C 2+ 6 8
3 a Work out the answer to each calculation. Use the diagrams to help you.b Write the answers to ii 2+11
2 a Work out the answer to each calculation. Use the diagrams to help you.b Write the answers to i ii 2+ 3 iv
1 a out the answer to each calculation. Use the diagrams Work to help you.b Write the answers to i wwwww. 3+1 2+2 iv 4+1
15 a This is part of Helena's homework.Carry on with Helena's homework to find the correct value for .x. bb. y is an integer.Use the same method as Helena to work out the value of y when yx7=99 8 Question xx5=651 x is an integer. Work out the value of x when xx5 = 65 Answer Try x = =10 3 =50 + 4 =
14 The diagram shows a cuboid.The length, width and height of the cuboid are shown on the diagram.a Estimate the volume of the cuboid.b Raj works out that the volume of the cuboid is 210cm3.Is Raj correct? Show your working. cm 12cm 4cm
13 a Work out the value of each of these cards. Write each answer in its simplest form.b the median Write down value.c the range of the values. Work out 5 9x8- 6 6x113 4 12x7- 15
12 Work out a b an estimate for the area of the grey section of this rectangle the accurate area of the grey section of this rectangle. 95 58 m E 215 2m
11 Alec works in a factory. His job is to pack boxes. It takes him 3 minutes to pack one box. How long will it take him to pack 60 boxes? Give your answer in hours and minutes.
10 For each of these calculations, work out i an estimate ii the accurate answer.Write each answer in its simplest form.3.1×15 2 ×12 b6-×10 aC 84 12
9 Write these cards in order of size, starting with the smallest. A 8x4 B 12x3 C 5x7 6 55 7
8 Which is greater, 325 or 421?Show all your working.
7 Rose buys carpet for her bedroom floor. Rosa rectangle with length 42 m and floor is a width 3 m. The Rosa estimates that the area of her bedroom floor is 12 m2.Is Rosa correct? Explain your answer.b Work out the area of her bedroom floor.Rosa buys carpet that costs $15 per square metre.She can
6 The diagram shows a square joined to a rectangle. Show that the total area of the shape is 131 cm. 4
5 Copy and complete each multiplication. 31x7=3x7+1x7 + = +3 62x5=6x+2x5 8+0- 80+0- -08 b 4x9=4x9+x9 =+1 =+2 80- d 4x8+-x8 8+0- 80+0= -08
3 Copy and complete each multiplication..#!# 4 Archie uses this formula in a science lesson. F=mxa a Estimate the value of F when m=21 and a=3 3 When m=21 and a=32, Archie works out that F=77. bi ii Use your answer to part a to help you decide if Archie could be correct. Work out the value of F to
2 This rectangle has a length of 12m and a width of 2m.Work out a an estimate for the area of the rectangle b the accurate area of the rectangle. 12m 2 14 B
1 Copy and complete each multiplication. C a 26=26+16 +3 51x9=5x+19 + b 3x8=3x8+ x8 d = 4x1 x15
16 The diagram shows four mixed numbers linked by lines. a Work out the total of any two of the linked mixed numbers. b Without working out all the answers, explain how you can decide which two mixed numbers give the greatest total? What is this total? Write your answer in its simplest form.c Work
15 Read what Arun says.If I add together two mixed numbers, my answer will always be less than the sum of the whole-number parts plus 1.Use at least two counter-examples to show that Arun's statement is not true.
14 The area of this compound shape is 15 m. The area of one rectangle is 94m. a estimate, then b calculate the area of the other rectangle.
13 The diagram shows two statues. Each statue is made from three parts. The height of each part, in metres, is shown.a Which statue is taller? Show your working. b What is the difference in height between the two statues? A E 23 B m 34 4m 3 m 14 m m 100 88
12 This is part of Beth's homework. She has made a mistake in her solution.Question Work out 3 4 -1 3 a Explain the mistake Beth has made.b Work out the correct answer.
11 The table shows the distances that Nia drives on Monday to Friday one week.Nia works out that the range of the distances she travels is 9112 km. Is Nia correct? Explain your answer. 20 Show all your working. Day Monday Tuesday Wednesday Thursday Friday 1 Distance (km) 126 7 187 105 95- 157- 4 8
9 Work out these subtractions. Show all the steps in your working.10 Xao is a plumber.He has two pieces of pipe.The first piece is 32 m long; the second is 4m long. He fixes them together, as shown in the diagram. a i estimate, then ii calculate the total length of the two pipes. Xao wants a pipe
8 Copy and complete this subtraction. 81-32 Step 1: Step 3: 10 33 39 4 10 20 20 Step 2: 3339 4 10 20 20 20 20 20 20
7 Silvie has a piece of wood 4 m long. She wants to make some shelves. She cuts two pieces of wood, each 1 m long, from the piece she has. How long is the piece of wood Silvie has left? m 34 11 m m
6 Bim and Yolander have been out for a training run.Bim ran for 82 kilometres. Yolander ran for 102 kilometres.b calculate, the answers to these questions.estimate, then a What is the difference between the distances run by Bim and i Yolander?ii How far in total did Bim and Yolander run?
5 One of these cards gives a different answer to the other two.Which one is it? Show all your working. A 4 19 20 7 -2- B 10 514-33 15 5 C 54-3-5 7 52 21
4 Work out these subtractions. Show all the steps in your working. a 55 11 b 6 12 C 16 100-8 d 61-35
3 Copy and complete each subtraction. a 9 11 24 18 11 b 31-1/4 00 S 8 4 4 4 8 900 8 4 8 C 533-2300 d 6-200 00 28 5 10 56 3 6 10 10 10 666 =3 4. 10 10 6
2 Work out these subtractions. Show all the steps in your working. a 325 2 15 b C 11 3 27 d 3 20
1 Copy and complete the steps in each subtraction. e 23 3 4 b = 2102029 79696 3 6 P 5 --- 275 S 315 5 5 5 C - 7 7
14 Arun has three fraction cards. He puts them in order, starting with the smallest.810 36 Read what Arun says. 29 13 I think that on a 18 number line_29 is exactly halfway 36 8 between and 13 a Is Arun correct? Explain your answer. 9 18 b On a number line, work out which fraction is exactly
13 In a drugs trial, two different drugs are tested on some patients. 145 patients are given drug A, and it helps 112 of them. 180 patients are given drug B, and it helps 137 of them. Use a calculator to work out which drug helped the greater percentage of patients.
12 One day, a baker sells 87% of his loaves of bread. The following day, he sells 30 out of 34 loaves.Use a calculator to work out on which day he sold the greater percentage of bread loaves.
11 Write these fractions in order of size, starting with the smallest. 61 7 49 107 6 7 100 8 12
10 Two swimming clubs compare the percentage of girl members.In the Dolphins club, 42 out of 60 members are girls.In the Seals club, 68% of members are girls.Which club has the higher percentage of girl members?Show how you worked out your answer.
9 Three friends sat a Spanish test on the same day.Amina scored 18, Ben scored 37, and Cynthia scored 73%.25 50 Who had the highest percentage score?
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