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Cambridge Lower Secondary Mathematics Workbook 8 2nd Edition Lynn Byrd, Greg Byrd, Chris Pearce - Solutions
10 Read what Zara says. I worked out on my calculator that 7+9=0.7777777778. This means that seven ninths is not a recurring decimal as the sevens don't go on for ever: there's an eight on the end.
9 This is part of Su's homework.a Use a calculator to check Su's homework.b Explain any mistakes she has made and write the correct answers. Question Write these fractions as decimals. 7 i 24 Answer 8 11 11 3 18 589 39 7 8 i = 0.2916 = 0.72 11 -0.16 w 5 = 0.1282051 24 11 18 39
8 Use a calculator to convert these fractions to decimals. a 69 b 52 13 =2
7 Use a calculator to convert each fraction to a decimal. a 68 b 4 15 12 28 29 P
6 Read what Marcus says:Is Marcus correct? Explain your answer. I know that and are recurring decimals. This means that any fraction with a denominator of 6 is also a recurring decimal.
5 Here are five fraction cards.5 15 48 AB CD E9 312 15 a Without doing any calculations, do you think these fractions are terminating or recurring decimals? Explain why.b Use a written method to convert each fraction to a decimal.c Write the fractions in order of size, starting with the smallest.
4 Here are five fraction cards.7 33 48 AB CD E8 510 20 25 a Without doing any calculations, do you think these fractions are terminating or recurring decimals? Explain why.b Use a written method to convert each fraction to a decimal.c Write the fractions in order of size, starting with the
3 Use your answers to Question 2 to write these fractions in order of size, starting with the smallest.7334 2 10 5 8 9 11
2 Copy and complete the workings to convert each fraction into a decimal. Write if the fraction is a terminating or recurring decimal. The first two have been done for you. a C e g i 2 25 34 50 6 70 10 0 52 25 =0.4 . 4 20 terminating decimal 0. 43 0 65 0 83 0 . . . . 30 0 50 0 30 0 10 7 70 0 . b d
1 Match each unit fraction with the correct equivalent decimal.Write if the fraction is a terminating decimal or a recurring decimal.One is done for you: 1=0.16, recurring decimal 61 1=14 1I 11 11 23 56 78 910 0.16 0.25 0.3 0.142857 0.5 0.2 0.1 0.1 0.125
8 Here is a question: How many questions are there in the exercises in this book? It would take a long time to look at every exercise in the book. Instead, you can answer this question by looking at a sample of exercises. Here are two ways of choosing a sample. a b C Look at all the exercises in
7 One way to choose a sample is to call people on the telephone and ask them to complete a questionnaire. a C How can you make sure you get a representative sample? Describe an advantage of this method. Describe a disadvantage of this method.
6 The guests at two hotels are asked to give a score for quality of service, on a scale of 1 to 5. 1 is poor and 5 is excellent. This chart shows the results.Here is a conjecture: Hotel A provides better service than hotel B.a Does the data support the conjecture? Give a reason for a your answer.b
5 The owner wants to give a survey to a sample of 50 customers. The owner says, 'I will interview all the customers who come to the coffee shop between 10:00 and 12:00 tomorrow morning." Write one disadvantage of this method of choosing a sample. Describe a better way to choose a sample. Justify
3 A supermarket has a car park. Here is a conjecture: Cars park for longer in the morning than in the afternoon. This chart shows the results of a survey of the parking time for 100 cars in the morning and 100 cars in the afternoon. The survey was done on a Tuesday.a Does the data support the
2 Zara wants to give a questionnaire to 100 people who travel on a bus route.a Describe an advantage of this method. Describe b Describe two disadvantages of this method. Describe C Describe a method that overcomes the disadvantages you identified in part b.d Describe one disadvantage of your
1 There are 850 students in a college. a Describe three ways to choose a sample of 40 students. Give an advantage and a disadvantage of each method.
9 Arm span is the distance between your fingertips when you spread your arms. The femur is the bone in your thigh.Here are two statements. A person's arm span and height are roughly the same length. The length of a person's femur is about one-quarter of their height. You are going to test these
8 Here is a statistical question: Do books for children have shorter sentences than books for adults? To answer this question, you are going to collect some data. a What data do you need to collect? b Describe a method of choosing a sample of sentences from a book. C Choose a book and try your
7 You want to answer this question.Are words in other languages longer than words in English?You can choose a language to test.What data do you need to collect to answer this question?How can you collect the data you need?Test your data collection method on a small sample.Was your data collection
6 Sudoku is a popular puzzle. Here are two questions: Are girls better than boys at Sudoku? Are 11-year-olds better than 14-year-olds at Sudoku? a What data do you need to collect to answer these questions? b How can you collect the data you need?
5 It is healthy to eat vegetables. Look at these statements.a What data do you need to answer these questions? b How can you collect the data you need? Do girls eat more vegetables than boys? Do older children eat more vegetables than younger children?
4 Here are three questions about customers at a large hotel.Why do people choose this hotel?What are they here for?How long do they stay?What data do you need to collect to answer these questions?How can you collect the data you need?
3 When babies are born, their gender, length and mass are recorded. a What type of data is this? b Write three statistical questions you could answer using C this data. How could you choose a sample of babies to collect data to answer your questions?
2 Here are two questions about homework. a discrete data How much homework do learners do each night? On which subject do learners spend most time? What data do you need to collect to answer these questions? b You decide to collect data from a sample of learners in your school. How will you choose
1 Your school has a record of personal data about you. Suggest a piece of information that might be in your record that is a C categorical data continuous data. b
11 Show all your construction lines in this question.a Make an accurate drawing of triangle ABC.b Draw the bisector of angle A.c The bisector of angle A meets BC at D. Measure BD.d Draw another copy of triangle ABC.e The perpendicular bisector of AB meets BC at E.Find the length of BE. A B 14cm C
10 Use compasses and a ruler for this question. Leave your construction lines on your drawing. a b C Make an accurate drawing of triangle XYZ. Draw the bisector of angle X. The bisector at angle X meets YZ at W. Mark W on your drawing and measure YW. 8.5cm Y 9.5cm X 10cm Z
9 Draw triangle ABC.Use compasses to draw the perpendicular bisector of BC.Show your construction lines on your drawing.Check the accuracy of your drawing with a protractor and a ruler. 8.4cm A B 70 5.7 cm C
8 a Draw a triangle with side lengths 8.4cm, 10.5cm and 6.3 cm.b This should be a right-angled triangle. Use this fact to check the accuracy of your drawing.
7 a Make an accurate copy of this shape.b The length BD should be 19.0cm. Use this fact to check the accuracy of your drawing.
6 The two shorter sides of a right-angled triangle are 9cm a and 6cm.i Draw the triangle.ii Measure the hypotenuse.b The hypotenuse of a right-angled triangle is 9cm and another side is 6cm.i Draw the triangle.ii Measure the third side.
5 a Draw a triangle with side lengths 10.5cm, 7.5 cm and 6.5cm.b Measure the largest angle of the triangle.
4 a Draw a triangle where two angles are 85° and 50° and the side a triangle where Draw between them is 9.2cm.b Measure the longest side of the triangle.
3 a Construct triangle ABC.b Measure angle B.c Measure BC. A 8.3 cm 57 C 10.5cm B
2 a Construct this triangle.b Measure the shortest side. 45 12cm 35
1 a Construct this triangle. b Measure the length of the third side. 6.5cm/ 60 8cm
11 a The exterior angles of a triangle are 105°, 115° and 140°.Calculate the three interior angles of the triangle.b Zara draws a different triangle.Look at what Zara says:Show that this is impossible. I have drawn a triangle. The exterior angles are 100, 120 and 130.
10 a Work out angle a.b Show that x + y = 270 155 D
9 Calculate the values ofa, b and c.Give a reason for each answer. 110 40 15 15 80 60 Co
8 Explain why x + y + z = 360. 130 Do
7 ABCD is a four-sided shape but two of the sides cross.Explain why the sum of the angles at A, B, C and a D must be less than 360°.b Find the sum of the angles at A, B, C and D.Give a reason for your answer. D A 120 C B
6 Use exterior angles to show that the angle sum of quadrilateral PQRS is 360°.
5 Show that the interior angles of this shape add up to 360.
4 Work out angles a and b. b 40%40 150
3 Find the values of x and y. 65 140 100
2 One of the exterior angles of an isosceles triangle is 30. How big are the other two exterior angles?
1 How big is each exterior angle of an equilateral triangle?
13 A. B. C and D are the four angles of a parallelogram.Show that angle A = angle C.Show that angle B = angle D. D < C B
12 Look at the diagram.Copy and complete the explanation that the angle triangle ABC is 180º. sum of Write the reason for each line1) Angle A of the triangle = angle PCA 2) Angle B of the triangle = angle QCB 3) Angle PCA + angle C of the triangle + angle QCB=180 Hence angle A + angle B + angle C
11 Use this diagram to show that the angle sum of triangle XYZ is 180.
10 Explain why the sum of a and b must be 180. 60
9 Are lines, and parallel? Give a reason for your answer. 75 50 125
6 Explain why only two of the lines /, m and n are parallel.
5 a Complete these sentences. i Two alternate angles are ABG ii and. Another two alternate angles are C CBE and iii Two corresponding angles are GEF and. b Read what Sofia says:Is Sofia correct? Explain your answer. HBC and DEG are alternate angles.
4 Look at the diagram. a b Which angles are 68 because they are corresponding angles? Which angles are 68 because they are alternate angles?
3 Find the values ofa, b, c and d.Give a reason for each angle. 75
2 a Look at this diagram. State why x and y are equal. Copy the diagram. b Mark all the angles that are corresponding to .x. Mark, in a different way, all the angles that are alternate to y.
1 Explain why vertically opposite angles are equal.
17 Here are four formula cards. Use the cards to work out the value of e when a=425 (d-28)0.03 0.4 d=cx0.45 c=4x(b+33)2.5 b=ax0.12
16 Work out using the factor method. a 3500.16 (use 0.16=0.20.8) b 1300.21 (use 0.21=0.3 0.7)
15 A formula used in science is a F=ma 9.9 m Work out the value of F when m=26 and a=0.45 b Work out the value of m when F-20.8 and a=0.4
14 The diagram shows a square of side length 9.9m. Work out a the perimeter of the square b the area of the square.
13 A formula used in maths is a S= Work out the value of S when a = 5.6 and r=0.6 b Work out the value of a when S=36 and r=0.8
12 Work out. Use the same method as in Question 4. a 700.15 Challenge
11 Work out. Look for different ways to make the calculations easier. a 2.526.54 0.41.6 C 0.1 e (280+170) 0.3 b 863.42.5 d 0.6x4.21 0.1 f (980-580) 0.03 b 124 0.35
10 The diagram shows an equilateral triangle of side length 9.9 m. The formula for the perimeter of an equilateral triangle is perimeter = 3x side length Work out the perimeter of the equilateral triangle.
9 The diagram shows a square of side length 0.99 m. The formula for the perimeter of a square is perimeter = 4x side length Work out the perimeter of the square.
8 Work out a 489.9 1.29.9 b 480.99 d 1.20.99
7 The diagram shows a rectangle. The width is 0.9m and the length is 8.7m. Work out the area of the rectangle.
6 Work out. Use the same method as in Question 2. a 160.9 b 360.9 C 5.20.9
5 Work out. Use the same method as in Question 1. (0.5+0.1)0.4 (0.9-0.3)1.1 b d (0.3+0.5)0.7 (1.7-1.3)x1.2
4 Complete the workings. Use factors to make these calculations easier. a 16x0.35 = 16x0.5x0.7 =80.7 == x7+10 -10 180.15 = 180.50.3 = x0.3 x3+10 10 b 120.45 = 12x0.5x0.9 x0.9 9+10 +10 d 26x0.35 =260.5 0.7 x0.7 x7 10 +10
3 Work out the answers to these calculations. Look for different ways to make the calculations easier. They have all been started for you. a 2.55.7x4 b 2.524.14 2.54=10 105.7= 2.5x4= 24.1= 0.3x1.3 C 8 x 1.2 2.5 0.1 8x2.5=20 0.3 20 x 1.2 2x10 1.2 =0.3 x 10= 0.1 =212 1.3=[ e (42+18)0.8 f (23+27) 0.7
2 Copy and complete the workings to make these calculations easier. All the missing numbers are in the trapezium. a 600.9 =60x (1-0.1) =60x1-60 x 0.1 =60-6 180.9 =18(1-0.1) = 181-180.1 b 21.6 1.8 42 420.9 =42x(1-0.1) 37.8 54 24 =42x1-420.1 2.4 4.2 18 16.2 d 240.9 = 24(10.1) =24x1-240.1
1 Copy and complete the workings for these questions. All the answers are in the rectangle. 0.54 a (0.2+0.1)0.4 x0.4 b (0.9-0.7)0.3 0.06 x0.3 0.16 0.12 (0.4+0.5)0.6 d (0.8-0.6)0.8 x0.6 x0.8
15 Carlos makes this number sequence, but he has spilled tea on his work. This is my number sequence: 1st term 2nd term 3rd term 4th term 7.2 8.64 My term-to-term rule is: multiply by Carlos thinks the term-to-term rule is multiply by 0.8. a Is Carlos correct? Explain your answer. b Work out the
14 The diagram shows a compound shape.xm 2.7 m arca = 8:58 m3 1.4 m 3.9 m The area of the shape is 8.58 m2 Work out the length xm.Explain how you worked out your answer.Show all your working.
13 The diagram shows a triangle with an area of 8.84m2.height arca = 8.84 mª5.2 m The base length of the triangle is 5.2m.Meghan works out that the height of the triangle is 3.64 m.a Show that Meghan is wrong.b Work out the correct height of the triangle Show all your working.
12 Work out. Give each answer to the degree of accuracy shown. b 76.94 1.3 (2 d.p.) a 2.97 0.7 (1 d.p.) -5479 1.8 (3 d.p.)
11 Work with a partner to answer this question. a Elin works out that 654 32=20928 Use Elin's calculation to work out i 2092832 iii 209283.2 ii 20928-654 iv 2092865.4 b Explain the method you used to work out the answers to parta. i d Use Elin's calculation to work out 2092.8+3.2 iii 20.928 +3.2 ii
10 a Complete the table below showing the 19 times table. b C 12 23456 19 38 57 Ana buys a piece of metal for $47.12. The piece of metal is 1.9m long. Work out the cost per metre of the metal. 7 Show how to check your answer to part b is correct. Use estimation and a reverse calculation.
9 Complete the table below showing the 13 times table. 2 3 4 5 6 7 8 9 13 26 39 b Use the table to help you work out 75.53+1.3 Show how to check your answer to part b is correct. Use estimation and a reverse calculation.
8 For each division, work out CL 1estimate of the answer an the accurate answer.-936-0.4 49.5-0.3 ba 11.5-0.5-351-0.6 56.94-0.7-3808-0.8
7 Harry pays $2.58 for a piece of ribbon 0.6m long. Harry uses this formula to work out the cost of the ribbon per metre. price of piece cost per metre length of piece What is the cost of the ribbon per metre?
6 Work out a 0.78+0.3 b 6.56+0.4 C -984-0.8 d -189-0.7
5 Which of these calculation cards is the odd one out? Explain why. A 60+0.5 B 24+0.2 C 44+0.4 D 12+0.1 E 36-0.3
4 This is part of Mia's homework. Mia has made a mistake in her solution. a Explain the mistake she has made. b Work out the correct answer. Question Work out 40 +0.5 Answer 40 40+0.5- 0.5 40 40 -8 0.510 5
3 Copy and complete these divisions. 210 v 5 2004- 0.4 0410 b 3+0.5- 3 310 0.5 0.510 c -6+0.2= -6x10 0.210 d -4+0.8 -4x10 0.8 0.810
2 Match each grey card with the correct white answer card. A 1.8+0.2 i 7 B 2.1+0.3 C 2.5 0.5 !!! D 2.4+0.6 iv 8 3 E 7.2+0.
1 Copy and complete these divisions. a 1.6+0.4- 1.6 1.610 0.4 0.4x10 4.5 b 4.5+0.9 4.510 0.9 0.910-24 -24x10 -24+0.3- 0.3 0.310 d-21+0.7--21 -21x10 0.7 0710
16 The formula to convert a temperature in degrees Centigrade (C) to degrees Fahrenheit (F) is F=Cx1.8+32 a Work out F when b i C=-15 Read what Marcus says. C=-20 Is Marcus correct? Explain your answer.
15 Jay is mixing concrete. She has 32.5 kg of concrete. She uses an additive to make the concrete waterproof. The instructions for the concrete mixture are: a b Mix 0.03 litres of additive with 1 kg concrete. Work out an estimate of the volume of additive, in litres, that Jay needs Calculate the
14 A chainsaw uses petrol and oil. The instructions for the chainsaw are: b Mix 31.25ml of oil with 1 litre of petrol. Work out an estimate of the volume of oil (mL) that are needed to mix with 2.4 litres of petrol. Calculate the accurate volume of oil (mL) that is needed to mix with 2.4 litres of
13 This is part of Tom's homework. b 0.244.5 d 0.610.742 Question Work out a 0.23x6.9 b 820.003 c 0.078x0.005 Answers a 1.587 b 0.0246 0.0039 Use estimation to check if Tom's answers could be correct. If you think they are incorrect, explain why.Use estimation to check if Tom's answers could be
12 Work out these multiplications. Show how to check your answers. a 7.2 x 8.3 0.876.35
11 a Work out 234 56 b Use your answer to part a to write the answers to these calculations i 23.456 iii 23.45.6 23.4x0.56 ii 2345.6 iv 2.345.6 vi 2.340.056
10 a Sort these cards into groups of equal value. You should have one card left over. A 0.040.03 B 0.80.02 b C 0.030,06 D 0.0020.9 E 0.001 16 F 0.050.4 G 0.6x0.002 H 0.0120.1 0.04x0,4 J 0.180.01 Write a different card that could go in the same group as the card that is left over.
9 Copy and complete these patterns. i 33-9 ii 47=28 0.33-[ 0,30,3- 0.3x0.03 0.3 0.003 b Work out i 0.10.05 0.40.07= 0.4x0.007- ii 0.4x0.6 0.47 [ 0.4x0.7- iii 0.080.3 iv 0.020.08 V 0.120.4 vi 0.040.15
8 Here are five calculation cards. A -240.52 B 0.07x-180 C 0.03x-430 D-200.65 E 0.9-15 a Work out the answer to each calculation. b Write the answers in order of size, starting with the smallest.
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