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Maths Frameworking Teacher’s Pack 9.3 Homework ISBN 0 00 718814
Algebra 1 & 2CHAPTER
1
Teacher’s Pack 3 Homework
LESSON 1.1
LESSON 1.2
Ho
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rk 1 Write down the first four terms of each sequence whose nth term is given below.
a 3n + 1 b 4n – 2 c n2 + 7 d n(n + 3) e (n + 3)(n – 1)
2 Find the nth term of each of the following sequences.
a 5, 7, 9, 11, … b 2, 5, 8, 11, … c 1, 4, 9, 16, … d 3, 6, 11, 18, …
3 Find the nth term of each of the following sequences of fractions.
a 1–2, 2–3, 3–4, 4–5, … b 1–3, 2–5, 3–7, 4–9, …
4 Find the nth term of each of the following sequences.
a 3.5, 5, 6.5, 8, 9.5, … b 5.1, 7.2, 9.3, 11.4, … c 3.6, 6.1, 8.6, 11.1, …
Ho
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rk Look at the following diagrams.
a Before drawing a diagram, can you predict, from the table, the number of crosses which are inDiagram 4?
b Draw Diagram 4, and count the number of crosses there are. Were you right?c Now predict the number of crosses for Diagrams 5 and 6.d Check your results for part c by Drawing diagrams 5 and 6.e Write down the term-to-term rule for the sequence of crosses. (Hint 4 = 22, 8 = 23)
Diagram 1 2 3 4 5 6Crosses 1 5 13
321
LESSON 1.3
Ho
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rk 1 Write down the inverse of each of the following functions.x
a x → 3x b x → x + 8 c x → 6 + x d x → –– e x → 2x + 1 f x → 4x + 3 g x → 3x – 52
2 Write down two different types of inverse function and show that they are self inverse functions.
3 Write down the inverse of each of the following functions.(6 + x)
a x → 3(x + 5) b x → 1–2(x + 5) c x → ———4
4 a On a pair of axes, draw the graph of the function x → 2x + 3.b On the same pair of axes, draw the graph of the inverse of x → 2x + 3.c Comment on the symmetries of the graphs.
Maths Frameworking Teacher’s Pack 9.3 Homework ISBN 0 00 718814
LESSON 1.4H
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ork 1 Sketch graphs to show how the depth of water varies with time when water drips steadily into the
following containers.
2 Sketch distance–time graphs to illustrate each of the following situations.
a A car accelerating away from traffic lights.
b A train slowing down to a standstill in a railway station.
c A car travelling at a steady speed and then having to accelerate to overtake another vehiclebefore slowing down to travel at the same steady speed again.
3 Sketch a graph to show the depth of water in a bath where it is filled initially with just hot water,then the cold water is also turned on. After 2 minutes, a child gets into the bath, splashes about for5 minutes before getting out, and pulling out the plug. It takes 6 minutes for the water to drainaway.
a b c
LESSON 1.5
Ho
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rk 1 A sequence starting at 1 has the term-to-term rule Add 3 and divide by 2.
a Find the first 10 terms generated by this sequence.
b To what value does this sequence get closer and closer?
c Use the same term-to-term rule with different starting numbers. What do you notice?
2 Repeat Question 1, but change the term-to-term rule to Add 4 and divide by 2.
3 What would you expect the sequence to do if you used the term-to-term rule Add 7 and divide by 2?
4 What will the sequence get closer to using the term-to-term rule Add A and divide by 2?
5 Investigate the term-to-term rule Add A and divide by 3.
Number 1CHAPTER
2
Teacher’s Pack 3 Homework
LESSON 2.1
Ho
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rk 1 Convert each of the following pairs of fractions to equivalent fractions with a common denominator.Then work out each answer, cancelling down and/or writing as a mixed number if appropriate.
a 22–5 + 21–4 b 22–3 + 11–8 c 25–8 – 15––12 d 3 5––12 – 13–4
2 Work out each of the following. Cancel before multiplying when possible.
a 1–6 × 3–8 b 2–3 × 3–4 c 2–9 × 3––16 d 41–5 × 13–7 e 23–8 × 13–5
3 Work out each of the following. Cancel at the multiplication stage when possible.
a 1–4 ÷ 1–3 b 3––16 ÷ 9––14 c 1–6 ÷ 1–3 d 25–8 ÷ 7––16 e 23–5 ÷ 3––10
Maths Frameworking Teacher’s Pack 9.3 Homework ISBN 0 00 718814
Shape, Space and Measures 1CHAPTER
4
Teacher’s Pack 3 Homework
LESSON 4.1
Ho
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rk 1 Calculate the length of the hypotenuse in each of the following right-angled triangles. Give your answers to one decimal place.
2 Calculate the length of the unknown side in each of the following right-angled triangles. Give youranswers to one decimal place.
3 a Calculate x in the right-angled triangle shown on the right.
b Calculate the area of the triangle.
5 cm
14 cm
9.8 cm7.2 cm7 cm
12 cma
b
ca b c
2 cm 6 cm
16 cm
10 cm3 cm9 cm
a b
c
a b c
24 cm
25 cmx
LESSON 4.2
Ho
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rk 1 A plane flies due east for 120 km from airport A to airport B. It then flies due north for 280 km toairport C. Finally, it flies directly back to airport A. Calculate the direct distance from airport C toairport A. Give your answer to the nearest kilometre.
2 The length of a football pitch is 100 m and the width of the pitch is 80 m. Calculate the length of adiagonal of the pitch. Give your answer to the nearest metre.
3 The regulations for the safe use of ladders states: For a 6 m ladder, the foot of the ladder must beplaced between 1.5 m and 2.2 m from the building.
a What is the minimum height the ladder can safely reach up the side of a building?
b What is the maximum height the ladder can safely reach up the side of a building?
4 Calculate the area of an equilateral triangle whose side length is 10 cm. Give your answer to onedecimal place.
Maths Frameworking Teacher’s Pack 9.3 Homework ISBN 0 00 718814
LESSON 4.3H
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ork 1 Using a ruler and compasses, construct the locus which is
equidistant from the points A and B.
2 Using a ruler and compasses, construct the locus which is equidistantfrom the perpendicular lines AB and BC.
3 Draw a diagram to show the locus of a set of points which are 4 cm orless from a fixed point X.
4 Two alarm sensors, 6 m apart, are fitted to the side of a house, as shownbelow. The sensors can detect movement to a maximum distance of 5 m.
Draw a scale drawing to show the region that canbe detected by both sensors. Use a scale of 1 cmto 1 m.
A B5 cm
A
BC
5 cm
5 cm
6 m
LESSON 4.4
Ho
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rk 1 Show that each of the following pairs of triangles are congruent. Give reasons for your answers andstate which condition of congruence you are using.
a b
c d
2 ABCD is a rectangle and E is the mid-point of AB.
Maths Frameworking Teacher’s Pack 9.3 Homework ISBN 0 00 718814
LESSON 4.5H
om
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ork 1 Calculate the size of the lettered angle in each of the following diagrams.
2 Use Pythagoras’ theorem to calculate the length x in each of the following diagrams. Give youranswers to one decimal place.
3 A circle passes through the three points A, B and C. On a copy of the diagram, construct the circle, using a ruler and compasses.
a b
7 cm
18 cm
20 cm
14 cm
xx
O•O
O
O
O•O
OO
43°
122°
56°
61°
38°
110°a
d
e f
b
c
a b c
d e f
A
B
C
c
3 cm 3 cm
3 cmx
Od
8.5 cm10 cm
x •O
LESSON 4.6
Ho
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rk 1 Work out, by making templates or by drawing diagrams, which of the following regular polygonstessellate, and which do not. In each case, write down a reason for your answer.
a Equilateral triangle b Square c Regular pentagon d Regular hexagon e Regular octagon
2 Draw a diagram to show how squares and equilateral triangles together form a tessellating pattern.
Maths Frameworking Teacher’s Pack 9.3 Homework ISBN 0 00 718814
LESSON 4.7H
om
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ork Practical demonstration with a difference
Cut out an 8 cm by 8 cm square and then cut it up Now rearrange the four pieces to make a into two right-angled triangles and two trapezia, rectangle, as in the diagram below.as in the diagram below.
What is the area of the square and of the rectangle?
Can you explain why this practical demonstration does not work?
5 cm3 cm
3 cm5 cm
5 cm
3 cm
Handling Data 1CHAPTER
5
Teacher’s Pack 3 Homework
LESSON 5.1
Ho
me
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rk Take a different topic to those already studied and prepare a new planning sheet.
LESSON 5.2
Ho
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rk 1 The test results of ten students are recorded for four different subjects. Here are the results.
a Plot the data for French and Spanish on a scatter graph.b Describe the relationship between French and Spanish.c Plot the data for English and Music on a scatter graph.d Describe the relationship between English and Music.e Plot the data for Spanish and English on a scatter graph.f Describe the relationship between Spanish and English.g Use your answers to parts d and f to state the correlation between Music and Spanish.
Student A B C D E F G H I JMusic 35 48 72 23 76 51 45 60 88 17Maths 42 57 80 32 65 69 50 71 94 25
LESSON 5.4
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Write a brief report on the similarities and differences between the visits from the UK for NorthAmerica and Western Europe. Make at least three statements. Try to give reasons for your answers.
Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov
Maths Frameworking Teacher’s Pack 9.3 Homework ISBN 0 00 718814
LESSON 6.4H
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In this exercise take π= 3.142 or use the key on your calculator.
1 Calculate the volume of each of the following cylinders. Give your answers correct to threesignificant figures.
2 The diagram below shows a metal pipe of length 1 m. It has an internal diameter of 2.8 cm, and anexternal diameter of 3.2 cm. Calculate the volume of metal in the pipe. Give your answer correct tothe nearest cubic centimetre.
3 A cylindrical can holds 2 litres of oil. If the height of the can is 25 cm, calculate the radius of thebase of the can. Give your answer correct to one decimal place.
3.2 cm
2.8 cm
1 m
3 cm
12 cm
5 cm
2 cm4 m
8 ma b c
π
LESSON 6.5
Ho
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rk 1 Find the distance travelled by a hiker who walks for 3 hours at an average speed of 2.5 mph.
2 Find the time taken to drive a car 125 km at an average speed of 75 km/h.
3 A runner runs a 1000 m race in 3 minutes 20 seconds. Find his average speed in m/s.
4 Find the density of a gold ingot that has a mass of 4825 g and a volume of 250 cm3.
5 The density of sea water is 1.05 g/cm3. If a bucket with a capacity of 5 litres is filled with seawater,find the mass of the water in the bucket. Give your answer in kilograms.
6 The density of cork is 0.25 g/cm3. Find the volume of a block of cork that has a mass of 120 g.
Maths Frameworking Teacher’s Pack 9.3 Homework ISBN 0 00 718814
LESSON 8.3H
om
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ork 1 A sledge sliding down a slope has travelled a distance, d metres, in time, t seconds, where
d = 5t + t2.
a Draw a graph to show the distance covered up to 6 seconds.
b Find the distance travelled after 3.8 seconds.
c Find the time taken to travel 50 metres.
2 The cost, C pence, for plating knives of length L cm is given by the formula C = 50L + 7L2.
a Draw a graph to show the cost of plating knives up to 10 cm long.
b What would be the cost of plating a knife 8.7 cm long?
c What would be the length of a knife costing £4 to plate?
LESSON 8.4
Ho
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rk 1 By drawing suitable graphs, solve this pair of simultaneous equations:
2x + y = 5 y = x3 – 1There is only one solution.
2 The distance, d metres, a rocket is above the ground is given by
d = 2t + t3
where t is the time in seconds.
Draw the distance–time graph for the first 3 seconds.
Handling Data 2CHAPTER
9
Teacher’s Pack 3 Homework
LESSON 9.1
Ho
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rk 1 Write down a reason why each of these statements is incorrect. a A bag contains black and white cubes, so there is a 50% chance of picking a black cube.b A bag contains black and white cubes. Last time I picked out a black cube, so this time I will pick
out a white cube.c A bag contains one black cube and many white cubes. So, I have no chance of picking out the
black cube.
2 Here are three different bags of cubes.A There are four black cubes and four white cubes in the bag.B There are two black cubes and five white cubes in the bag.C There are seven black cubes and five white cubes in the bag.
Here are three statements about the bags of cubes.X There is a probability of 2–5 that I will pick a black cube.Y There is an even chance that I will pick a black cube.Z There is a probability of 5––12 that I will pick a white cube.
For each bag, say whether the statements are correct or incorrect.
Maths Frameworking Teacher’s Pack 9.3 Homework ISBN 0 00 718814
LESSON 9.2H
om
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ork 1 Ten pictures are shown, which are all face down. A picture is picked at random.
a What is the probability of choosing a picture of a guitar?
b What is the probability of choosing a picture of a guitar or a boat?
c What is the probability of choosing a picture of a horse or a doll?
d What is the probability of choosing a picture which is not of a boat?
2 A bag contains a large number of discs, each labelled either A, B, C or D. The probabilities that a disc picked at random will have a given letter are shown below.
P(A) = 0.2 P(B) = 0.4 P(C) = 0.15 P(D) = ?
a What is the probability of choosing a disc with a letter D on it?
b What is the probability of choosing a disc with a letter A or B on it?
c What is the probability of choosing a disc which does not have the letter C on it?
LESSON 9.3
Ho
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rk 1 A builder is working on a patio. The probability that the weather is fine is 0.6, and the probabilitythat he has all the materials is 0.9. To complete the job in a day, he needs the weather to be fineand to have all the materials.a Draw a tree diagram to show all the possibilities.b Calculate the probability that he completes the job in a day.c Calculate the probability that it is not fine and he does not have all the materials.
2 A game is played three times. The probability of winning each time is 1–2.a Show that the probability of winning all three games is 1–8.b What is the probability of winning exactly one game?
Maths Frameworking Teacher’s Pack 9.3 Homework ISBN 0 00 718814
LESSON 9.4H
om
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ork A spinner has different coloured sectors. It is spun 100 times and the number of times it lands on blue
is recorded at regular intervals. The results are shown in the table.
a Copy and complete the table.b What is the best estimate of the probability of landing on blue?c How many times would you expect the spinner to land on blue in 2000 spins?d If there are two sectors of the spinner coloured blue, how many sectors do you think there are
altogether? Explain your answer.
Number of spins 20 40 60 80 100
Number of times lands on blue 6 10 15 22 26
Relative frequency 0.3
Shape, Space and Measures 3CHAPTER
10
Teacher’s Pack 3 Homework
LESSON 10.1
Ho
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rk 1 Draw copies of (or trace) each of the following 2 Copy the diagram below onto a coordinate shapes. Enlarge each one by the given scale grid and enlarge the triangle by scale factor 11–2factor about the centre of enlargement O. about the origin (0, 0).
Maths Frameworking Teacher’s Pack 9.3 Homework ISBN 0 00 718814
LESSON 10.4H
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ork 1 The stays on a flagpole are 10 m long and make an angle of 65°
with the horizontal ground. Calculate the height of the flagpole.
2 The diagram on the right shows a ramp for wheelchairs. Calculate the angle the ramp makes with the ground.
3 A helicopter takes off from an army base on a bearing of 075° and flies for 52 km.
a How far east has the helicopter flown?
b How far north has the helicopter flown?
4 A plane takes off from an airport, climbing at a constant angle. When the plane has flown for 3.2 km, it reaches an altitude of 1000 m. Calculate the angle at which the plane is climbing.
5 The diagram on the right shows a wooden truss of a roof. Calculate the height, h, of the roof.
10 m
65°
1.3 m
25 cm
9.8 m
h25° 25°
Algebra 5CHAPTER
11
Teacher’s Pack 3 Homework
LESSON 11.1
Ho
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rk 1 Expand each of the following.
a x(3x + 4) b t(3t – 1) c m(4m – 3) d y(5y + 3)
e m(5 – 4m) f k(1 + 6k) g t(3 – 4t) h x(2 + 5x)
2 Expand and simplify each of the following.
a 3(m + 2) + 2(1 – 3m) b 4(2k + 3) + 2(1 – 3k)
c 5(3x – 2) + 3(2 – 4x) d 4(5x + 2) + 5(1 – 5x)
3 Write down the missing lengths in each of the following rectangles.
Maths Frameworking Teacher’s Pack 9.3 Homework ISBN 0 00 718814
LESSON 12.6H
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ork 1
1 When two dice are rolled the probability of a double one is —–.36
a When two dice are rolled what is the probability of a double 2?
b Which answer shows the probability of a treble six when three dice are rolled.
1 1 3 1— —— —— —18 216 216 42
2 The bar chart shows the distances that 50 students threw a discus.
a What is the probability that a pupil chosen at random will have thrown the discus more than 30 metres?
b What is the probability that a pupil chosen at random will have thrown the discus more than 45 metres?
c Work out the mean length of throw for the 50 pupils.
00
5
10
15
10 20Distance (m)
Num
ber
of p
upils
30 40 50
6
10
14
11 9
Handling Data 3CHAPTER
13
Teacher’s Pack 3 Homework
LESSON 13.1
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rk 1 The weights (in kg) of 24 men are given below. a Use the data to copy and complete the frequency table.
b In which class is the median weight?c Complete a table of cumulative frequencies,
draw the cumulative frequency graph and use it to calculate the median and interquartile range.
d Explain why these weights are not representative of the whole adult population.2 These tables show the average monthly temperatures for Paris and Madrid over the course of one year.
Paris
Madrid
a Draw suitable graphs to represent both sets of data.b Comment on the differences between the average monthly temperatures in Paris and Madrid.
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec°C 5.3 6.7 9.7 12.0 16.1 20.8 24.6 23.9 20.5 14.7 9.3 6.0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec°C 3.7 3.7 7.3 9.7 13.7 16.5 19.0 18.7 16.1 12.5 7.3 5.2
Maths Frameworking Teacher’s Pack 9.3 Homework ISBN 0 00 718814
LESSON 13.2H
om
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ork Choose one of the following tasks.
1 Complete the investigation started in the lesson by writing up the report.
2 Collect data in order to investigate the pop singers example.
3 Carry out and write up a detailed investigation of your own choice.
Shape, Space and Measures 4CHAPTER
14
Teacher’s Pack 3 Homework
LESSON 14.1
Ho
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rk 1 Find the area of each of the following shapes.
a b c d
2 Calculate i the circumference and ii the area of each of the following circles. Take π= 3.14 or usethe key on your calculator. Give your answers to one decimal place.