CHAPTER 1 Algebra 1 & 2 - Kineton Maths Departmentkinetonmathsdepartment.weebly.com/uploads/5/5/2/7/55272917/book_… · Algebra 1 & 2 CHAPTER 1 Teacher’s Pack 3 Homework LESSON

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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.

2 www.CollinsEducation.com © HarperCollinsPublishers Ltd 2003


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

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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


LESSON 2.1

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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



LESSON 2.2H

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ork 1 How much would you have in the bank if you invest as follows?

a £450 at 3% interest per annum for 4 years.

b £6000 at 4.5% interest per annum for 7 years.

2 Stocks and shares can decrease in value as well as increase. How much would your stocks andshares be worth if you had invested as follows?

a £1000, which lost 14% each year for 3 years.

b £750, which lost 5.2% each year for 5 years.

LESSON 2.3

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rk 1 A packet of biscuits claims to be 24% bigger! It now contains 26 biscuits. How many did it havebefore the increase?

2 After a 10% price decrease, a hi-fi system now costs £288. How much was it before the decrease?

3 This table shows the cost of some items after 171–2% VAT has been added. Work out the cost of eachitem before VAT.

4 A pair of designer jeans is on sale at £96, which is 60% of its original price. What was the originalprice?

5 A pair of boots, originally priced at £60, were reduced to £36 in a sale. What was the percentagereduction in the price of the boots?

Item Cost inc VAT Item Cost inc VAT

Radio £112.80 Cooker £329

Table £131.60 Bed £376

Ho

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rk 1 In 4 hours a man earns £45. How much does he earn in 5 hours?

2 A man walking one dog takes 20 minutes to walk one mile. How long will it take him to cover onemile if he walks two dogs?

3 In a week, grass grows 21 mm. How much does it grow in 4 days?

4 Fifty litres of petrol costs £35. How much will 20 litres of petrol cost?

5 Eight men dig a ditch in 9 days. How long would six men take?

6 A camping party of three has enough food to last them 4 days. If another person joins the party, howlong will the food last?

7 At £6 an hour, Jack takes 16 hours to earn enough for a guitar. If he had earned £8 an hour, howlong would it have taken him to earn the money?

8 Three bell ringers ring a tune on 6 bells in 5 minutes. How long would four bell ringers take to ringthe same tune?

LESSON 2.4



LESSON 2.5H

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ork 1 Two similar, plane shapes, A and B, have lengths in the ratio 1 : 4. The area of shape A is 10 cm2.

What is the area of shape B?

2 Two similar, plane shapes, P and Q, have lengths in the ratio 1 : 2. The area of shape Q is 100 cm2.

What is the area of shape P?

3 Two similar solids, C and D, have lengths in the ratio 1 : 3. The volume of solid C is 15 cm3.

What is the volume of solid D?

4 Two similar solids, R and S, have lengths in the ratio 1 : 2. The volume of solid S is 72 cm3.

What is the volume of solid R?

LESSON 2.6

Ho

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rk Say which of these statements is true. If it is not true, give a counter-example.

a The square of a number between 0 and 1 is also between 0 and 1.

b The square of a number between 0 and –1 is also between 0 and –1.

c Dividing any number by a number between 0 and 1 always gives a bigger answer.

d Dividing any positive number by a number between 0 and 1 always gives a bigger answer.

LESSON 2.7

Ho

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rk 1 a Find, as decimals, the reciprocals of all the integers from 21 to 25.

b Which of the reciprocals are recurring decimals?

2 Find the reciprocals of each of the following numbers. Round your answers if necessary.

a 50 b 0.004 c 60 d 0.625

LESSON 2.8

Ho

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rk 1 By rounding each value to one significant figure, estimate the answer to each of the following.

a 0.83 × 793 b 618 ÷ 0.32 c 812 ÷ 0.38

d 0.78 × 0.049 e (38 × 3.2) ÷ 0.487 f (2.7 + 6.3) × (0.52 – 0.17)



Algebra 3CHAPTER

3


LESSON 3.1

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rk 1 4x + y = 14 2 6x + 3y = 33 3 3x + y = 10

2x + y = 8 2x + 3y = 21 8x – y = 1

4 5x + 2y = 22 5 5x – 4y = 36 6 5x + 3y = 50

7x – 2y = 2 2x – 4y = 6 9x – 3y = 48

LESSON 3.2

Ho

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rk 1 3x + y = 8 2 6x + 4y = 36 3 5x + 2y = 47

2x + 5y = 27 2x + y = 11 3x – y = 26

4 3x + y = 24 5 7x – 4y = 16 6 8x – 4y = 36

5x + 2y = 41 x – y = 1 x + 3y = 8

LESSON 3.3

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rk 1 Find the first five terms of each of the following sequences given by:

a T(n) = n2 + 7n – 3 b T(n) = 5n2 + 3n + 1 c T(n) = 6n2 – 5n

2 Find the nth term for each of the following quadratic sequences.

a 13, 25, 41, 61, 85 b 12, 18, 26, 36, 48 c 7, 14, 27, 46, 71

d 1–3, 2–7, 3––13, 4––21, 5––31 e 1–9, 4––18, 9––31, 16––48, 25––69 f 12––21, 25––46, 44––83, 69—–132, 100—–193

LESSON 3.4

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rk 1 Solve each of the following equations.

3x 3t 6m 2x 2wa —– = 12 b —– = 6 c —– = 18 d —– = 8 e —– = 6

5 5 8 5 7

2 Solve each of the following equations.

x + 1 x + 5 2x + 4 3x + 1a ——– = 5 b ——– = 8 c ——— = 6 d ——— = 2

3 4 5 8


x – 1 x + 1 2x + 3 x – 2 3x – 2 x + 4a ——– = ——– b ——— = ——– c ——— = ——–

3 4 3 2 5 2


5 3 4 5 7 5a ——– = ——– b ——— = ——— c ——— = ———

x – 1 x + 1 3x – 2 2x + 1 5x – 2 3x + 5



LESSON 3.5H

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ork 1 Solve the following inequalities and illustrate their solutions on number lines.

a 5x + 7 ≥ 22 b 2x – 3 ≤ 10 c 4x + 3 < 11

d 2(x + 4) > 20 e 4(3t + 7) ≤ 16 f 2(5x – 4) ≥ 17

2 Write down the values of x that satisfy the conditions given.

a 2(4x + 3) < 50, where x is a positive, prime number.

b 2(3x – 1) ≤ 60, where x is a positive, square number.

c 4(5x – 3) ≤ 100, where x is positive but not a prime number.

3 Solve the following inequalities and illustrate their solutions on number lines.

a 5x – 4 < 11 b 3(2x + 5) ≤ 9x > –1 x > –4

LESSON 3.6

Ho

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rk A baby squid is weighed from birth at midday for its first 5 days. The results are shown in the tablebelow.

a Plot the points on a graph and join them with a suitable line.

b Is the increase in weight during a time interval directly proportional to the length of the interval?

c Write down the equation of the line showing the relationship between the weight (W ) and the age(D) of the squid.

d If the relationship held, at what age would the squid first weigh over 15 kg?

Day 1 2 3 4 5Weight (kg) 1.7 3.1 4.5 5.9 7.3

LESSON 3.7

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rk 1 a On the same pair of axes, draw the graphs of the equations y = 2x + 1 and y = 2x + 3.

b Explain why there is no solution to this pair of simultaneous equations.

2 a Does every pair of linear simultaneous equations have a solution?

b Explain your answer to part a.

3 a Does every pair of simultaneous equations which do have a solution, have a unique solution?

b Explain your answer to part a.

4 Sketch a pair of graphs, one quadratic and one linear, which represent a pair of simultaneousequations that will have only one solution.



Shape, Space and Measures 1CHAPTER

4


LESSON 4.1

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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

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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.



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.

Explain why ∆AED is congruent to ∆BEC.

A F

B C D E6 cm 6 cm

5 cm 5 cm

40° 40°

G J K

LH I8 cm

9 cm 9 cm 8 cm

7 cm

7 cm

M Q

O P

R

10 cm

10 cm

N55° 75°

75°

55°

T U

S

V W

X

15 cm

15 cm

9 cm

9 cm

D C

A BE



LESSON 4.5H

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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

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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.



LESSON 4.7H

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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


LESSON 5.1

Ho

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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 French Spanish English MusicA 45 52 63 35B 64 60 56 45C 22 30 46 58D 75 80 70 30E 47 60 55 42F 15 24 40 50G 80 74 68 42H 55 65 53 48I 85 77 75 41J 33 47 51 50



LESSON 5.3H

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ork 1 The table shows the scores of some students in a music exam and in a maths exam.

a Plot the data on a scatter graph. Use the x-axis for the music exam scores, from 0 to 100, and they-axis for the maths exam scores, from 0 to 100.

b Draw a line of best fit.

c One person did not do quite as well as expected on the maths test. Who do you think it was?Give a reason.

2 A survey is carried out to compare the ages of people with the reaction time in a test.

a Plot the data on a scatter graph. Use the x-axis for the range of ages, from 0 to 90 years, and they-axis for reaction times, from 0 to 1 seconds.

b Draw a line of best fit.

c Use your line of best fit to estimate the reaction time of a 30-year-old.

d Explain why it would not be sensible to use the line of best fit to predict the reaction time ofsomeone aged 100.

Age (years) 45 62 83 24 76 63 44 42 37 50

Reaction time (seconds) 0.15 0.31 0.58 0.20 0.62 0.43 0.21 0.25 0.18 0.49

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

2001 2002

North American Western Europe

0

500

1000

1500

Vis

itors

(×10

00)



LESSON 5.5H

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ork 1 Two fair spinners are spun and the scores are

added together to get a total score. This isrecorded in the two-way table, shown below.

a Complete the table of total scores.b List all the total scores which are prime

numbers.c State the most likely total scores.d Write down the probability of getting a total

score of 7. Give your answer as a fraction inits simplest form.

e Write down the probability of getting a totalscore of 5. Give your answer as a fraction inits simplest form.

2 A year group recorded the days of the week onwhich they were born. Here are the results.

a Write a comment on the births of boys andgirls.

b Write a comment about the number of birthson different days of the week.

Second spinner+ 1 2 31 2 3

First2 3spinner34

Day Boys GirlsMonday 23 19Tuesday 19 25Wednesday 27 28Thursday 31 26Friday 35 41Saturday 14 17Sunday 12 11Total 161 167

4

3

2

13 2

1

LESSON 5.6

Ho

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rk For each table of data:

a Copy and complete the cumulative frequency table.

b Draw the cumulative frequency graph.

c Use your graph to estimate the median and the interquartile range.

1 The height of 100 plants.

2 The time that the school bus is late on 40 days.

Time, t (min) Number of days Time, t (min) Cumulative frequency0 < t ≤ 5 12 t ≤ 55 < t ≤ 10 15 t ≤ 10

10 < t ≤ 15 6 t ≤ 1515 < t ≤ 20 7 t ≤ 20

Height, h (cm) Number of plants Height, h (cm) Cumulative frequency0 < h ≤ 10 6 h ≤ 10

10 < h ≤ 20 24 h ≤ 2020 < h ≤ 30 27 h ≤ 3030 < h ≤ 40 30 h ≤ 4040 < h ≤ 50 13 h ≤ 50



LESSON 5.7H

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ork Copy and complete each table of values given below.

a Complete each table including the totals.

b Calculate an estimate of each mean.

1

2 Time, t, (hours) Frequency, f Mid-value, x, of time (hours) f × x (hours)0 < t ≤ 2 2 1 22 < t ≤ 4 74 < t ≤ 6 106 < t ≤ 8 5

Total = Total =

Age, A (years) Frequency, f Mid-value, x, of age (years) f × x (years)11–12 5 12 6013–14 815–16 1217–18 5

Total = Total =

Ho

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rk 1 State whether each of the pairs of triangles below are similar.

2 a Explain why triangle ABC is similar to triangle PQR.

b Find the length of the side QR.

3 In the triangle below DE is parallel to BC. Find the length of BC.

42°

5 cm

4 cm

2 cm 4 cm 8 cm

10 cm

51°

87°

42°30°46°

30°

114°

a

c d

b

2cm

6 cm6 cm 4 cm

9 cm

9 cm

88°35°A

C

B9 cm

12 cm R

P

Q57°88°

6 cm

A

B C

ED4 cm

6 cm6 cm


6


LESSON 6.1



LESSON 6.2H

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ork 1 Express each of the following in mm2.

a 3 cm2 b 8 cm2 c 4.5 cm2 d 0.8 cm2

2 Express each of the following in m2.

a 40 000 cm2 b 70 000 cm2 c 32 000 cm2 d 5000 cm2

3 Express each of the following in cm3.

a 2 m3 b 9 m3 c 3.7 m3 d 0.3 m3

4 Express each of the following in litres.

a 8000 cm3 b 12 000 cm3 c 23 500 cm3 d 250 cm3

5 A rectangular park is 620 m long and 340 m wide. Find the area of thepark in hectares.

6 Calculate the volume of the box on the right. Give your answer in litres.40 cm

10 cm

25 cm

LESSON 6.3

Ho

me

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rk In this exercise take π= 3.142 or use the key on your calculator.

1 Calculate (i) the length of the arc and (ii) the area of the sector for each of the following circles.

Give your answers correct to three significant figures.

2 Calculate the total perimeter of the sector on the right. Give your answer correct to three significant figures.

3 Calculate the area of the sector below. Give your answer correct to three significant figures.

3.5 cm 3.5 cm150°

π

8 cm

40°5 cm30° 10 cm

135°

a b c

12 cm 12 cm

45°



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

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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.



Number 2CHAPTER

7


LESSON 7.1

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rk 1 Write each of the following numbers in standard form.

a 63 000 000 b 0.000 74 c 322 000 d 83 300

e 0.000 000 71 f 92 321 g 0.009 35 h 0.000 0005

2 Write each of the following standard form numbers as an ordinary number.

a 4.9 × 104 b 4.36 × 10–3 c 8.4 × 103 d 5.68 × 10–2

e 8 × 109 f 4.82 × 10–4 g 9.2 × 106 h 6.03 × 10–1

3 Write each of the following numbers in standard form

a 68 × 103 b 37.8 × 10–5 c 0.87 × 10–3 d 58 × 10–4

LESSON 7.2

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rk 1 Do not use a calculator for this question. Work out each of the following and give your answer instandard form.

a (4 × 102) × (2 × 106) b (5 × 103) × (4 × 102) c (6 × 10–3) × (2 × 10–4)

d (9 × 10–2) × (3 × 108) e (5 × 10–5) × (8 × 10–3) f (7 × 103) × (7 × 103)

2 You may use a calculator for this question. Work out each of the following and give your answer instandard form. Do not round off your answers.

a (2.1 × 105) × (3.4 × 103) b (3.2 × 103) × (1.5 × 104) c (3.6 × 103) × (2.8 × 10–8)

d (1.5 × 10–2) × (2.5 × 10–4) e (3.8 × 10–4) × (2.8 × 104) f (8.6 × 104) × (1.5 × 10–7)

LESSON 7.3

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rk 1 Do not use a calculator for this question. Work out each of the following and give your answer instandard form.

a (8 × 105) ÷ (2 × 103) b (4 × 105) ÷ (5 × 107) c (6 × 103) ÷ (2 × 10–4)

d (1.2 × 10–3) ÷ (3 × 10–2) e (6 × 106) ÷ (8 × 10–1) f (5 × 102) ÷ (8 × 10–3)

2 You may use a calculator for this question. Work out each of the following and give your answer instandard form. Do not round off your answers.

a (6.15 × 105) ÷ (1.5 × 102) b (3.15 × 106) ÷ (1.4 × 10–1)

c (3.19 × 103) ÷ (1.45 × 10–2) d (2.32 × 10–3) ÷ (2.9 × 10–5)

e (5.85 × 10–3) ÷ (6.5 × 103) f (1.495 × 106) ÷ (4.6 × 10–2)



LESSON 7.4H

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ork Do not use a calculator for Questions 1 and 2.

1 Find the upper and lower bounds between which the following quantities lie.

a In a hive there are 2000 bees to the nearest 100.

b The amount of honey in a jar is 200 ml to the nearest 10 ml.

c The width of a field is 70 m to the nearest metre.

d The mass of a loaf is 0.6 kg to the nearest 100 grams.

2 A poster is 2.5 metres by 1.5 metres, each measurement accurate to the nearest 10 cm.

a What are the upper and lower bounds for the length of the poster?

b What are the upper and lower bounds for the width of the poster?

c What are the upper and lower bounds for the perimeter of the poster?

3 A bottle of water holds 1 litre to the nearest centilitre.

a What is the smallest possible amount in the bottle?

b What is the greatest possible amount that 10 bottles could hold?

LESSON 7.5

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me

wo

rk 1 a = 10, b = 20 and c = 30. All values to the nearest whole number.

a Write down the upper and lower bounds of a, b and c.

b Work out the upper and lower bounds of each of the following.

i a × b ii c ÷ a iii (a × b) + c iv c2

2 A rectangle has an area of 120 cm2, measured to the nearest 10 cm2. The length is 15 cm, measuredto the nearest cm.

a What is the greatest possible width of the rectangle?

b What is the least possible width of the rectangle?

LESSON 7.6

Ho

me

wo

rk 1 Write each of the following fractions as a recurring decimal.

a 4–7 b 85–––101 c 17––33

2 Write each of the following recurring decimals as a fraction in its simplest form.

a 0.5·4·

b 0.2·46

·c 0.2

·d 0.1

·2·

e 0.37·

LESSON 7.7

Ho

me

wo

rk 1 Use a calculator to evaluate each of these.

63.4 × 21.02 19 7a [2.42 + (6.7 – 1.04)]2 b ——————— c —– – —–

2.9(4.5 – 1.72) 21 18

2 Use the power key to evaluate each of these.

a 2.75 b 42.8752–3



Algebra 4CHAPTER

8


LESSON 8.1

Ho

me

wo

rk 1 Estimate the square root of each of the following. Then using a calculator find the result to onedecimal place and see how close you were.

a √—–46 b √

—–31 c √

—–74 d √

——129 e √

——215

2 Without a calculator, state the cube roots of each of the following numbers.

a 64 b 343 c 216 d 729 e 512

3 a Estimate the integer closest to the cube root of each of the following.

i 96 ii 110 iii 55 iv 297 v 3000

b Use a calculator to find the accurate value of the above. Give your answers to one decimalplace.

4 State which, in each pair of numbers, is the larger.

a √—–20, 3√

—–55 b √

—–28, 3√

——149 c √

—–18, 3√

—–79

5 Estimate the cube root of each of these numbers without a calculator.

a 15 b 61 c 400 d 150 e 850

6 Try to estimate the cube root of each of these numbers without using a calculator.

a 25 000 b 8000 c 57 000 d 41 000 e 83 000

7 Write down the value of each of the following without using an index.

a 491–2 b 512

1–3 c 16

1–4 d 1024

1–5 e (–343)

1–3

Ho

me

wo

rk 1 Expand the following, and find their value (use a calculator if necessary).

a 26 b 35 c 64 d 45 e 172 f 143 g 272 h 114

2 Write down the following in index form:

a t × t × t × t b t × t × t × t × t c m × m d q × q × q

3 a Write m + m + m + m + m + m as briefly as possible.

b Write t × t × t × t × t × t as briefly as possible.

c Show the difference between 6m and m6.

d Show the difference between t4 and 4t.

4 Simplify each of the following:

a 2x3 × 4x7 b 12t6 ÷ 3t c 20m5 ÷ 5m3 d 3y × 2y5 e x–2 ÷ x–3

5 Simplify each of the following, leaving your answer in fraction form:

a x3 ÷ x5 b 4m2 ÷ m5 c 8x–4 ÷ 2x d 2x5 ÷ 3x8 e Ax × Bx–5 f Ax ÷ Bx–5

LESSON 8.2



LESSON 8.3H

om

ew

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

me

wo

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.


9


LESSON 9.1

Ho

me

wo

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.



LESSON 9.2H

om

ew

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

me

wo

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?



LESSON 9.4H

om

ew

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


10


LESSON 10.1

Ho

me

wo

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).

a Scale factor 1–3

b Scale factor 1–2

O

O

00

1 2 3 4 5 6 7 8

1

2

3

4

5

6

7

8



LESSON 10.2H

om

ew

ork 1 Find the value of � for each of the following. Give your answers to 1 decimal place.

a tan� = 0.12 b tan� = 0.956 c tan� = 3.45

2 Find the value of each of the following. Give your answers to 3 significant figures.

a 5tan31° b 14tan51° c 23tan58.9°

3 Calculate the angle marked � in each of the following triangles. Give your answers to 1 decimal place.

4 Calculate the length of the side marked x in each of the following triangles. Give your answers to 3 significant figures.

7 cm25°

15°62°

9.5 cm

xx x

a b

14.2 cm

c

10 cm

4 cm�

18 cm

10 cm

�

a b

5 cm

12 cm

�

c

LESSON 10.3

Ho

me

wo

rk 1 Find the value of � for each of the following. Give your answers to 1 decimal place.

a sin� = 0.25 b sin� = 0.854 c cos� = 0.752 d cos� = 0.235

2 Find the value of each of the following. Give your answers to 3 significant figures.

a 5sin62° b 12sin52.6° c 21cos86° d 3.7cos42.3°

3 Calculate the angle marked � in each of the following triangles. Give your answers to 1 decimalplace.

4 Calculate the length of the side marked x in each of the following. Give your answers to 3significant figures.

11 cm

31° 17°55°

4.8 cmx x

x

a b

42 cm

c

9 cm3 cm

�

28 cm

25 cm�

13 cm

15 cm

�

a b c



LESSON 10.4H

om

ew

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


LESSON 11.1

Ho

me

wo

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.

a b

8x + 4

3y + 5

?A3x + 1 B

2y

D

C

?

?A3x

4y

7x + 5

B

3

C

D?



LESSON 11.2H

om

ew

ork 1 Factorise each of the following.

a 3x + 9 b 4t + 12 c 2m + 8 d 5y + 15

e 10 + 2m f 4 + 6k g 10 + 15t h 12 + 9x

i 6x – 4 j 8t – 12 k 6m – 9 l 20y – 8

m 21 – 7m n 18 – 3k p 12 – 10t q 15 – 5x

2 Factorise each of the following.

a x2 + 5x b t2 + 3t c m2 + 4m d y2 + 8y

e 6m + m2 f 2k + k2 g 7t + t2 h x + x2

i x2 – 4x j 2t2 – 3t k m2 – 5m l 5y2 – 4y

m 3m – m2 n 6k – 5k2 p 6t – t2 q 8x – 5x2

LESSON 11.3

Ho

me

wo

rk 1 Expand and simplify each of the following expressions.

a (x + 4)(x + 7) b (x + 3)(x – 6) c (x – 5)(x + 7)

d (x + 3)(x – 5) e (x – 4)(x – 3) f (x – 8)(x + 5)

g (x + 3)2 h (x – 5)2 i (x + 4)(x – 4)

2 Without using a calculator, find the result of each of the following calculations.

a 752 – 252 b 9.72 – 0.32 c 18.72 – 1.32

LESSON 11.4

Ho

me

wo

rk Factorise each of the following.

1 x2 + 6x + 8 2 x2 – 9x + 20 3 x2 + 3x – 4

4 x2 – 4x – 12 5 x2 + 4x + 4 6 x2 – 14x + 49

7 x2 – 16 8 x2 – 1 9 x2 – 4x – 21



LESSON 11.5H

om

ew

ork 1 Change the subject of each of the following formulae as indicated.

a Make I the subject of the formula W = IPT.

b i Make P the subject of F = P + MK. ii Make M the subject of F = P + MK.

c i Make m the subject of T = 3m + 2n. ii Make n the subject of T = 3m + 2n.

abhd Make b the subject of V = ——.

3

19R2 The formula C = —— + 40 is used to calculate the cost in pounds of making a boiler of radius

8R (cm).

a Make R the subject of the formula.

b Use this formula to find the radius of a boiler that cost £150 to make.

3 Draw a graph of each of the following equations on the same pair of axes.

a y – 2x – 1 = 0 b y – 2x – 3 = 0 c y – 2x + 1 = 0 d y – 2x + 3 = 0

Comment on the similarities and differences between the graphs.

Solving Problems and RevisionCHAPTER

12


LESSON 12.1

Ho

me

wo

rk 1 In a sale, a hi-fi is reduced by 15%. The sale price of the hi-fi is £459, what was the original price?

2 For each part of the question, where n is always an integer, write down the answer which is true andexplain your choice.

n2 – 2a When n is even, ——— is:

2

Always odd Always even Sometimes odd, sometimes even

n2 – 2b When n is odd, ——— is:

2

Always an integer Always a fraction Sometimes an integer, sometimes a fraction



LESSON 12.2H

om

ew

ork 1 p = 1.2 × 107, q = 2.5 × 108, r = 6.3 × 10–3

Work out each of the following, giving your answer in standard form.

a p + q b p × q c r2

2 Light green paint is made by mixing yellow paint and blue paint in the ratio 2 : 3.

Dark green paint is made by mixing yellow paint and blue paint in the ratio 1 : 3.

One litre of light green paint and one litre of dark green paint are poured into a large bucket.

How much more yellow paint needs to be added to the bucket to produce light green paint?

LESSON 12.3

Ho

me

wo

rk 1 a Explain why (x – 4)(x – 4) ≠ x2 – 16

b Expand and simplify each of the following.

i 2(x – 3) + 3(2x – 1) ii (x + 4)(x – 7)


2x + 3a 6 + 2x = 8 + 4x b ——— = 5 c 5(1 + x) = 3(x + 2)

3

LESSON 12.4

Ho

me

wo

rk 1 By drawing the graphs y = 2x, y = –2 and x = 3, work out the area of the triangle enclosed by all three lines.

2 Give the four inequalities which describe the shaded region.

001234

y

x1 2 3 4

LESSON 12.5

Ho

me

wo

rk 1 Find the length x in the triangle shown on the right.

2 Find the length x and the angle y in each of the triangles shown below.

a b

20 cm13 cm

x cm

12 cm

7 cm

y°

7 cm

x cm

57°



LESSON 12.6H

om

ew

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


13


LESSON 13.1

Ho

me

wo

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

62 48 55 67 81 40 45 59 58 6272 65 70 82 66 48 59 68 71 6554 57 76 74

Weight, W (kg) Tally Frequency40 ≤ W < 5050 ≤ W < 6060 ≤ W < 7070 ≤ W < 8080 ≤ W < 90



LESSON 13.2H

om

ew

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.


14


LESSON 14.1

Ho

me

wo

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.

a b

3 Calculate the volume of this prism.

π

9 cm

5 cm 8 cm

6 cm

12 cm

15 cm

15 cm

6 cm

5 cm

8 cm 20 cm

2 m

5 m

3 m

12 m



LESSON 14.2 and 14.3H

om

ew

ork Complete the investigation you started in the lesson.

LESSON 14.4

Ho

me

wo

rk Design a logo for a badge for your school, which has both reflection and rotational symmetry.

LESSON 14.5 and 14.6

Ho

me

wo

rk Complete the investigation you started in the lesson.


15


LESSON 15.1

Ho

me

wo

rk Two four-sided spinners are each spun 80 times. The results are shown below.

For each spinner state whether you think it is biased by comparing i the individual frequencies ii the experimentaland theoretical probabilities.

1st spinner

2nd spinner Number on spinner 1 2 3 4

Frequency 25 17 16 22

Number on spinner 1 2 3 4

Frequency 20 21 19 20



LESSON 15.2H

om

ew

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 ability of teenagers and adults at working out theoreticalprobabilities.

3 If you have completed the report of your first investigation, then carry out and write up anotherdetailed investigation of your own choice.

GCSE PreparationCHAPTER

16


LESSON 16.1

Ho

me

wo

rk 1 Solve these equations.

a (x + 3)(x – 4) = 0 b (x – 1)(x + 6) = 0 c (x – 7)(x + 6) = 0

d (x + 5)(x + 2) = 0 e (x – 3)(x + 6) = 0 f (x – 9)(x – 3) = 0

2 First factorise, then solve these equations.

a x2 + 8x + 15 = 0 b x2 + 13x + 30 = 0 c x2 + 4x – 5 = 0

d x2 – 9x + 14 = 0 e x2 + 4x – 21 = 0 f x2 – 4x + 4 = 0

LESSON 16.2

Ho

me

wo

rk 1 Expand these brackets into quadratic expressions.

a (3x + 1)(x – 4) b (3x – 1)(x + 5) c (2x – 1)(2x + 3)

d (3x – 2)(3x + 2) e (3x – 1)2 f (2x + 5)2

2 Factorise the following quadratic expressions.

a 2x2 – 7x – 4 b 2x2 + 13x + 15 c 3x2 + 5x – 2

d 4x2 + 23x – 6 e 6x2 – 5x + 1 f 6x2 + 11x + 3

g 5x2 – 26x + 5 h 6x2 – 5x – 6 i 4x2 – 16x + 15



LESSON 16.3H

om

ew

ork 1 Solve these equations.

a 2x2 – 15x + 7 = 0 b 3x2 – 5x + 2 = 0 c 2x2 – 9x – 5 = 0

d 24x2 + 14x – 5 = 0 e 6x2 + 23x + 20 = 0 f 6x2 – 23x + 7 = 0

2 Solve these equations

a x2 + x = 6 b 2x(x + 4) = 3(x – 1) c 8x2 – 3x + 4 = 2x2 + 2x + 3

LESSON 16.4

Ho

me

wo

rk 1 Solve these equations using the quadratic formula. All answers are whole numbers or fractions.

a x2 + 4x – 5 = 0 b 2x2 + 5x – 3 = 0 c 6x2 – 19x + 10 = 0

2 Solve these equations, giving your answers to 2 decimal places.

a x2 + 7x – 10 = 0 b 2x2 – x – 4 = 0 c 4x2 + x – 7 = 0

3 Solve these equations, giving your answer in surd form.

a x2 – 4x – 2 = 0 b x2 + 6x – 1 = 0 c x2 + 5x – 2 = 0

LESSON 16.5

Ho

me

wo

rk 1 Complete the square for the following.

a x2 + 12x b x2 – 6x c x2 – 20x

2 Rewrite the following quadratic expressions by completing the square.

a x2 + 12x – 9 b x2 – 6x + 3 c x2 – 20x + 100

3 Solve the following quadratic equations using the completing the square method.

a x2 + 12x – 9 = 0 b x2 – 6x + 3 = 0 c x2 – 20x + 100 = 0

d x2 – 10x + 5 = 0 e x2 + 4x – 7 = 0 f x2 – 8x – 5 = 0

LESSON 16.6

Ho

me

wo

rk 1 Expand these brackets into quadratic expressions.

a (x + 11)(x – 11) b (2x – 3)(2x + 3) c (5x – 2y)(5x + 2y)

2 Factorise the following quadratic expressions.

a x2 – 144 b x2 – 225 c 4x2 – 36

d 81x2 – 64 e x2 – 4y2 f 16x2 – 121

g x2 – 9z2 h 4x2 – 25y2 i 81x2 – 16y2



LESSON 16.7H

om

ew

ork Students could be asked to continue the work at home if they have computer facilities or asked to look

on the Internet for information on the quadratic equation.

Documents

CHAPTER 1 Algebra 1 & 2 - Kineton Maths Departmentkinetonmathsdepartment.weebly.com/uploads/5/5/2/7/55272917/book_… · Algebra 1 & 2 CHAPTER 1 Teacher’s Pack 3 Homework LESSON