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Cambridge Lower Secondary Mathematics Workbook 8 2nd Edition Lynn Byrd, Greg Byrd, Chris Pearce - Solutions

For each of the following equations, state the two variables which are inversely proportional to each other and explain your answer. (a) y= (c)= (e) q 4 (p+1) (b) y= (d) 11 = 7 m 1
If is inversely proportional to w and z = 9 when w = 9(i) find an equation connecting wand(ii) find the value of when w = 16(iii) calculate the value of w when z = 3.
If x is inversely proportional to y and x = 50 when y = 2(i) find the value of x when y = 4(ii) find an equation connecting x and y,(iii) calculate the value of y when x = 3.2
The force, F newtons (N), between two particles is inversely proportional to the square of the distance, dm, between them. When the particles are 2 m apart, the force between them is 10 N. Find(i) the force between the particles when they are 5 m apart,(ii) the distance between the particles when
In a computer simulation of an experiment, a drug is added to two identical flasks, each containing the same amount of a certain bacteria. The drug is allowed to react with the bacteria for various times in hours. It is found that the amount of bacteria left, s units, is inversely proportional to
If y is inversely proportional to and v = 6 when x = 9 find the value of v when x = 25
1. If y is inversely proportional to r and x = 2 when x = 4(i) find the value of y when x = 8(ii) find an equation connecting x and y(iii) calculate the values of x when v = 8
It v is inversely proportional to and v = 6 when t = 4(calculate the value of y when x = 16(ii) find an equation connecting and y.(iii) find the value of x when x = 4
A contractor agrees to lay a road 3000 m long in 30 days. 50 men are employed and they work for 8 hours per day. After 20 working days, he finds that only 1200 m of the road is completed. How many more men does he need to employ in order to finish the project on time if each man now works 10 hours
Tap A takes 6 minutes to fill a tank and Tap B takes 9 minutes to fill the same tank. Pipe C can empty the tank in 15 minutes. How long will it take to fill up the tank if the pipe is in use when both taps are turned on?
A consignment of fodder can feed 1000 sheep for 20 days. Assuming that all the sheep consume the fodder at the same rate, how many consignments of fodder are needed to feed 550 sheep for 400 days?
12 glassblowers can make 12 identical vases in 9 minutes. Assuming that all the glassblowers work at the same rate, how long will it take 8 glassblowers to make 32 such vases?
The time, hours, needed to complete a job is inversely proportional to N. where N is the number of men employed for the job. 3 men can complete the job in 8 hours.(i) Find an equation connecting / and N.(ii) Find the number of hours needed by 6 men to complete the job.(iii) If the job is to be
If B is inversely proportional to A and B = 3.5 when A = 2 find the value of B when A = 1.4
If is inversely proportional tox and 5 when x = 7 find the value of a when z = 70
At a sports camp, there is sufficient food for 72 athletes to last 6 days. If 18 athletes are absent from the camp, how many more days can the food last for the other athletes? State the assumption made.
A consignment of fodder can feed 1260 cattle for 50 days. Given that all the cattle consume the fodder at the same rate, find(i) the number of cattle an equal consignment of fodder can feed for 75 days,(ii) the number of days an equal consignment of fodder can last if it is used to feed 1575 cattle.
For each of the following, y is inversely proportional to x. Copy and complete the tables. (a) (b) x 2 2.5 3 y 24 4 1.5 k 3 4 25 y 9 8 2.5
- The frequency, /kilohertz (kHz), of a radio wave is inversely proportional to its wavelength, A m. The frequency of a radio wave that has a wavelength of 3000 m is 100 kHz. Find(i) the frequency of a radio wave that has a wavelength of 500 m,(ii) the wavelength of a radio wave that has a
35 workers are employed to complete a construction project in 16 days. Before the project starts, the boss of the company is told that he needs to complete the project in 14 days. Assuming that all the workers work at the same rate, how many more workers does he need to employ in order to complete
IIQ is inversely proportional to P and Q = 0.25 when P = 2(i) express in terms of P.(ii) find the value of Q when P = 5(iii) calculate the value of P when Q = 0.2
If x is inversely proportional to y and x = 40 when y = 5 find(i) the value of x when v = 25(ii) an equation connecting x and y,(iii) the value of v when x = 400
Eight men can build a bridge in 12 clays. Find the time taken for 6 men to build the same bridge. State the assumption made.
Which of the following quantities are in inverse proportion? State the assumption made in each case.(a) The number of pencils Farhan buys and the total cost of the pencils.(b) The number of taps filling a tank and the time taken to fill the tank.(c) The number of men laying a road and the time
The current, / amperes (A), flowing through a wire is inversely proportional to its resistance, R ohms (2). Given that the current flowing through a wire with a resistance of 0.5 2 is 12 A, find(i) the current flowing through the wire when its resistance is 3 2,(ii) the resistance of the wire when
Boyle's Law states that the volume, V dm³, of a fixed mass of gas at constant temperature is inversely proportional to its pressure, P pascals (Pa). The pressure of 1 dm' of a gas in an airtight container is 50 Pa. Assuming that the temperature in the container is constant, calculate the volume of
Given that y is inversely proportional to x, copy and complete the table. x x y 0.5 22 3 0.8
If y is inversely proportional to x and y = 0 when x = 2 find the value of y when x = 3.
If y is inversely proportional to a and y = 5 when x = 2 find(i) the value of y when x = 8.(ii) an equation connecting x and y(iii) the value of x when y = 10.
If y is inversely proportional to x and x = 3 when x= 4, find(i) the value of y when x = 8(ii) an equation connecting x and v(iii) the value of x when x = 48
The braking distance of a vehicle is directly proportional to the square of its speed. When the speed of the vehicle is b m/s, its braking distance is d m. It the speed of the vehicle is increased by 200%, find the percentage increase in its braking distance.
y is directly proportional to x and y a for a particular value of x. Find an expression for y in terms ofa, when this value of x is doubled,
If y is directly proportional to a and the difference in the values of y when x = 1 and x = 3 is 32, find the value of v when x = - 2.
During a certain period in the life of an earthworm, its length, L em, is directly proportional to the square root of N, where N is the number of hours after its birth. One hour after an earthworm is born, its length is 2.5 cm.(i) Find an equation connecting L and N.(ii) Find the length of an
Given that the mass, m g, of a sphere is directly proportional to the cube of its radius, rcm, copy and complete the table. 0.2 0.7 1.5 m 0.25 6.75 11.664
Given that y is directly proportional to x, copy and complete the table. x 3 + 6 y 375 648 1029
If g is directly proportional to (1) and q = 20 when p = 3 find the values of when q = 80.
If is directly proportional to and 8 when x = 4 find the values of when x = 9.
For each of the following equations, state the two variables which are directly proportional to each other and explain your answer.(a) v = 4v ^ 2(b) x = 3sqrt(x)(c) y ^ 2 = 5x ^ 3(d) p= a
It is given that y is directly proportional to ".Write down the value of in when(i) y m² is the area of a square of length x m.(ii) y em' is the volume of a cube of length x cm.
It is directly proportional to wand z = 4 when 1=8,(i) find an equation connecting w and(ii) find the values of when w = 18.(iii) calculate the value of w when z = 5.(iv) draw the graph of z against w.
If x is directly proportional to y' and x = 32 when v = 2(i) find an equation connecting x and y,(ii) find the value of x when x = 6.(iii) calculate the value of y when x = 108.(iv) draw the graph of x against y.
The volume, Vem, of a solid is directly proportional to the cube of its radius, rem. When the radius of the solid is 6 cm, its volume is 905 cm.(i) Find an equation connecting V and(ii) Calculate the volume of the solid when its radius is 10 cm.
If y is directly proportional to x and v = 20 when x = 2.(i) find an equation connecting & and v.(ii) calculate the value of y when x = 3.(iii) find the values of a when v = 1.25 A.(iv) draw the graph of y against v.
For each of the following equations, state the two variables which are directly proportional to each other and explain your answer.(a) v = 6v ^ 2(b) sqrt(x) = x ^ 4
For each of the following equations, state the two variables which are directly proportional to each other and explain your answer.(a) y = 5 * x deg(b) y2 = √x
A machine which manufactures ice needs to be run for 10 minutes to warm up before the production of ice begins. The mass, in tonnes, of ice produced is directly proportional to the number of hours of production. Given that 20 tonnes of ice are produced when the machine runs for half an hour, find
The total monthly income, SD, of a salesman who sells tyres consists of a basic salary of $600 and a variable amount which depends on the number of tyres he sells. For each tyre he sells. he receives $8.(i) If the salesman sells 95 tyres in a particular month, find his total income for that
The amount of voltage, V volts, needed to send a fixed amount of current through a wire, is directly proportional to its resistance, Rohms. When R = 6 V = 9(i) Find an equation connecting V and R.(ii) Find the value of V when R = 15(iii) Calculate the value of R when V = 15(iv) Draw the graph of V
The pressure, P pascals, of a gas in a container is directly proportional to its temperature, 7 kelvin, When 710, P = 25.(i) Find an equation connecting P and 7.(ii) Find the value of P when T = 24.(iii) Calculate the value of 7 when P = 12.(iv) Draw the graph of P against 7.
The net force, F newtons, needed to push a block along a horizontal surface is directly proportional to the mass, m kg, of the block. When m = 5 F = 49.(i) Find an equation connecting Fand m.(ii) Find the value of F when m = 14.(iii) Calculate the value of m when F = 215.6.(iv) Draw the graph of F
If is directly proportional to y and 48 when v = 6,(i) find an equation connecting y and(ii) draw the graph of against v.
If y is directly proportional to x and y = 20 when x = 5(i) find an equation connecting v and y,(ii) draw the graph of y against x.
For each of the following, y is directly proportional to x. Copy and complete the tables. (a) * x 4 20 24 6 9 11 (b) y x 2 3 5.5 y 3.6 9.6 11.4
If B is directly proportional to A and B = 3 when A= 18, find the value of B when A = 24.
If is directly proportional to and 12 when 3, find the value of when = 18.
5/9 of a piece of metal has a mass of 7 kg. What is the mass of of the piece of metal?
Find the cost of(a) 10 kg of tea leaves when 3 kg of tea leaves cost $18,(b) a kg of sugar when b kg of sugar cost Se.
If Q is directly proportional to P and Q = 28 when P = 4.(i) express Q in terms of P,(ii) find the value of Q when P = 5(iii) calculate the value of P when Q = 42.
If x is directly proportional to y x = 4.5 when x = 3 find(i) an equation connecting x and y,(ii) the value of x when x = 6(iii) the value of y when v = 12
In a bookstore, 60 identical books occupy a length of 1.5 mon a shelf. Find(i) the length occupied by 50 such books on a shelf,(ii) the number of such books needed to completely occupy a shelf that is 80 cm long.
108 iclentical books have a mass of 30 kg. Find(i) the mass of 150 such books,(ii) the number of such books that have a mass of 20 kg.
The cost, SC, of transporting goods is directly proportional to the distance covered, d km.The cost of transporting goods over a distance of 60 km is $100.(i) Find an equation connecting C and d.(ii) Find the cost of transporting goods over a distance of 45 km.(iii) If the cost of transporting
The expenses, SE, of a tea party are directly proportional to the number of guests, N. present. When there are 30 guests present at the tea party, the expenses incurred are $210.(i) Find an equations connecting E and N.(ii) Calculate the expenses incurred when there are 80 guests present at the tea
Given that y is directly proportional tox, copy and complete the table. y x 4 50 30 7 48 57
If y is directly proportional to x and v = 5 when x = 2 find the value of y when x = 7.
If y is directly proportional to x and x = 10 when x = 2 find(i) an equation connecting x and y,(ii) the value of y when c 10.(iii) the value of x when v = 60
As a increases, y also increases. Can we conclude that y is directly proportional to x? Explain your answer.
If y is directly proportional to x, then the graph of y against x passes through the origin. If the graph of y against x does not pass through the origin, is y directly proportional to x? Explain your answer.
Suppose y is directly proportional to x. If we plot the graph of x against v, will we get a straight line that passes through the origin? Explain your answer.
If y is directly proportional to x, is directly proportional to y? Explain your answer.
3 Copy each diagram and translate the rectangle using the given column vector.
2 Write the missing numbers and words to complete each statement. a The column vector () The column vector (1) means move the shape units right and 5 units [ b means move the shape 1 unit and units up. C The column vector means move the shape 2 units | and 4 units
1 Match each column vector to the correct description. The first one is done for you: A and iv A 23 i Move the shape 2 units left and 3 units down B ii C iii D LU E LL F (3) Move the shape 3 units right and 2 units up Move the shape 2 units left and 3 units up iv Move the shape 2 units right and 3
14 The midpoint of the line segment GH is at (3,2). Work out three possible pairs of coordinates for G and H. Show all your working.
13 A is the point (16, 0) and B is the point (0, 8). C is the midpoint of AB. D is the midpoint of BC. E is the midpoint of CD. Show that the coordinates of E are (6, 5).
12 P is the point (0, 9) and the midpoint of PQ is (5, 7). Find the coordinates of Q.
11 ABCD is a square. The coordinates of A are (-2, -6). The coordinates of Care (-3, -1). Where is the centre of the square? Explain how you worked out your answer.
10 A is the point (2.4, 6.2), B is the point (3.6, 2.4) and C is the point (-3.8, -1.4). Find the midpoint of AC. a the midpoint of AB b
9 ABCD is a rectangle.Find the midpoint of the line segment AC. b Show that the midpoint of the line segment BD is the same as the midpoint of the line segment AC. -5 D 432-1 y 3- 2- 0 2 3 4 5 B 2- 3 A H
8 Sasha works out the midpoint of the line joining the points (-3, 8) and (5,-2). This is what she writes.Is Sasha correct? Explain your answer. x-coordinate: -3-1-2-3-3/5--21/2 y-coordinate: 13 8+5-12-62 Midpoint is at (-2, 6-1/2)
7 Find the midpoint of the line segment joining each pair of points. a (4, 2) and (10, 12) b (5,-3) and (-3, -7) C (-6, 8) and (8, -6).
6 A is the point (-8, 0), B is the point (6, 0) and C is the point (4, 10). Work out the midpoint of the line segments 6 a i AB b ii AC iii BC. Draw a coordinate grid. Plot the points A, B and C. Check your answers to part a by finding the midpoints on your diagram.
5 Copy and complete the workings to calculate the midpoint of the line segment joining each pair of coordinates. C a (1, 4) and (7, 6) (7,4+)-(229)=() b (18, 0) and (8,8) 18+8 0+8 2 (7,3) and (5, 10) d (1, 4) and (4, 15) 2 + 2 + 2 2 (00) - (63)-6 + 0,6:9)-(699) -(08-09) 2
4 The diagram shows four line segments, PQ, RS, TU and VW. Use the diagram to copy and complete these coordinates. a Pis() Q is ( The midpoint of PQ is ( b Ris() Sis ( The midpoint of RS is ( Tis ( U is ( The midpoint of TU is ( d Vis() Wis ( The midpoint of VW is (
3 Make a copy of this coordinate grid. Read what Sofia says.Is Sofia correct? Use the coordinate grid to help you explain your answer. I think the midpoint of (1, 3) and (6, 3) is at (3, 3).
2 Work out the midpoint of the line segment joining each pair of points. Write whether A, B or C is the correct answer.Write whether A, B or C is the correct answer. a (2, 3) and (2, 7) A (2,4) B (2,5) C (2, 10) D b (8, 12) and (8, 20) A (8,8) B (8, 15) C (8, 16) PD (4, 1) and (6, 1) A (5, 1) B
1 The diagram shows three line segments, AB, CD and EF. Use the diagram to copy and complete these coordinates. 731 6 5 4 43 3 2 B S 1 0 234 -2 C -6-5-4-3-2-1 3 4 5E F 6 9 D x
11 The diagram shows a regular hexagon, ABCDEF. All the internal angles are 120. Write the bearing to get from A to B. Work out the bearing to get from a b i B to C ii C to D iv E to F v F to A. D to EIs Zara correct? Explain your answer. I think the bearing of B from E is 030.
10 The diagram shows three points: A, B and C. The diagram is not drawn accurately. a Write the bearing of B from A. b Work out the bearing of A from B. C Show that the bearing of C from B is 110.d Read what Marcus says.e Is Marcus correct? Explain your answer. Do you think it is possible to work
9 a For each diagram, measure and write i the bearing of X from Y ii the bearing of Y from X.b What do you notice about each pair of answers in part a? For each diagram i write the bearing of X from Y ii work out the bearing of Y from X.8 A NB N X X N Z- C N N X Y
8 a For each diagram, measure and write i the bearing of Y from X ii the bearing of X from Y.b C i What do you notice about each pair of answers in part a? For each diagram write the bearing of Y from X ii work out the bearing of X from Y. A B C Z N
7 Bethan enters a running competition. The diagram shows the position of the start and finish and the four checkpoints Bethan must find. Measure and write the bearing Bethan takes to run from a C the start to checkpoint 1 checkpoint 1 to checkpoint 2 checkpoint 2 to checkpoint 3 d checkpoint 3 to
6 The diagram shows the positions of a park and a library.a Write the bearing of the park from the library.b Write the bearing of the library from the park. N Library N Z- Park
5 This is part of Ivan's homework.Question Write the bearing of B from A in this diagram. Answers Bearing is 152Is Ivan correct? Explain your answer. N Z- 152 A 208 B
4 Draw a diagram, similar to those in Question 3, to show each bearing of Y from X.a 065 b 105 C 230 d 350
3 Use a protractor to measure each of the angles shown. Write the bearing you need to walk on to get from X to Y. E Z- b Z- Z- X
2 For each diagram, write the bearing you need to walk on to get from C to D. The first one is done for you. a N C 115 D Bearing 115 d D b Z- Z- N Z- 240 60 325 132 D
1 Match each diagram to the bearing you need to walk on to get from A to B. The first one is done for you: A and iii A N B N C Z- N D B 35 E B 80 A Z- 160 A A 236 B B 300 i 160ii 300 080 iv 035 v 236
7 a Can you throw a coin fairly? Do an experiment to find out. Decide how many times you will throw the coin. b Use your results to calculate experimental frequencies and compare them with the theoretical frequencies. State your conclusion about your throwing. Give a reason. How can you modify your

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