Questions and Answers of Cambridge Checkpoint Lower Secondary Mathematics

Use the calculator to evaluate 172. 17 O 00 289
A child is covering a square board with mosaic tiles.The board is 40 × 40 cm.Each mosaic tile is 2 × 2 cm.a. How many mosaics are needed for one complete row?b. The mosaics come in packs of 30.(i)
Without using a calculator evaluate √0.36.0.36 can be written as a fraction.Therefore √0.36 = 0.6. 0.36= √36 √0.36 == √100 fo=0.6
Use a calculator to work out √729. √7 729 (2) (9) ((~) (=) 27
Evaluate the following without using a calculator.a. b. c. d. e. f. g. h.
Without using a calculator evaluate √0.81.0.81 can be written as a fraction.Therefore √0.81 = 0.9. 0.81= √0.81==10 = 0.9 10
a. Evaluate the following without using a calculator.(i). √25(ii). √9(iii). √121(iv). √169b. Check your answers to (a) using a calculator.
How many 1 cm × 1 cm × 1 cm cubes would make up cubes with the following side lengths?a. 4 cmb. 6 cmc. 10 cmd. 9 cm
Using the yx button on your calculator, evaluate the following.a. 113b. 203c. 2.53d. 6.23
A tiler has 100 square tiles for tiling two square panels in a bathroom.a. Explain why the panels cannot be of the same size.b. Each tile is 10 × 10 cm. What are the dimensions of the two square
Use a calculator to work out 83. 8 [yx| 3 || 512
Look at the graphs below.(i). (ii). a. For each graph copy and complete the x- and y coordinate table below.b. Describe in words the relationship between the x- and y-coordinates for each
A sugar cube manufacturer wants to sell 500 sugar cubes in a box also in the shape of a cube.a. Assuming there are no gaps in the box, explain why this will not be possible.b. What is the closest
The pattern below shows an arrangement of squares.The small blue square has dimensions 1 × 1 unitsa. How many blue squares would fit into the whole of the pattern?b. Use your answer to (a) to
A shop owner buys a three-digit combination number padlock for his door.He wants to choose a number which he can remember.He decides to choose a two-digit number (i.e. a three-digit number starting
Without using a calculator, work out the cube roots of the following numbers.a. 8b.125c. 27d. 1000
In each of the following identify the coordinates of some of the points on the line and use these to find the equation of the straight
An equation of a straight line is given as y = 3x.a. Copy and complete the table below for the coordinates of some of the points on the line.b. Using the table of results, plot the graph of y =
Look at the graph below.a. Copy and complete the table of coordinates.b. Describe in words the relationship between the x- and y-coordinates.The y-coordinate is always 1 less than the x-coordinate.c.
Without using a calculator if possible, work out the following.a. 3√64b. 3√343c. 3√216
The exchange rate between pounds Sterling (£) and US Dollars ($) is given as £1 = $1.25.a. Using the number of dollars as D and the number of pounds as P, write a formula linking P and D.D =
A child’s box of building bricks contains the following numbers of cubes:Eight cubes with dimensions 2 × 2 × 2 cm.Sixty cubes with dimensions 1 × 1 × 1 cm.Petra wants to build a large 5 × 5 ×
a. Copy and complete the coordinate tables below for the two equations y = x+ 4 and y = 3/2 x.b. On the same axes plot both graphs.c. One point belongs to both graphs. Explain how you can tell from
A line has the equation y = x+ 5.a. Which of the coordinates A, B, C and D, given below, lie on the line?A(1, 6)B(−2, 3)C(0, 5)D(−4, 1)b. Give the coordinates of another point that lies on the
A rectangle ABCD is shown on the axes below.Calculate the equation of the lines passing through the following vertices:a. A and Bb. B and Cc. A and C B -4 -3 -2 -1 6 fp 34 24 13 2 10 2
In the following questions, work out, just by looking at the equation, whether if plotted it would produce either a horizontal or vertical line.a. y = 6b. x = 3c. x = −3d. y = −2e. x = 6f. y =
By looking at the coordinates of some of the points on the line below, establish the equation of the straight line.By looking at the table it can be seen that the only rule that all the points have
A photocopier manages to print on average 2.5 sheets of paper per second. If t is the time in seconds and n the number of sheets printed:a. Write an equation linking n and tb. Pot a graph of n
An art gallery has a small plot of land with 10 sculptures.The sculptures are shown as points on the grid below.The distances are measured in metres.a. The gallery is building a rectangular enclosure
By looking at the coordinates of some of the points on the line below, establish the equation of the straight line.By looking at the table it can be seen that the only rule that all the points have
Two taxi firms operate different pricing policies on the amount they charge ($y) for the distance travelled (x km).Taxi firm A uses the equation y = 2x.Taxi firm B uses the equation y = x + 15.The
The coordinates of seven points are given below.Three of the points lie only on one line, three of the remaining points lie only on a second line.One point lies on both lines.P (4, 12)Q (2, 10)R (3,
Each of these sketches shows the plan view of a room and its actual dimensions.(i) Draw a scale diagram of each room using the scale suggested.(ii) Write the dimensions (in centimetres) on each
The grid below shows vertical lines V1, V2, V3 and V4 with equations x = 8, x = 16, x = 24 and x = 32 respectively. It also shows horizontal lines H1, H2, H3 and H4 with equations y = 6, y = 12,
Copy and complete the sentences below.a. There are ______ centimetres in one metre.b. A centimeter is ____ part of a metre.c. There are_____ metres in one kilo metre.d. A metre is _____ part of a
Copy and complete the sentences below.a. 1 m is cm, so to change from m to cm____ to change from cm to m____ .b. 1 m = mm, so to change from m to mm____ to change from mm to m____ .c. 1 cm = mm, so
Copy and complete the following.a. 5 cm2 = _____ mm2b. 8 m2 = _____ cm2c. _____ m2 = 7.2 had. 64 000 cm2 = _____ m2e. _____ cm2 = 5600 mm2
Calculate the actual length (in metres) represented by each of these lengths on a scale drawing. The scale of each diagram is given in brackets.a. 10 cm (1 : 50)b. 35 cm (1 : 30)c. 40
Change 5.84 km to metres.1 km = 1000 m, so multiply by 1000.5.84 × 1000 = 5840 m
Convert these to millimetres.a. 4 cmb. 6.2 cmc. 28 cmd. 1.2 me. 0.88 mf. 3.65 mg. 0.008 mh. 0.23 cm
A bathroom is in the shape of a cuboid with dimensions as shown.The door is 80cm × 200cm.Square wall tiles are 10cm × 10cm and come in boxes of 50.Each box costs $12.50.Assuming only whole boxes
Write an estimate for each of the following using a sensible unit.a. The area of a football fieldb. The area of a stampc. The area of a city
Calculate the length (in centimetres) that represents each of these actual lengths on a scale drawing. The scale of each diagram is given in brackets.a. 60 m (1 : 150)b. 120 m (1 :
Change 3640 mm to metres.1000 mm = 1 m, so divide by 1000.3640 ÷ 1000 = 3.64 m
Write an estimate for each of the following using a sensible unit.a. Your heightb. Your massc. The capacity of a cupd. The distance to the nearest towne. The mass of an orangef. The quantity of blood
Convert these to metres.a. 260 cmb. 8900 cmc. 2.3 kmd. 0.75 kme. 250 cmf. 0.4 kmg. 3.8 kmh. 25 km
In each of these pairs of lengths, the first is the length on a scale drawing and the second is the corresponding length in real life.Calculate the scale in each case.a. 20
This diagram shows the plan of a room drawn to a scale of 1 : 50.Calculate the area of the room in m2. A F LL B C D E
Change 0.872 tonne to kilograms.1 tonne = 1000 kg, so multiply by 1000.0.872 × 1000 = 872 kg
Convert these to kilometres.a. 2000 mb. 26 500 mc. 200 md. 750 me. 100 mf. 5000 cmg. 15 000 cmh. 75 600 mm
Change 4200 kg to tonnes.1000 kg = 1 tonne, so divide by 1000.4200 ÷ 1000 = 4.2 tonnes
Copy and complete the sentences below.1 kg is ____ g, so to change kg to g ____ and to change g to kg____ .
This sketch shows the dimensions of a room. Draw a scale diagram of the room with a scale of 1 : 150.1 : 150 means that the lengths on the diagram must be 150 times smaller than those of the actual
Draw a scale diagram of your classroom.You will need a tape measure, pencil and squared paper.
Change 2.4 litres to millilitres.1 litre is 1000 ml, so multiply by 1000.2.4 × 1000 = 2400 ml
Convert these to kilograms.a. 2 tonnesb. 7.2 tonnesc. 2800 gd. 750 ge. 0.45 tonnesf. 0.003 tonnesg. 6500 gh. 7 000 000 g
The ground floor of a building is drawn to scale. 1 cm on the drawing represents 10 m in real life.a. The length is 8.3 cm on the scale drawing. Calculate the length of the real building.b. The width
Change 4500 ml to litres.1000 ml is 1 litre, so divide by 1000.4500 ÷ 1000 = 4.5 litres
Convert these to millilitres.a. 2.6 litresb. 0.7 litrec. 0.04 litred. 0.008 litre
A diagram is drawn to a scale of 1 : 25. A line on the diagram has length 20 cm. What actual length does it represent?1 : 25 means that the actual lengths are 25 times bigger than those drawn.20 ×
Convert these to litres.a. 1500 mlb. 5280 mlc. 750 mld. 25 ml
Using an atlas or the internet, find a map of your local area.a. What is the scale of the map that the map uses?b. Choose two towns or cities on your map and estimate the actual distance between them
How much water is left in a 1-litre bottle after 400 ml is drunk?
A circular arena is being built. On a scale drawing, the radius of the arena is 8 cm. The radius of the actual arena is 120 m. Calculate the scale of the drawing.To calculate the scale factor of
How much water is left in a 1.5-litre bottle after 750 ml is drunk?
A landscape artist makes a scale drawing of a public garden. The scale used is 1 cm to represent 10 m.a. The width of the garden on the scale drawing is 18.2 cm. Calculate its real width. 1 cm
A tile pattern is made of two different coloured tiles, red and blue.The ratio of red : blue tiles is 50 : 75. Write this ratio in its simplest form.The highest common factor of both 50 and 75 is 25,
A pile of bricks has a mass of 16 kg. 9450 g of bricks are removed. What mass is left?
I am travelling to a city 250 km away.I take a break after 173 000 m. How many kilometres do I have left to travel?
A cyclist travels for five days and covers 375 000 m in total.He covers 67 km, 78 km, 46 km and 89 km on the first four days.How far does he travel on day 5?
The masses of four containers loaded on a ship are 28 tonnes, 45 tonnes, 16.8 tonnes and 48 500 kg. What is the total mass in tonnes?
Three test tubes contain 0.08 litre, 0.42 litre and 220 ml of solution.a. What is the total volume of solution in millilitres?b. How many litres of water need to be added to make the volume of
A school has 40 teachers and 720 students.Write the teacher : student ratio in the form 1 : n.The teacher : student ratio is 40 : 720.Therefore to write 40 : 720 in the form 1 : n and keep the ratios
A company sends the same parcel to each of its customers.On average the company sends out 150 parcels a week.Each parcel uses 40 cm of string.A ball of string costs $2.25 and has string wrapped
A heater uses 3 units of electricity in 40 minutes.How many units does it use in 2 hours?
The ratio of girls to boys in a class is 6 : 5.There are 18 girls. How many boys are there?
Copy these sets of equivalent ratios and fill in the blanks.4 : 5 = 8 :____ = ____: 50 = 12 :____.
A school has 20 teachers and 480 students.What is the teacher : student ratio in its simplest form?
A machine prints 1500 newspapers in 45 minutes.How many does it print in 12 hours?
Sand and gravel are mixed in the ratio 4 : 3 to make ballast. 80 kg of sand is used. How much gravel is used?
Copy these sets of equivalent ratios and fill in the blanks.7 : 2 = 14 :____ = ____: 10 = 49 :____.
A college has 250 staff and 3500 students.What is the staff : student ratio in its simplest form?
A bricklayer lays 1200 bricks in an average 8-hour day.How many bricks does he lay in a 40-hour week?
A paint mix uses blue and white in the ratio 3 : 10.6.6 litres of blue paint are used. How much white paint is used?
The teacher : student ratio in a school is 1 : 18.There are 25 teachers. How many students are there?The ratio is given in the form 1 : n so the values need to be multiplied to keep the ratio
A machine for making bread rolls makes 1500 rolls in 20 minutes.How many rolls will it make in 3 hours?Let x be the number of rolls made in 3 hours.The ratios have to be equivalent. You multiply the
Copy these sets of equivalent ratios and fill in the blanks.8 : 5 =____ : 50 = 32 : ____= 4 :____.
A town in America has 2400 families and 4200 cars.What is the family : car ratioa. In its simplest formb. In the form 1 : n.
Gaby uses the following recipe to make 12 chocolate shortbread biscuits.a. How much of each quantity does Gaby need to make 15 biscuits?b. If Gaby only has 200 g of plain flour, what is the maximum
A machine puts tar on a road at the rate of 4 metres in 5 minutes.a. How long does it take to cover 1 km of road?b. How many metres of road does it cover in 8 hours?
A necklace has green and blue beads in the ratio 2 : 3.There are 24 green beads on a necklace. How many blue beads are there?
Copper and nickel are mixed in the ratio 5 : 4.48 g of nickel is used. How much copper is used?Let x grams be the mass of copper needed.The ratios have to be equivalent. You multiply the mass of
An alloy contains copper and tin in the ratio 3 : 1.40 g of tin is used to make the alloy.How much copper is used?
The pie chart below shows the proportion, in degrees, of the different colour hair of pupils in a class.Write the ratio of Blonde : Brown : Black in its simplest form. 180° Hair
A tile pattern is made up of three different coloured tiles, red, blue and yellow as shown.a. Write the ratio of yellow : blue : red tiles in its simplest form.b. If a complete tile pattern has 320
Three colours of paint, white, blue and orange, are mixed in a certain ratio. Part of this ratio is shown below as a ratio and part shown as a pie chart in degrees.White : Blue :
The size of the three angles, x, y and z, of a triangle are in the ratio 1 : 3 : 5 respectively.Calculate the size of each of the angles.
The three distance–time graphs below show the motion of a car over time.Assuming the three graphs are drawn to the same scale, which one shows the car travelling the slowest? Justify your answer.
In a batch of 10 dozen eggs, 25 are cracked.a. What is the ratio of cracked eggs to un-cracked eggs in:(i) Its simplest form(ii) In the form 1 : n.b. If this ratio is the average for all batches, how
A stadium is holding a festival. When the gates are opened, the total number of people in the stadium is recorded every 20 minutes over a 3-hour period. The results are shown in the table.a. Plot a

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