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mathematics
cambridge checkpoint lower secondary mathematics

Cambridge Checkpoint Lower Secondary Mathematics Student's Book 7 3rd Edition Frankie Pimentel, Ric Pimentel, Terry Wall - Solutions

Multiply the following fractions, simplifying your answer where possible. a.b.c.d.e. 2/10 X
Complete the following table showing the equivalent fractions, decimals and percentages. Fraction 12 14 21 50 Decimal 0.2 0.375 0.64 Percentage 10% 17.5% 13.2%
a. The rectangle below has the dimensions shown.Explain why the area of the rectangle can be calculated by the calculation (7.1 × 10) + (7.1 × 2). b. Work out the area of the rectangle below. Show your working clearly. Is there a different calculation you could have used? Which calculation
Write the decimal 0.7 as a fraction in its simplest form.By entering 0.7 into a place value table we get:The ‘7’ is worth seven-tenths. As a fraction this can therefore be written as 7/10. Units 0 Tenths 7
Eight cards are shown below. Match each fraction with its reciprocal. NIW 5/5 3 115 5/3 5 WIN
The following cards show fractions, decimals and percentages. a. Group together equivalent fractions, decimals and percentages.b. One card has no equivalent value on the other cards.(i) Which card is this?(ii) Write down the missing equivalent values to this card. 0.92 17 20 23 25 160% 185%
Write the decimal 0.625 as a fraction in its simplest form. By entering 0.625 into a place value table we get Six-tenths, two-hundredths and five-thousandths is equivalent to 625-thousandths. As a fraction this can therefore be written as 625/1000. So, 625/1000 can be simplified to 5/8, by
The pyramid opposite has some mixed numbers already written in some of the blocks.The pyramid is constructed in a way such that the fractions in the blocks in the top two rows are the sum of the two fractions in the blocks directly beneath them.Calculate the missing fractions. Ni- 미니 2 m100
Work out the following. a. b. c. d. e. f. 15×12×1 4
Sadiq spends 1/5 of his earnings on his mortgage. He saves 2/7 of his earnings. What fraction of his earnings is left? Show all your working clearly.
The addition below sees three mixed numbers being added together. a. Describe the pattern from one fraction to the next.b. Calculate the sum of the first five mixed numbers in this sequence. 11/2+2 +4 4 8
Divide the following fractions, simplifying your answer where possible. a.b.c.d.e. Z÷2
The pyramid below also has some mixed numbers already written in some of the blocks. As in question 2 each block has a fraction which is the sum of the two fractions directly beneath it. a. Which block(s) of a, b, c or d can only have one possible fraction as an answer? Justify your
Two athletes drink different fractions of liquid from identical water bottles. Athlete A drinks 11/24 of his bottle, whilst athlete B drinks 9/16 of her bottle. Show all your working clearly. Which athlete has drunk the most? Justify your answer.
A fraction in its simplest form and its equivalent decimal are shown below. However, most of the numbers are covered. The hidden digits, in no particular order, are as follows: a. Explain why the number before the decimal point must be the zero.b. Explain why both digits in the units
Convert each of the following percentages to a fraction.a. 152.5% b. 30.25% c. 205.2% d. 10.05%
The numerators of two fractions are hidden as shown. The sum of the two fractions is 23/40. Calculate the value of both numerators. Show all your working clearly. 8 + | 5 23 40
A farmer uses five out of seven equal strips of his land for cereal crops and 1/8 of his land for root vegetables. What fraction of his land is available for other uses? Show all your working clearly.
The numerators of these two fractions are hidden as shown. The difference of the two fractions is 31/60. Calculate the value of both numerators. Show all your working clearly. 12 5 31 60
Without working out the following divisions, decide whether each statement is true or false. Justify your answer each time. a.b.c.d.e. 3x3> 3
Three identical fruit juice dispensers P, Q and R in a hotel restaurant have the same amount of juice at the start of breakfast. The fraction of juice left at the end of breakfast in each dispenser is given below. a. Which dispenser has the most juice left at the end? Justify your
Order the following fractions from the smallest to the largest د 113 N د
Convert 19/100 to a decimal. As 19 is being divided by 100, 19/100 can be written as 0.19.
Look at the four calculations below. a. Which of the four calculations will produce a different answer? Justify your answer.b. Write another fraction calculation which will produce the same answer as the other three. Justify your choice. ∞lw X 7|7 •+• WIN 2/3 X ∞ 1 X 00|N
Multiply the following fractions 3/8 × 4/7. Multiplying the numerators together and multiplying the denominators together gives:The answer can be simplified as both numerator and denominator are divisible by 4. Therefore 12/56 = 3/14.It is possible to make the calculation easier by simplifying the
Multiply the following fractions 3/7 × 4/5. Multiplying the numerators together and multiplying the denominators together gives: 3 4 3x4 3 x 4 12 75 7x535
An artist wants to mix two paints X and Y together to create a new colour. He knows that to get the colour he wants he must add between 7/18 of tube X to 5/9 of tube Y. Give two different fractions of tube X that he can add.
Convert 8/25 to a decimal. As 25 is a factor of 100, by multiplying both the numerator and denominator by 4, the fraction 8/25 can be written in an equivalent form as 32/100. Therefore 8/25= 32/100=0.32.
Multiply the following fractions 8/15 × 5/32. The multiplication is difficult to do without simplifying first. Here both numerator and denominator are divisible by 5.But both numerator and denominator are also divisible by 8. Therefore 8/15 × 5/32 can be simplified first to 1/3 × 1/4 =
Work out the following division, 1/3 ÷ 2/5. The division can be written as a multiplication by multiplying the first fraction by the reciprocal of the second one. Therefore: OGIN || 13 X 5/2 II 5/6
Work out the following division, 5/8 ÷ 3/4.Changing the division to a multiplication becomes 5/8 × 4/3. As before this can be simplified before multiplication as 4 is a factor of both the numerator and denominator. 1 516 || X 10 N II X 10102 2
A family is driving to a small village. The distance of the village from their current position is between 18 1/5 km and 18 2/7 km away.Can the village be 18 12/35 km away? Justify your answer.
The diagrams below show three different spinners. a. Which spinner(s) show equally likely outcomes? Justify your answer.b. For the spinner(s) with equally likely outcomes, state the probability of getting each colour. A B
A spinner has four colours as shown.a. List all the possible outcomes.Yellow, Blue, Red and Greenb. Explain whether the outcomes are mutually exclusive. Yes, they are mutually exclusive outcomes, because they cannot occur at the same time. For example, the spinner cannot land on both yellow and red
Work out the following without a calculator.0.5 × 9 × 10It is possible to carry out the multiplication in the order it is written. So, as 0.5×9=4.5 the calculation becomes 4.5×10=45.However, as multiplication is commutative, it can be done in a different order.You may find it easier to do the
A board game states that to start playing, a player must roll a 6 with the dice.a. What are the possible outcomes for a player when rolling a dice?b. What is the probability that the player rolling the dice will start the game on their first attempt?
Carla is playing a game of football with her team. She says that as there are only three outcomes – win, lose or draw – the probability of her team winning is 1/3 . Explain whether Carla is right or wrong.
A child goes into a tropical fish shop to buy a fish from the tank shown below. a. Explain why the probability of picking a red fish may not be 6/15 .b. What condition is necessary for the probability of picking a red fish to be 6/15 ? O
Three different medicine manufacturers test the effectivess of their own brand of medicine for curing patients of a certain illness.The results of the tests are as follows:• Manufacturer A tested 1 patient and the patient recovered. They claim that their medicine is effective in 100% of cases.•
a. List five different weather outcomes possible for tomorrow. Rain, Wind, Sun, Warm, Coldb. Explain whether the weather outcomes are mutually exclusiveNo, they are not mutually exclusive because they can happen at the same time, for example a day can be both rainy and cold, or windy, sunny and
An archer fires an arrow at the target to the right.a. The archer hits the target with his first arrow.List the possible outcomes.b. Are the outcomes you listed in part (a) equally likely? Justify your answer.c. Are the outcomes listed in part (a) mutually exclusive? Justify your answer.d. The
A school offers its students the option of two sports to play, volleyball (V) and basketball (B). Below is a Venn diagram showing the probability of students who choose each. a. What is the probability of a student not playing either sport?b. A student is chosen at random. What is the
Three cards, with the numbers 1, 2 and 3 are turned over and shuffled as shown. A card is then picked at random.a. Calculate the theoretical probability of picking the 2.b. Calculate the theoretical probability of not picking the 2. There are two ways in which this can be calculated.As
It is not known whether a coin is biased or not. It is flipped three times and the results shown below. a .Is the coin biased? Choose one of the following answers: Yes___No___Not able to tell yet____b. Justify your answer to part (a) ❤❤❤
A school hockey team plays a match. The probability of their winning is estimated to be 0.5 and the probability of losing 0.3. Explain why the probability of the team drawing must be 0.2.In a match the only outcomes are winning, losing or drawing and these outcomes are mutually exclusive (i.e. a
In a school sports day, the number of students taking part in three of the field events are shown in the two-way table below. a. A student is picked at random. What is the probability of picking one who does the long jump?b. List the different possible outcomes displayed in the table.c. Are
A biased dice is rolled.a. Explain why the theoretical probability of getting a 6 is not likely to be 1/6. The numbers on a biased dice are not equally likely, therefore the probability of getting a 6 cannot be calculated using the formula for theoretical probability.b. How can the probability of
A gameshow uses 10 numbered cards (1–10). The cards are arranged in a line, facing downwards. A card is then turned over one at a time. Before each card is turned over the contestant has to predict whether the next card to be turned is greater than five or not.The diagrams below show the game
a. For the spinner shown calculate the probability of getting:(i) Yellow.(ii) Light blue.(iii) Any blue.b. The spinner is spun 60 times. (i) Estimate the number of times you would expect to get the colour red.(ii) Would you definitely get red that number of times? Explain your answer.
Count the number of faces, edges and vertices on each of the following shapes. Number of faces = 6 Number of edges = 12Number of vertices = 8Number of faces = 3 (2 flat and 1 curved) Number of edges = 2 Number of vertices = 0 A cube 1 -----)
For the pyramids below count the number of faces, edges and vertices.a. Square-based pyramid b. Hexagonal-based pyramid
In the following table several cuboids are drawn. Each cuboid is made from 1cm3 cubes. For each cuboid write down the length, width and height and work out its volume. a e Cuboid Length Width Height Volume
Calculate the volume of the composite shapes in Questions. 4cm 6cm 2 cm 2 cm 8cm 6 cm
Calculate the surface area of the following cuboids. a.b.c. 10 cm 8cm 5 cm
Calculate the volume of this ‘n’-shaped prism. The shape can be broken down into three cuboids, labelled A, B and C. The volume of the prism is therefore the sum of the volumes of the three cuboids. Volume of cuboid A=2×8×5=80 cm3 Volume of cuboid B=3×8×3=72cm3 Volume of
Calculate the volume of the composite shapes in Questions. 5 cm 15 cm 5 cm 5cm 5 cm 5 cm
The net of a cube is shown below. Calculate a. The surface area of the cubeb. The volume of the cube. 5cm
Calculate the surface area of this cuboid. There are two ways of solving this problem. Method 1: By calculating the area of each rectangular face:As the front is the same as the back, the top the same as the bottom and the two sides equal to each other, the area can be worked out in
Sketch and name each of the three-dimensional shapes with the following properties: a. Only one face and no edges or vertices. b. Two faces, one edge and one vertex. c. Five faces, nine edges and six vertices.
a. Describe in words the relationship between the length, width and height of a cuboid and its volume. b. Write the relationship you described in part (a) as a formula.
Calculate the volume of each of these cuboids, where L = length, W = width and H = height. Give your answers in cm3.a. L=4 cm W=2cm H=3cm b. L=5 cm W=5cm H=6cm c. L=10cm W=10mm H=4cm d. L=40cm W=0.2m H=50cm e. L=50mm W=30cm H=0.1m Length Height Width
Calculate the volume of the composite shapes in Questions. 8cm 8 cm 8 cm 4 cm 4cm
Four different types of pyramid are shown below: a. It is stated that for every pyramid, there is always an even number of edges.(i) Is this true for the four different pyramids above?(ii) Explain whether you think the statement is always true. Give a convincing reason for your answer.b. It is
Two friends are discussing the properties of three-dimensional shapes. One states that if two different three-dimensional shapes have the same number of faces, then they must have the same number of edges. Prove convincingly that this is not true, by sketching two three-dimensional shapes with the
This cuboid has a volume of 360 cm3. Calculate the length (in cm) of the edge marked x. 5cm 12 cm x cm
A cube has an edge length of x cm.a. Show that the total surface area (A) can be calculated using the formula A=6x2. b. Use the formula to calculate the total surface area of a cube of edge length 10 cm.
The volume of this cuboid is 180cm3. Calculate the length (in cm) of the edge marked y. 6cm 6cm ycm
a. This cuboid has volume 768 cm3 and the edges marked a are equal in length. Calculate the value of a. b. In another cuboid of length 12cm and volume 768 cm3, the width and height are not equal. Give a pair of possible values for their length. acm acm 12 cm
Design your own composite shape which can be split into two cuboids, with a total volume of 200cm3.
For the cuboid drawn below:a. Draw two possible nets for the cuboid b. Calculate the total surface area of both nets, showing clearly the dimensions of each part of the net. 12 cm 3 cm 15 cm
A cube has an edge length of 3 cm.a. Calculate its total surface area. b. If the edge length is doubled, how many times bigger does the surface area become? c. If the edge length of the original cube is trebled, how many times bigger does the surface area become? d. Predict, without
The cuboid below has dimensions as shown: A cuboid with a depth of 4 cm but a length and width of x cm is cut out from one corner of the original cuboid as shown. The remaining shape has a volume of 199 cm3. Calculate the value of x. Show all your working clearly. 8cm 4cm 10 cm 8cm xcm x cm 4
Design your own composite shape which can be split into three cuboids, with a total volume of 500 cm3.
A tank of water in the shape of a cuboid has a length of 50 cm, a width of 25 cm and a height of 20 cm. The depth of water in the tank is 12cm as shown below. a. A cube of side length 10cm is placed at the bottom of the tank and the water level rises to a depth d cm as shown. Calculate
A room in the shape of a cuboid is shown below. The room has two identical square windows and a door with the dimensions given. Vladimir wants to decorate the room, including the ceiling, with two coats of paint (he will not paint the floor, windows or door). If each paint pot claims it can
Four cards are arranged below to form a four-digit number. a. Arrange the four cards so that the number is:(i) Divisible by 5 (ii) Divisible by 9 (iii) Divisible by 6 (iv) Divisible by 8. b. In one of the questions in part (a) the order of the cards does not matter. Which
Copy the following table and tick the squares when the number is divisible by a number written along the top. One example has been started for you. a b с d e 50 270 1120 135 302400 2 ✓ 3 4 5 ✓ 6 7 8 9 10 25 100
Type this formula into cell A1 in a spreadsheet: = RANDBETWEEN(0,500).This will generate a random integer (whole number) between 0 and 500. Copy the formula down to cell A20 to generate 20 random numbers in the first column of the spreadsheet, for example as shown here.a. Use divisibility tests to
Three cards each have a different factor of 18 written on them. Two of the numbers are shown, the third is hidden. If the number on the third card is not a multiple of 3, what must it be? 6 □■
Two students, Beatriz and Fatou, are discussing the relationship between a cuboid’s volume and its total surface area. Beatriz states that cuboids with the same volume must have the same surface area. Fatou thinks Beatriz is wrong. Which student is correct? Give a convincing reason for your
Find the highest common factor of the following numbers:a. 8, 12 b. 10, 25 c. 12, 18, 24 d. 15, 21, 27 e. 36, 63, 108
The factors of 24 are arranged in a 3×3 grid, leaving one square blank. The totals of each row and column are shown below. a. Explain why the number 24 must appear in the bottom left square of the grid. b. Explain why the blank square must appear in the top row. c. Copy and complete
Find the lowest common multiple of the following numbers: a. 6, 14 b. 4, 15 c. 2, 7, 10 d. 3, 9, 10 e. 3, 7, 11
Five cards are numbered with a different number from 1 to 10 as shown below. One card is covered. A card is chosen at random. What could be the number on the covered card if: a. The probability of picking an even number is 0.4b. The probability of picking a number less than five is 20%c.
The lowest common multiple of two numbers is 60. a. What two numbers could they be? b. Is another pair of numbers possible? If so, what numbers are they?
In one school, students have the option of studying either French (F) or Spanish (S) or neither. The incomplete Venn diagram below shows the number of students studying each language. A student is chosen at random. If the probability of choosing a student who studies French is 1/4,
a. Write down at least 15 words which are used in everyday language to describe the likelihood of an event happening. b. Draw a probability scale similar to the one above. Write each of your words from part (a) where you think they belong on the probability scale.
You will need isometric dot paper for this question. Part of a pattern using four rhombuses is drawn on isometric dot paper below. By drawing two more rhombuses, complete the pattern so that it has a rotational symmetry of order 3. :: .....
The letters T, C and A can be written in several different orders. a. Write the letters in as many different orders as possible. b. If a computer writes these three letters in a random. order, calculate the probability that:(i) The letters will be written in alphabetical order.(ii) The
500 balls numbered from 1 to 500 are placed in a large container. A ball is picked at random.a. Are the numbers an example of equally likely outcomes? Justify your answer.b. Calculate the probability that the ball:(i) Has the number 1 on it(ii) Has one of the numbers 1 to 50 on it (iii) Has
In the magic square on the right, the numbers 1–9 are arranged so that all the rows, columns and main diagonals add up to the same total.a. Copy and complete the magic square by filling in the missing numbers.b. Use your answer to (a) to complete a magic square for the numbers 11–19. c.
Round the following numbers to one decimal place.a. 6.37b. 4.13c. 0.85d. 8.672e. 1.093f. 0.063
(i) Estimate the answer to the following calculations.(ii) Work out the answer to each calculation. a. $27.43 + $89.29 b. $100 − $57.57 c. $4.62 + $0.82 + $105.62 d. $500 − $46.30 − $3.88 e. $26.43 + $102.11 − $37.28
Multiply the following numbers by 10.a. 630 b. 4.6 c. 0.84 d. 0.065 e. 1.07
In each of the following multiplications:(i) Estimate the answer(ii) Multiply each pair of numbers using either long multiplication or the grid method. a. 2.7 × 31 b. 4.6 × 21 c. 5.7 × 69
Round the following numbers (i) to one decimal place and (ii) to two decimal places.a. 4.383 b. 5.719 c. 5.803 d. 1.477 e. 3.999 f. 6.273
A triangle is drawn inside a rectangle as shown. If the area of triangle 1 is half the area of triangle 2, calculate the length x. 6 cm x cm 12 cm 2
A family of four people check in their suitcases at the airport. The weights of the four cases are 18.5kg, 26kg, 15.4kg and 23.7kg.a. Calculate the total weight of the four cases. b. The weight limit for the four cases is 100kg. Calculate how much extra weight the family could have carried.
Multiply the following numbers by 102.a. 45 b. 7.2 c. 0.96 d. 0.0485 e. 6.033
A bridge over a road is 3.2m high at its lowest point. A lorry 2.65m high passes under the bridge. Calculate the height of the gap between the bridge and the lorry, giving your answer in centimetres. CO LOW BRIDGE 3.2M

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