Questions and Answers of Cambridge Checkpoint Lower Secondary Mathematics

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. 36.1 × 21 b.
a. Give one advantage and one disadvantage of using a questionnaire for collecting data. b. Give one advantage and one disadvantage of using an interview for collecting data.
Round the following numbers (i) to two decimal places and (ii) to three decimal places.a. 0.5682 b. 3.4765 c. 8.8467 d. 3.9995
Salma uses her calculator to work out an answer. Salma writes down the answer correct to two decimal places as 3.46. Below are four possible calculator screens. Which one could not be the answer on
A boy is 81.4 cm tall. He needs to be at least 1m tall before he can go on a particular ride at a theme park. How much more does the boy need to grow before he will be allowed on the ride?
Divide the following numbers by 10.a. 680 b. 72 c. 8.9 d. 0.64 e. 0.054
Without working out the exact answers, state which of the following calculations must definitely be wrong. Justify your answers.a. 72.4 × 15 = 1086 b.
Divide the following numbers by 102.a. 3500 b. 655 c. 5.62 d. 0.8 e. 0.034
The formula for the area (A) of a trapezium is given as A = 1/2 (a+ b)h, where a, b and h are the lengths shown in the diagram.Calculate the area of the trapezium if a = 8 cm, b = 13cm
A charity holds a raffle. Each raffle ticket costs $4.50. They manage to sell 4238 raffle tickets. The first prize of the raffle is $10 000 and there are also two second prizes of $2500 each.
A student wants to work out the answer to the following calculation: 3 + 5 × 4 He writes the following steps:3 + 5 × 4 = 8×4 = 32a. (i) Explain what mistake he has made.(ii) What should the
Each stage of this calculation chain involves a multiplication or division by a power of 10. Write down the missing powers of 10. The first has been done for you. 5 x10² 500 a -50 000- 5000- b
A shop is offering a promotion on one of its products. Originally a pack of two items could be bought for $13.22. With the promotion, a pack of three items can be bought for the same amount. a.
A pizzeria offers the following pizzas for sale. Margherita $6.25 La Reine $8.15Veneziana $6.85 Fiorentina $7.95 A group of friends order one Margherita pizza, two La Reine
Find the value of the following.a. 46 ×103 b. 6.4 ÷ 102 c. 6.8 × 103 d. 46 ÷ 103 e. 3.8 × 104 f. 0.0084 × 105 g. 0.7 × 106 h.
In each of the following divisions:(i) Estimate the answer (ii) Work out the answer. a. 52.5 ÷ 15 b. 96.0 ÷ 40 c. 93.5 ÷ 17 d. 97.2 ÷ 12 e.
Two blocks of wood A and B are joined as shown below. The length of block A is 35.926 cm to 3 decimal places. The total length of A and B is 50.00 cm to 2 decimal places. If the length of
Starting with 0.2, four operations involving powers of 10 are used to give a final answer of 2, as shown in the calculation chain below. The four operations used are as follows ÷102
Eduardo collects data about the number of people in cars passing his house one afternoon. He presents the results both as a pie chart and a waffle diagram as shown. Explain whether the diagrams are
In a race, six runners complete 100m in the following times:10.402s 10.395s 10.382s 10.374s 10.404s 10.406sWhich times are the same when given to two decimal places?
Work out the value of the letter in each of the following. a. 31 × x = 37.2 b. y × 14 = 86.8c. p × 8 = 65.6d. 85.1 ÷ x = 37e. 83.3 ÷ a = 17f. 9.81 ÷ d = 9
Two cubes P and Q are placed on top of each other. The volume of P is eight times the volume of Q. If the combined volume of the two cubes is 243 cm3, calculate the side length of each of the two
A carpenter has a plank of wood of length 3.52m. He cuts the wood in to 7 pieces of equal length. Calculate the length, in cm, of each piece correct to: a. 1 decimal place. b. 2 decimal
A four-digit number is given below. Unfortunately one of the digits is covered with ink. a. (i) If the four-digit number is divisible by 4, what digit can the missing one be? (ii) Justify
A class of students is asked what their favourite sport is. The results are shown in the table.A student is chosen at random. What is the probability that: a. It is a girl b. It is a
A football team scores these numbers of goals in its matches. 1 3 2 4 4 2 2 5 2 3 Calculate the mean number of goals scored per match. The mean number of goals scored per match is:
The reading age of a book is based mainly on the average length of the words used in the book. The mean, median, mode and range of word length are calculated for three different sections of the book;
Two discus throwers keep a record of their best throws (in metres) in the last ten competitions.As a coach, you can only choose one of them for the next competition. Which would you choose?
This frequency table shows the numbers of fish caught by the competitors in the first two hours of a fishing competition.a. Calculate: (i) The mean number of fish caught (ii) The modal
Find the mean, median, mode and range of each set of numbers. a. 1 1 2 3 3 4
The numbers of passengers in cars and minibuses driving past a school gate one Wednesday morning were recorded.The results of the survey are shown in the table. The total number of vehicles
Two basketball teams A and B each play seven matches against various opponents. The number of points they scored in each match are given in the table below. Calculate the mean, median and modal
a. A school carries out a survey to find out how many siblings the students have. Some students are chosen and the results are shown in the frequency table.Calculate the mean, median, mode and range
Five cards are numbered as shown. A sixth card is covered. a. Calculate the mean, median and mode of the five known cards. b. If the sixth card has a number greater than 15, which
Measure the height of the students in your class.a. Find the mean, median, mode and range of heights of the students. b. As one of the group, are you average or not? c. Give mathematical
The year of manufacture of five cars parked in a car park are as shown below. One of the cars drives off. If the mean year of manufacture of the remaining four cars is 1990, work out which
A factory makes cans of tomatoes. On average, a full can should have a mass of 410g. A sample of 20 cans is tested. The masses are shown below. Does the canning machine need to be adjusted? Give
The mean mass of the 15 players in a rugby team is 85.2kg. The mean mass of the team plus a substitute is 85.4kg. What is the mass of the substitute?
After eight matches a basketball player has a mean of 27 points. After ten matches his mean was 31 points. How many points in total did he score in his last two matches?
Copy the following diagram and reflect the quadrilateral in the mirror line shown. B -4-3-2 A 7 6 5 4 3 2 1 -1.0 4 -2 3- -4- -5 D C 1 2 3 4 5 6
In each of the diagrams below, compare shape B with shape A. a. Decide whether B is an enlargement of A. If not explain why not. b. If B is an enlargement of A, calculate the scale factor
a. (i) Write down five possible numbers with a median of 10 and a range of 12. (ii) Explain if a different combination of five numbers is possible. b. (i) Write down five possible numbers
In each of the following questions, copy the grid and the object. a. Rotate the object by the angle and direction stated about the centre of rotation O. b. Label your image in each case P.
Copy each of the diagrams below and enlarge each of the objects by the given scale factor of enlargement. Scale factor of enlargement of 2
The following set of five numbers has an interesting property in that the mean = median = mode. 11 14 14
Triangle Y is an enlargement of triangle X. Calculate the scale factor of enlargement. Each of the lengths of triangle Y are three times that of triangle X. Therefore the scale factor of
Copy and complete this classification table of the symmetry properties of different types of shapes. Square Rectangle Rhombus Parallelogram Shape Isosceles trapezium Kite Equilateral
Copy the following diagram and reflect the shape in the mirror line shown. A 7 6 L 4 3 21 C -4 -3 -2 -1.0 1 2 3 415 D 1 -~- B -m 4 5 -6 7 -00
For each of these capital letters, write down (i) The number of lines of reflection symmetry (ii) The order of rotational symmetrya.b. c.d.e.f.g.h. A
In each of the following questions, copy the grid and the object. a. Rotate the object by the angle and direction stated about the centre of rotation O. b. Label your image in each case P.
In each of the diagrams below, compare shape B with shape A. a. Decide whether B is an enlargement of A. If not explain why not. b. If B is an enlargement of A, calculate the scale factor
Copy each of the diagrams below and enlarge each of the objects by the given scale factor of enlargement. Scale factor of enlargement of 4
Copy the following diagram. a. Reflect triangle ABC in the mirror line M1 and label it A’B’C’. b. Reflect triangle A’B’C’ in the mirror line M2 and label it
Copy each of these diagrams onto squared paper. Draw in additional lines so that the final shape has the symmetry stated. a. 1 line of reflection symmetry. Rotational symmetry of order 1.b. 4
In each of the following questions, copy the grid and the object. a. Rotate the object by the angle and direction stated about the centre of rotation O. b. Label your image in each case P.
Copy each of the diagrams below and enlarge each of the objects by the given scale factor of enlargement. Scale factor of enlargement of 2
In each of the diagrams below, compare shape B with shape A. a. Decide whether B is an enlargement of A. If not explain why not. b. If B is an enlargement of A, calculate the scale factor
The diagram below shows a polygon ABCD and its position A’’’B’’’C’’’D’’’ after three reflections. Three mirror lines M1, M2 and M3 are shown. Work out which order the
In each of the following questions, copy the grid and the object. a. Rotate the object by the angle and direction stated about the centre of rotation O. b. Label your image in each case P.
Make four copies of this 4 × 4 grid. Shade in squares so that the final shape has: a. 4 lines of reflection symmetry and rotational symmetry of order 4 b. 0 lines of reflection
In each of the diagrams below, compare shape B with shape A. a. Decide whether B is an enlargement of A. If not explain why not. b. If B is an enlargement of A, calculate the scale factor
Copy each of the diagrams below and enlarge each of the objects by the given scale factor of enlargement. Scale factor of enlargement of 3
Three shapes formed of squares are shown below: Arrange the three pieces together to form a shape with:a. Four lines of reflective symmetry and a rotational symmetry of order 4 b.
In each of the following questions, copy the grid and the object. a. Rotate the object by the angle and direction stated about the centre of rotation O. b. Label your image in each case P.
Copy each of the diagrams below and enlarge each of the objects by the given scale factor of enlargement. Scale factor of enlargement of 5
In each of the diagrams below, compare shape B with shape A. a. Decide whether B is an enlargement of A. If not explain why not. b. If B is an enlargement of A, calculate the scale factor
In each of the following questions, copy the grid and the object.a. Rotate the object by the angle and direction stated about the centre of rotation O. b. Label your image in each case P.
In each of the diagrams below, compare shape B with shape A. a. Decide whether B is an enlargement of A. If not explain why not. b. If B is an enlargement of A, calculate the scale factor
Copy each of the diagrams below and enlarge each of the objects by the given scale factor of enlargement. Scale factor of enlargement of 2
Ibrahim and Isabel are discussing the diagram below. Ibrahim says that the square P has been rotated 180° about the origin to map on to square Q. Isabel says that square P has been reflected in a
A quadrilateral PQRS is drawn on a coordinate axes. The coordinates of each of the vertices are as follows: P(3, 8) Q(2, 4) R(7, 2) S(7, 6) The shape is then enlarged by a
Below are six cards, each with a number on them. Select three cards each time. Use multiplication or division to produce as many correct calculations as possible. -3 JODODE 6 12 2 -18 -9
a. Copy and complete the multiplication table below. One is completed for you.b. Using the table above, rewrite the multiplications to form a division. For example, −24 ÷ 12 = −2
Work with a friend and without a calculator. Calculate the answers to the following questions.a. 38 + 12 b. 45 + 25 c. 66 + 34 d. 23 + 27 e. 59 + 31 f. 34 − 12 g. 45
Multiply the following pairs of numbers. a. 150 × 5 b. 14 × 70 c. 16 × 40 d. 130 × 50 e. 12 × 30 f. 180 × 7 g. 90 × 16 h. 70 × 330 i. 24
At the start of a journey a car’s distance meter reads 1421km. A family set off on a journey that is 289km long.
Divide the following pairs of numbers.a. 124 ÷ 4 b. 168 ÷ 8 c. 2400 ÷ 6 d. 320 ÷ 80 e. 4900 ÷ 70 f. 560 ÷ 8 g. 440 ÷ 44 h. 3600 ÷ 60 i. 4800 ÷ 80
A 3 × 3 magic square contains each of the numbers 1 – 9 arranged in such a way that each row, column and diagonal add up to the same total. a. Copy the 3 × 3 grid opposite and enter the
State the answer to each of the following calculations and explain how the above calculation was used to work it out.36 × 18 = 648 a. 648 ÷ 18 b. −36 × 18 c. 18 × 18 d.
A bar of chocolate is made of square-shaped pieces. The bar is four pieces wide and 12 pieces long. Amir needs 336 pieces to make some chocolate cakes. How many bars should he buy?
What will the car’s distance meter read at the end of the journey? a. 123 + 27 b. 334 + 56 c. 67 + 153 d. 42 + 478 e. 567 + 23 f. 43 − (−17) g. 176 −
A child buys five packets of sweets each containing 80 sweets. How many sweets does he buy in total?
A glass with capacity 230ml is filled from a jug containing 725ml of water. How much water is left in the jug after: a. One glass of water is poured b. Two glasses of water are
For a school concert 360 chairs are arranged in rows of 20. How many rows are there?
a. Copy and complete the following table to classify regular polygons and their symmetry properties.b. What do you notice about the relationship between the number of sides a regular polygon has, the
A tricycle is like a bicycle, but with three wheels. A shop has a stock of 19 tricycles and 112 bicycles. How many wheels are there in total?
The following diagram shows two congruent isosceles right-angled triangles. The two triangles can be arranged side by side to form a larger isosceles right-angled triangle as shown: Using only
Copy and complete the following table to classify the properties of quadrilaterals. The first line has been started for you. Opposite sides equal in length All sides equal in length Rectangle
The geometric pattern below shows a square and equilateral triangle inside a circle. All their vertices are on the circumference of the circle. The square and equilateral triangle have a common point
A lift states that the maximum load it can carry is 500kg. Six people want to get in the lift. The masses of the first five people are 62kg, 88kg, 79kg, 91kg and 86kg. The sixth person
The diagram below shows two equilateral triangles. Which quadrilateral(s) can be formed by arranging the two triangles so that their sides are fully in contact? Use a sketch to justify your
The geometric pattern below shows a regular hexagon and equilateral triangle inside a circle. All their vertices are on the circumference of the circle. The regular hexagon and equilateral triangle
Copy and complete these sentences to give the definitions of the terms shown in the diagram above. a. A line that is always the same distance from a single fixed point is called a____. b.
Write a sentence linking the two words given below. The first one has been done for you.a. Radius and diameter The radius is half of the diameter length.b. Diameter and chord c. Arc and
A designer wants to design a new company logo. She decides that the logo will consist of a circle with two regular polygons drawn inside it. The vertices of the regular polygons all lie on the
A school canteen wishes to know what sort of food to sell to students. It carries out interviews with a number of students to find out their opinions. Here is the transcript of the interviewer’s
Decide which of the following types of data are discrete, which are continuous and which are categorical.a. The mass of a baby (kg). b. The type of transport students use to get to
Using an alphabetical list of all the students in your class, try the following methods of selecting a representative sample. a. Choose the first 10 students on the list.b. Has this method
Calculate the area of each of the shapes below: 8cm 15 cm 4 cm ↓
An athletics club has the following number of members They decide on surveying 20 members. As there are four categories, they decide to randomly choose five members from each group. a. Give

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