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mathematics
cambridge checkpoint lower secondary mathematics

Questions and Answers of Cambridge Checkpoint Lower Secondary Mathematics

A teacher wants to find out what school clubs the students would like the school to offer. The school has a population of 1500 students so he decides that he will ask a sample of the student
Use the formula for the area of a triangle to work out the missing values in the table below: a b U d Base length 7.2 cm 20 cm Perpendicular height 4.8 cm 15 cm 11 cm Area 100 cm² 15 cm² 55 cm²
A teacher wants to interview a sample of the students in the whole school about what they find difficult in mathematics. She surveys a sample of her own students, by putting their names in a hat and
Calculate the area of each of the triangles below: a.b.c. 3cm 4 cm
The school in question 1 above also gives out the following questionnaire to the students. Please tick the appropriate box for each question. ● What year are you in? 7 Year____.8
Three triangles P, Q and R share a common base and lie between two parallel lines. Which of the three triangles (if any) has the biggest area? Give a reason for your answer. d
Calculate the area of each of the shapes below: 30 cm 20 cm
Using an alphabetical list of all the students in your class, try the following methods of selecting a representative sample. a. Select every (i) 10th person(ii) 5th person(iii) 3rd
Calculate the area of each of the shapes below: -30 cm- -22 cm 44 cm 4 cm
Using an alphabetical list of all the students in your class, try the following methods of selecting a representative sample. a. Number each student 1, 2, 3 etc. then use the random number
Two congruent (identical) right-angled triangles are placed inside a square as shown. The square has a side length of 8 cm. If half the area of the square is not covered by the triangles,
Four congruent right-angled triangles are arranged to form two squares as shown: a. What is the area of the smaller square as a fraction of the larger square? b. Assuming the size of the
The line PQ in the grid below is the base of a triangle. Each square in the grid is 1 cm2.a. Copy the diagram and mark on your grid a point R, so that triangle PQR has an area of 8cm2.b. Mark on
The diagram below shows a sequence of Sierpinski triangles, which are made of black and white equilateral triangles.If the first large triangle has an area of 64cm2, calculate the total area of black
a. Draw a triangle similar to the one drawn opposite.(i) Measure the length of side AB and let this be the base of the triangle.(ii) Draw on your diagram a line which represents the height of
The lines below have the lengths shown. In each case write an expression for the length of the line. a.b.c.d. 7 X
Insert any of the following symbols, +, −, ×, ÷ or ( ), in between the numbers to make the calculations correct. a 8 b8 C 7 d 7 e 7 6 4 6 4 6 3 6 3 i 2 3 6 f8 g 8 4 4 h 2 3 3 9 3 N N 1010
Work out the following. a. 4+3×2−1b. 6×2+4×3 c. 3×5−2−7 d. 8+4×8−40 e. 6−2×3×4 f. 7×(4+2)−3 g. 8+(6+3)÷3h. 16÷(2+2)2+8i.
Two pupils, Carla and Ibrahim, are discussing the following calculation. 3×22 Carla says the answer is 12, whilst Ibrahim says the answer is 36. a. Which pupil is right? Give a
In the following calculations, insert brackets in order to make them correct. a. 3 + 2 × 5 + 4 = 29b. 3 + 2 × 5 + 4 = 21
(i) Write an expression for the distance around the edge of each of these shapes. (ii) Simplify your expression where possible.a.b. c. d. e. f. g. h. X 4
Write an expression for the area of each of the following shapes. a.b. 8 ーj → -j- 3
Explain whether the use of brackets in the following calculations are necessary. Give a convincing reason for your answers. a. 8 + (2 × 6) = 20 b. (3 + 2) 2 − 6 = 19 c. (42 −
Evaluate the expressions in questions 1 and 2 when p = 2, q = 3 and r = 5. a. 3p + 2q b. 4p − 3q c. p −q − r d. 3p − 2q + r
A compound shape is given opposite. a. Show that the total perimeter of the shape is given by the expression 6x + 12. b. Show that the total area of the shape is given by the expression 10x
Marta and Raul are studying the two rectangles A and B below. a. They calculate that the perimeter of A is given by the formula P = 6x + 4 and that the perimeter of B is given by the
Calculate the perimeter and area of each of these rectangles of length l and breadth b. Write the units of your answers clearly. a. l = 4cm, b = 7 cm b. l = 8cm, b = 12cm c. l = 4.5
A box contains wooden building blocks of two different lengths p cm and q cm as shown. Describe how the following expressions for length can be represented using these blocks. a. p + qb. p
The number of litres of milk consumed in a group of 160 houses per week are shown in the table. a. Calculate the fraction of the total for each number of litres consumed. b. Draw a pie
A rectangle has dimensions as shown. a. Write an expression for the area and perimeter of the rectangle. b. The rectangle is split in half as shown. A pupil makes the following statement:
A square piece of card is cut in half and the two pieces placed side by side as shown. a. If the large square has a side length of 4a, write an expression for the total perimeter of the two
In a school sports day, pupils can enter track events (T) and field events (F). The Venn diagram shows the number of pupils taking part in each type of event.a. How many pupils entered track
In physics this formula is used in calculations about electricity:V =IRV is the voltage in a circuit in voltsI is the current in ampsR is the resistance in ohms.Without using a
A girl has an age of x years. Her grandfather is aged y years. Write an expression for: a. Their combined age.b. The difference between their ages. c. The grandfather’s age 10 years
A baker’s shop sells brown (B), white (W), wholemeal (M) and soda (S) bread. It keeps a record of the types of loaves it sells. The data is shown below. a. Construct a tally and frequency
The midday temperature (°C) of all the days in July at a holiday resort are recorded and the results shown in the frequency table below.a. How many days had a temperature of at least 29°C?b. How
A coffee shop produces the following infographic: a. What do you think this infographic is showing? b. Describe one thing that you like about this infographic. c. Describe one thing
The lengths (cm) of 50 worms of the same species are measured and recorded. The first 45 results are shown in the grouped frequency table below.a. Explain whether the length of a worm, measured as
The members of a book group are asked whether they like fiction (F) or non-fiction (N) literature. The results are shown in the Venn diagram.a. 20 people like fiction and 17 like non-fiction. One
Twelve people were asked which sandwiches they had bought from a sandwich shop. Their answers
A survey is carried out amongst 40 children in a school to see what is their favourite animal. The results are presented in the two-way table below.a. Copy and complete the table.b. How many girls
Ten shapes are shown below.a. Paul decides to classify the shapes in a Carroll diagram and draws one as shown:Explain why Paul’s Carroll diagram is not suitable for organising the 10 shapes.b.
A gardener measures the temperature (°C) in his greenhouse in two-hour intervals between 10:00 and 20:00 one day. The results are shown in the table below:a. Plot a line graph of the data. b.
A sports club canteen keeps a record of the number of drinks it sells over two days. Part of the dual frequency graph is shown. Bottles of water are sold for $1.20 and cans of soft drink are
Five different types of data collection are listed: Discrete Continuous Grouped discrete Grouped continuous Categorical a. Give an example of a data collection for each
90 students sat a maths exam. On the way out of the hall, they were asked whether they found it hard, OK or easy. Here are the responses expressed as a fraction of the total with one value
Three scatter graphs are shown below. Data is collected for three different investigations. These are:(i) The number of ice-creams sold per hour by an ice-cream vendor and the temperature during
Four pie charts are shown below. Three of them can be paired with a waffle diagram which represents the same data. a. Match three of the pie charts with their corresponding waffle
A fitness club carries out a survey to find out the ages of its members. Here are the results. a. Make a grouped tally and frequency table using the age groups 1–10, 11–20, 21–30
A zoologist weighs a sample of mice found in a field. The mass (g) of 50 mice is recorded, grouped and shown in the two-way table below. Unfortunately the zoologist’s pen leaked during

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