Mathematics Tutorial for Yr 7 OC 7
Total – 100 Marks
Time – 1 hr 30 mins
1. Work these out. [4 M]
(a) −7 + −8 =
(b) 6 − −9 =
(c) −10 − −8 =
(d) 5 + −12 =
2. (a) Find the lowest common multiple of 24 and 30. [3 M]
(b) Find the highest common factor of 26 and 32. [3 M]
3. Nimrah thinks of a number, n. [4 M]
Write an expression for the number Nimrah gets each time.
(a) She multiplies the number by 4.
(b) She subtracts 6 from the number.
(c) She multiplies the number by 3 then adds 5.
(d) She divides the number by 6 then subtracts 1.
4. Write down the first four terms of the sequence that has a first term of 5 and a term-to-term
rule of: ‘Multiply by 3 then subtract 5.’ [2 M]
5. Work these out. [4 M]
(i) 49 × 10 =
(ii) 2.3 ÷ 10 =
(iii) 0.034 × 1000 =
(iv) 876 ÷ 100 =
6. Round 4753: [3 M]
(a) to the nearest 10
(b) to the nearest 100
(c) to the nearest 1000.
7. Round 76.189: [2 M]
(a) to the nearest whole number
(b) to one decimal place.
8. Sion sees this sign in a supermarket. [2 M]
What is the cost of one jar of coffee?
9. Write the decimal measurements in each set in order of size, starting with the smallest.
(a) 0.125 kg, 0.08 kg, 95 g [2 M]
(b) 6250 m, 6.2 km, 6.05 km [2 M]
10. Tiago has a 0.3 l bottle of medicine. He is told to take two 5 ml spoonfuls of medicine three times
a day. How many days will the medicine last? Show your working. [3 M]
11. Write down the value shown on each of these scales. [3 M]
12. Some people were asked to choose their favourite sport out of football (F), rugby (R), basketball
(B), hockey (H) and tennis (T). The results are below.
RRBF, FFHF, RTTR, BFTT, RFRH, BRRT
(a) Draw a frequency table to show this information. [3 M]
(b) What is the most popular sport? [1 M]
(c) How many people were asked? [1 M]
13. Write the following decimal numbers as fractions in their simplest form. [3 M]
(a) 0.7 =
(b) 0.26 =
(c) 0.045 =
14. In the New York marathon there were 45360 runners. [2 M]
7
10
of the runners were women. How many of the runners were men?
15. Simplify each expression. [4 M]
(a) 2x + 3x =
(b) 7y − 2y =
(c) 4p + 3q + 2p − q =
(d) 5t + 7 − 3t + 3 =
16. Multiply out the brackets. [4 M]
(a) 4(3x + 2) =
(b) 2(2y − 3) =
(c) 5(5 + 3z) =
(d) 3(7 − 4v) =
17. Solve each of these equations and check your answers. [4 M]
(a) 3b + 2 = 17
(b) 4c − 1 = 19
𝑑
(c) 3
+2=9
𝑏
(d) −1=4
7
18. A group of 25 children were asked how many sisters they had. The frequency table shows the
results.
(a) From the table, four children have no sisters. [1 M]
How many children have more than two sisters?
(b) What is the modal number of sisters? [1 M]
(c) What is the median number of sisters? [1 M]
19. The mean age of five children in a family is 12 years. [3 M]
Work out the total age of the children.
20. A man has a mass of 120 kg. He reduces his mass by 15%. How many kilograms is that? [3 M]
21. Ma’s Mango Chutney is sold in 250 g jars. [3 M]
Each jar contains 135 g of mangoes.
Pa’s Mango Chutney is sold in 400 g jars.
Each jar contains 248 g of mangoes.
Which brand has the greater percentage of mangoes?
22. Every New Year Auntie Bea gives $320 to be shared between her nieces in the ratio of their ages.
This year the nieces are aged 3 and 7. How much more will the younger niece receive, in five
years’ time, than she receives this year? [4 M]
23. The total length of three fence panels is 5.4 m. [2 M]
Work out the total length of ten fence panels.
24. Meril starts driving at 14 00.
(a) How far had she travelled at 14 30? [1 M]
(b) Draw the graph. At 15 00 she stopped for half an hour. [2 M]
Show this on your graph.
(c) She continued her journey. She took 90 minutes to travel another 100 km.
Show this on your graph. [2 M]
25. (a) A train leaves Thane at 14 21 and arrives at Panvel at 15 15.
Work out the time the journey takes. [2 M]
(b)A train leaves Thane at 17 48. It takes 32 minutes to get to Nerul. What time will it arrive?
[2 M]
26. Aisha chooses a whole number from 1 to 20, at random. Here are three possible outcomes.
F: a multiple of 4
S: a multiple of 7
P: a prime number
Find the probability of each of the outcomes F, S and P. [3 M]
27. The table shows the numbers of points scored by a basketball team in 20 matches.
(a) Complete the frequency diagram to show the information. [3 M]
(b) Draw a pie chart to show this information. [3 M]
28. Abeeku carries out a survey on the favourite sport of the students in his year group at school.
The bar charts show his results.
(a) Compare the bar charts and make two comments. [2 M]
(b) Which sport is the favourite for the same number of boys as girls? [1 M]
(c) Which sport is the favourite of twice as many girls as boys? [1 M]
(d) Write down the modal sport for [2 M]
(i) the boys
(ii) the girls.
