Foundation Grade 5 Mini Test B
A 45-minute, 40-mark test using only authored grade 5 questions, focused on number, sequences, geometry, measures, trigonometry and statistics.
Questions
Question 1 [1 marks]
Statistics and Probability
Using the diagram in Question 10, find P(F').
Question 2 [2 marks]
Fractions, Decimals and Percentages
A restaurant automatically adds a service charge of 12.5% to the price of a meal. The total bill, including the service charge, is £81.00. Work out the price of the meal before the service charge was added.
Question 3 [2 marks]
Pythagoras and Trigonometry
In right-angled triangle XYZ, the right angle is at Y. The side opposite angle X is 7 cm and the side adjacent to angle X is 4 cm. Calculate the size of angle X. Give your answer correct to 1 decimal place.
Question 4 [2 marks]
Angles and Geometrical Reasoning
a + b = (7, 2). a = (3, -5). Find b as a column vector.
Question 5 [3 marks]
Area, Volume and Measures
Quadrilateral ABCD is mathematically similar to quadrilateral WXYZ, with AB corresponding to WX, BC corresponding to XY, CD corresponding to YZ, and DA corresponding to ZW. AB = 9 cm, WX = 15 cm and CD = 12 cm.
Question 6 [3 marks]
Number and Calculation
A rectangle has been measured with length 8.4 cm and width 5.6 cm, each correct to 1 decimal place. Use your calculator to work out the upper bound for the area of the rectangle, giving your answer to 2 decimal places.
Question 7 [4 marks]
Fractions, Decimals and Percentages
Liam works out 30% of 150 by calculating 150 - 30 = 120. He says the answer is 120.
Explain the mistake in Liam's method.
Work out the correct value of 150 reduced by 30%.
Question 8 [5 marks]
Statistics and Probability
A charity raffle sells 50 tickets, 4 of which win a prize. Chloe buys two of the raffle tickets.
Find the probability that both of Chloe's tickets win a prize.
Find the probability that at least one of Chloe's tickets wins a prize.
Question 9 [7 marks]
Sequences
Arjun is training for a marathon. In week 1, he runs 8 km. Each week after that, he runs 3 km more than the week before.
Work out how far Arjun runs in week 6.
Find an expression, in terms of n, for the distance, in km, Arjun runs in week n.
Arjun wants to know the first week in which he will run at least 50 km. Find this week number.
Question 10 [8 marks]
Statistics and Probability
A school asked 120 pupils their favourite sport. A bar chart gave these frequencies: Football 48, Netball 30, Rugby 12, Tennis 20, Other 10. (a) What fraction of pupils chose Netball? Give your answer in lowest terms and as a percentage. (b) Work out and simplify the ratio Football : Tennis.
Question 11 [3 marks]
Number and Calculation
Work out 1234 ÷ 11. Give the exact answer as a mixed number and as a recurring decimal.
Model solutions
| Question 1[1 mark] | |
|---|---|
| Answer or working | Marks |
| 14/24 oe (= 7/12), ft from n(F) | B1 |
| Final answer: 14/24 = 7/12 | |
| Question 2[2 marks] | |
|---|---|
| Answer or working | Marks |
| 81 / 1.125 | M1oe |
| £72 | A1cao |
| Question 3[2 marks] | |
|---|---|
| Answer or working | Marks |
| tan X = 7/4 | M1oe |
| awrt 60.3 (degrees) | A1 |
| Final answer: angle X = 60.3 degrees (1 d.p.) | |
| Question 4[2 marks] | |
|---|---|
| Answer or working | Marks |
| b = (7, 2) - (3, -5) | M1 |
| (4, 7) | A1cao |
| Question 5[3 marks] | |
|---|---|
| Answer or working | Marks |
| scale factor = 15/9 oe (= 5/3) | M1 |
| 12 x their 5/3 | M1 |
| 20 (cm) | A1cao |
| Final answer: 20 cm | |
| Question 6[3 marks] | |
|---|---|
| Answer or working | Marks |
| upper bounds identified: length 8.45 and width 5.65 | M1 |
| correct unrounded product 47.7425 (or awrt) seen | M1 |
| 47.74 awrt 2 d.p. | A1cao |
| Final answer: 47.74 cm^2 | |
| Question 7[4 marks] | |
|---|---|
| Answer or working | Marks |
| identifies that Liam has subtracted the number 30, treating it as an amount, instead of finding 30% of 150 | B1 |
| states that the correct method requires working out 30% of 150 (as an amount) and then subtracting that amount from 150 | B1 |
| 30% of 150 = 45 (oe: 0.3 x 150) | M1 |
| 105 | A1 |
| Final answer: Liam subtracted the number 30 instead of subtracting 30% of 150 (which is 45) | 105 | |
| Question 8[5 marks] | |
|---|---|
| Answer or working | Marks |
| 4/50 x 3/49 | M1 |
| 6/1225 oe (e.g. 12/2450, awrt 0.0049) | A1 |
| 46/50 x 45/49 ( = P(neither ticket wins) ) | M1 |
| 1 - 46/50 x 45/49 | M1 |
| 38/245 oe (e.g. 380/2450, awrt 0.155) | A1 |
| Final answer: 6/1225 | 38/245 | |
| Question 9[7 marks] | |
|---|---|
| Answer or working | Marks |
| 8 + 5 x 3 oe, or lists terms up to week 6 | M1 |
| 23 km | A1cao |
| common difference of 3 used correctly, e.g. 3n + c | M1oe |
| 3n + 5 oe | A1cao |
| 3n + 5 >= 50 oe (ft their expression) | M1 |
| 3n >= 45 oe, leading to n >= 15 | M1 |
| week 15 | A1cao |
| Final answer: 23 km | 3n + 5 | Week 15 | |
| Question 10[8 marks] | |
|---|---|
| Answer or working | Marks |
| form fraction 30/120 and simplify | M1 |
| 1/4 | A1cao |
| 25% | A1cao |
| form ratio 48 : 20 | M1 |
| divide both sides by common factor 4 or 2 as part of simplification | M1 |
| 12 : 5 or 12:5 | A1cao |
| show working or state simplified form explicitly | M1 |
| final simplified ratio 12:5 | A1cao |
| Final answer: 1/4 and 25% (30/120 = 1/4 = 25%). | 12 : 5 (Football 48 : Tennis 20 = 48:20 = divide by 4 -> 12:5). | |
| Question 11[3 marks] | |
|---|---|
| Answer or working | Marks |
| correct division showing 1234 = 11 x 112 + 2 or equivalent | M1 |
| mixed number 112 2/11 | A1cao |
| recurring decimal 112.18... with 18 recurring, i.e. 112.(18) | A1cao |
| Final answer: 112 2/11 and 112.(18) | |