12 marks
A pair of trainers costs £60.
In a sale the price is decreased by 20%.
Work out the sale price. You may use the multiplier 0.8
Show answer
£48
Weekly check: Foundation crossover
20 mixed questions from 20 grades 4 and 5 topics, 50 marks.
Type your answers below for an instant mark and a score, or print the sheet, mark it with the answers sheet, and use the solutions to see every step written out by hand. Set one a week and watch the score climb.
The questions
24 marks
For each pair of triangles, write down the condition (SSS, SAS, ASA, RHS) that shows they are congruent, or write "not enough information".
- Both triangles have sides of 6 cm and 8 cm with an angle of 50° between them.
- Both triangles have a side of 7 cm with an angle of 40° at one end and an angle of 60° at the other end.
- Both triangles have a right angle, a hypotenuse of 13 cm and one other side of 5 cm.
- Both triangles have angles of 50°, 60° and 70°.
Show answer
a) SAS b) ASA c) RHS d) not enough information
32 marks
Here are the first four terms of an arithmetic sequence.
3 10 17 24
Find an expression, in terms of n, for the nth term of the sequence.
Show answer
7n - 4
42 marks
Zak plays two games of darts. He draws a probability tree diagram.
On the first pair of branches he writes P(win) = 0.6 and P(lose) = 0.5.
He then works out P(win both games) = 0.6 + 0.6 = 1.2.
Write down two mistakes Zak has made.
The games are independent, with the same probability of winning each game. There are no draws.
Show answer
The first pair of branch probabilities do not add up to 1 (0.6 + 0.5 = 1.1); he should have multiplied along the branches, not added (and a probability cannot be more than 1).
52 marks
Two straight lines are parallel. A third line crosses them. Two angles lie between the parallel lines, on the same side of the crossing line, in a C shape. One of these angles is 108°.
Work out the size of the other angle. Give the name of this type of angle.
Show answer
72 degrees, co-interior angles
6
3 marks
A hockey team played 25 matches. The table shows the number of goals the team scored in each match.
| Goals scored | Frequency |
|---|---|
| 0 | 4 |
| 1 | 7 |
| 2 | 9 |
| 3 | 3 |
| 4 | 2 |
- Write down the modal number of goals scored.
- Work out the total number of goals the team scored in the 25 matches.
Show answer
a) 2 b) 42
72 marks
- Write down the value of 50
- Write down the value of 2−3 as a fraction
Show answer
a) 1 b) 1/8
8
3 marks
A taxi company charges a fixed fee plus a cost for each kilometre travelled. The table shows the cost, in pounds, for some journeys. The points lie on a straight line graph.
| Distance (km) | 0 | 2 | 4 | 6 |
|---|---|---|---|---|
| Cost (£) | 3 | 7 | 11 | 15 |
- Work out the gradient of the line.
- What does the gradient represent?
- What does the y-intercept represent?
Show answer
a) 2 b) The cost per kilometre, £2 per km c) The fixed fee of £3 (cost when distance is 0)
93 marks
A = {factors of 12} B = {factors of 18}
- List the members of A ∩ B.
- Is 9 a member of A ∪ B? Give a reason for your answer.
Show answer
a) 1, 2, 3, 6 b) Yes, because 9 is in B (9 is a factor of 18), so it is in the union
104 marks
- Complete the table of values for y = x3 - 2x2
x -1 0 1 2 3 y 0 9 - Use the table to write down two values of x for which y = 0
Show answer
a (x = -1)) -3 a (x = 1)) -1 a (x = 2)) 0 b) x = 0 and x = 2
113 marks
Leon walks to his friend's house. He leaves home at 10:00. The distance-time graph is a straight line which reaches 3 km at 10:45. He keeps walking at the same speed.
- Work out his speed in km/h.
- His friend lives 7 km from Leon's home. At what time does Leon arrive?
Show answer
a) 4 km/h b) 11:45
123 marks
- Write 0.0698 in standard form.
- Which is greater, 7.3 × 10−2 or 0.0698?
You must show your working.
Show answer
a) 6.98 × 10-2 b) 7.3 × 10-2 (0.073 > 0.0698)
132 marks
Write 84 as a product of its prime factors.
Show answer
22 × 3 × 7
143 marks
Solve x + 43 = 2x − 15
Show answer
x = 23
152 marks
Solve 4x + 3 = x + 18
Show answer
x = 5
162 marks
Solve 4x + 3 < 19
Show answer
x < 4
172 marks
A locker code is made up of one letter followed by two digits.
The letter is chosen from the 26 letters A to Z.
Each digit is chosen from 0 to 9, and digits may repeat.
Work out the number of different codes that are possible.
Show answer
2600
182 marks
Hannah puts £2400 into a savings account.
The account pays 3% simple interest each year.
Work out the total amount of interest Hannah gets after 3 years.
Show answer
£216
192 marks
Each exterior angle of a regular polygon is 30°.
Work out the number of sides of the polygon.
Show answer
12
202 marks
The mass of a parcel is 340 g, correct to the nearest 10 g.
Complete the error interval for the mass, m grams, of the parcel.
....... ≤ m < .......
Show answer
335 ≤ m < 345
Your score
Answer the questions above and your score appears here.
Every question here is original and written by Robinson Tuition, drawn from the grades 4 and 5 topic worksheets. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.