12 marks
Ravi writes 56 000 as 56 × 103.
Is this in standard form? Give a reason, and write 56 000 correctly in standard form.
Show answer
No, 56 is not between 1 and 10. 5.6 × 104
Weekly check: Grade 4
20 mixed questions from 20 grade 4 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
22 marks
An L-shape is made by joining a rectangle 8 cm by 5 cm to a rectangle 4 cm by 3 cm. The two rectangles do not overlap.
Work out the total area of the L-shape.
Show answer
52 cm²
32 marks
A cuboid measures 6 cm by 4 cm by 3 cm.
Work out the volume of the cuboid.
State the units of your answer.
Show answer
72 cm³
43 marks
A ship sails 24 km due north and then 10 km due east.
Work out the straight-line distance of the ship from its starting point.
Show answer
26 km
52 marks
A pupil is constructing a 60° angle at point P on a straight line. She puts the compass point on P, sets the radius to 5 cm and draws an arc that crosses the line at Q. She keeps the compasses at 5 cm, puts the point on Q and draws a second arc that crosses the first arc at R.
Explain why angle RPQ is 60°.
Show answer
PQ = PR = QR = 5 cm, so triangle PQR is equilateral and each angle is 60 degrees
6
3 marks
The table shows the heights, h cm, of 20 plants.
| Height (h cm) | Frequency |
|---|---|
| 140 ≤ h < 150 | 3 |
| 150 ≤ h < 160 | 8 |
| 160 ≤ h < 170 | 6 |
| 170 ≤ h < 180 | 3 |
- Work out an estimate for the mean height.
- Explain why your answer to part (a) is only an estimate.
Show answer
a) 159.5 b) We do not know the exact heights, only which class they are in, so we assume each is at the midpoint
73 marks
Priya invests £1500 in a savings account for 4 years.
The account pays simple interest at a rate of R% per year.
At the end of 4 years, Priya has received a total of £180 in interest.
Work out the value of R.
Show answer
3
83 marks
Amber runs 15.6 km in 1 hour 30 minutes.
Work out her average speed in km/h.
Show answer
10.4 km/h
92 marks
Work out the value of (35 × 3−2) ÷ 3
Show answer
9
102 marks
Is 97 a prime number? Show how you know.
Show answer
Yes, 97 is not divisible by 2, 3, 5 or 7
11
2 marks
Complete the table of values for y = x2 - 2
| x | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y | 2 | -2 | 2 |
Show answer
x = -1) -1 x = 1) -1
122 marks
Work out 5 − 238
Give your answer as a mixed number.
Show answer
258
132 marks
Here are the first four terms of an arithmetic sequence.
20 17 14 11
Find an expression, in terms of n, for the nth term of the sequence.
Show answer
23 - 3n
143 marks
In a sale a pair of boots is reduced by 30%. The sale price is £42.
Work out the original price of the boots.
Show answer
£60
154 marks
Triangle A has vertices at (2, 2), (4, 2) and (2, 6).
Triangle B has vertices at (1, 1), (2, 1) and (1, 3).
Triangle C has vertices at (−1, 1), (−2, 1) and (−1, 3).
- Describe fully the single transformation that maps triangle A onto triangle B.
- Describe fully the single transformation that maps triangle B onto triangle C.
Show answer
a) enlargement, scale factor 1/2, centre (0, 0) b) reflection in the y-axis
163 marks
Find the lowest common multiple (LCM) of 15 and 18
Show answer
90
172 marks
Find the value of n in each of these.
- 7n × 74 = 710
- 38 ÷ 3n = 35
Show answer
a) n = 6 b) n = 3
182 marks
The exchange rate is £1 = €1.14.
Nadia changes £250 into euros.
Work out how many euros she gets.
Show answer
€285
194 marks
A school buys pens in packs of 12 and pencils in packs of 20.
The ratio of the number of packs of pens to the number of packs of pencils bought is 5 : 2.
Show that the ratio of the number of pens to the number of pencils bought is 3 : 2.
Show answer
For every 5 packs of pens and 2 packs of pencils there are 60 pens and 40 pencils; 60 : 40 = 3 : 2
202 marks
The probability that a bus is late is 0.12.
Tamsin catches the bus on 250 days. Work out how many days you would expect the bus to be late.
Show answer
30
Your score
Answer the questions above and your score appears here.
Every question here is original and written by Robinson Tuition, drawn from the grade 4 topic worksheets. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.