13 marks
Solve x2 - 11x + 28 = 0
Show answer
x = 4 or x = 7
Weekly check: Grade 5
20 mixed questions from 20 grade 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
23 marks
Solve 7x − 4 > 3x + 12
Show answer
x > 4
33 marks
Use trial and improvement to find the cube root of 300, correct to 1 decimal place. Do not use the cube root key on your calculator. You must show all your trials.
Show answer
6.7
43 marks
There are 60 students in Year 10 and Year 11 at a small school.
24 of the students are in Year 10 and the rest are in Year 11.
Of the Year 10 students, 15 study French and 9 do not.
Of the Year 11 students, 21 study French.
- Work out the number of students in Year 11.
- Work out the number of Year 11 students who do not study French.
Show answer
a) 36 b) 15
52 marks
Solve x3 + 2 = 6
Show answer
x = 12
62 marks
Work out 58 ÷ 34
Give your answer in its simplest form.
Show answer
5/6
73 marks
The graph shows the temperature of a cup of coffee as it cools.
- Write down the temperature of the coffee at the start.
- Find the temperature of the coffee after 20 minutes.
- Find how long the coffee takes to cool to 30°C.
Show answer
a) 90°C b) 40°C c) 35 minutes
82 marks
In a sale, all prices are reduced by 15%.
The sale price of a jumper is £68.
Work out the normal price of the jumper.
Show answer
£80
92 marks
ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {even numbers} B = {multiples of 5}
Kim draws a Venn diagram. She puts:
2, 4, 8 in A only 6, 10 in the intersection of A and B 5 in B only 1, 3, 9 outside both circles.
Write down two mistakes Kim has made.
Show answer
6 should be in A only, not in the intersection (6 is not a multiple of 5); the number 7 is missing from the region outside both circles.
103 marks
A cylindrical tin has a diameter of 8 cm and a height of 10 cm.
Work out the volume of the tin.
Give your answer correct to 3 significant figures.
Show answer
503 cm³
112 marks
Ben buys a car for £16 000.
The value of the car depreciates by 15% each year.
Work out the value of the car at the end of 2 years.
Show answer
£11560
122 marks
In triangle PQR, angle PQR = 90° and angle PRQ = 52°.
PQ = 9 cm.
Work out the length of PR.
Give your answer correct to 3 significant figures.
Show answer
11.4 cm
13
2 marks
A line graph shows the midday temperature in a town on the first day of each month. The table gives the plotted values.
| Month | Temperature (°C) |
|---|---|
| January | 6 |
| February | 7 |
| March | 10 |
| April | 13 |
| May | 17 |
| June | 21 |
- Write down the month in which the temperature was 13°C.
- Work out the difference between the temperature in June and the temperature in January.
Show answer
a) April b) 15
142 marks
In triangle ABC, angle A = 35° and angle B = 80°.
In triangle DEF, angle D = 80° and angle E = 65°.
Show that triangle ABC is similar to triangle DEF.
Show answer
Angle C = 180 - 35 - 80 = 65 degrees, so both triangles have angles 35, 80 and 65 degrees; triangles with the same three angles are similar
153 marks
A bag contains only red, blue and yellow counters.
The numbers of red, blue and yellow counters are in the ratio 2 : 3 : x.
A counter is taken at random from the bag.
The probability that it is yellow is 27.
Work out the value of x.
Show answer
2
164 marks
- Expand and simplify (y + 7)(y - 7)
- Factorise x2 + x - 30
Show answer
a) y2 - 49 b) (x + 6)(x - 5)
173 marks
5 identical pipes can fill a storage tank in 4.8 hours.
Only 3 of the pipes are working.
Work out how long the 3 pipes will take to fill the tank.
Show answer
8 hours
182 marks
The pressure on a floor is 45 N/m2. The area in contact with the floor is 0.8 m2.
Work out the force.
Show answer
36 N
192 marks
Ali throws a fair coin 3 times.
Each throw lands on heads (H) or tails (T).
List all the possible outcomes of the 3 throws. One outcome, HHH, has been done for you.
Show answer
HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
202 marks
Triangle DEF is a right-angled triangle with the right angle at E.
The hypotenuse DF = 20 cm and DE = 8 cm.
Work out the length of EF.
Give your answer correct to 1 decimal place.
Show answer
18.3 cm
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 5 topic worksheets. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.