14 marks
In triangle ABC, AB = 3 cm, AC = 5 cm and BC = √19 cm.
Find the size of angle BAC.
Show answer
60°
Weekly check: Grade 7
20 mixed questions from 20 grade 7 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
Show that √12 + √27 can be written as 5√3.
Show answer
2√3 + 3√3 = 5√3
32 marks
ABCD is a parallelogram. AB = 12 cm, AD = 7.5 cm and angle DAB = 65°.
Calculate the area of the parallelogram. Give your answer correct to 3 significant figures.
Show answer
81.6 cm2
44 marks
A and B are two events.
P(A) = 0.5, P(B) = 0.4 and P(A ∪ B) = 0.7
- Work out P(A ∩ B).
- Work out P(B | A).
Show answer
a) 0.2 b) 0.4
53 marks
A, B and C are points on a circle with centre O.
B lies on the major arc AC.
Angle AOC = 128°.
Work out the size of angle ABC. Give a reason for your answer.
Show answer
64°
63 marks
The line y = ax + 5 is perpendicular to the line by = 3x − 2.
Find b in terms of a.
Show answer
b = -3a
72 marks
Work out the value of (3625)12
Show answer
65
82 marks
Write x2 + 8x + 3 in the form (x + a)2 + b, where a and b are integers.
Show answer
(x + 4)2 - 13
93 marks
Two mathematically similar candles, C and D, are made from the same wax.
C has surface area 36 cm2 and D has surface area 81 cm2.
The volume of C is 24 cm3.
Work out the volume of D.
Show answer
81 cm³
10
2 marks
The frequency densities for the times, t minutes, that 80 customers waited in a post office queue are shown in the table.
| Time (t minutes) | Frequency density |
|---|---|
| 0 < t ≤ 10 | 2 |
| 10 < t ≤ 30 | 1.5 |
| 30 < t ≤ 40 | 3 |
Mia says, "The 0 < t ≤ 10 class must have the most customers because its bar is tall." Is Mia correct? You must show your working.
Show answer
No: 0-10 has 20 customers, 10-30 has 30, 30-40 has 30. The 0-10 class has the fewest.
112 marks
Factorise 2x2 + 7x + 3
Show answer
(2x + 1)(x + 3)
123 marks
In triangle ABC, angle BAC = 52°, angle ACB = 63° and AC = 11 cm.
Calculate the length of BC. Give your answer correct to 3 significant figures.
Show answer
9.56 cm
133 marks
p is inversely proportional to q.
When q = 5, p = 12.
- Find a formula for p in terms of q.
- Find the value of p when q = 8.
Show answer
a) p = 60/q b) 7.5
142 marks
A park keeper wants to estimate the number of fish in a lake.
She catches 30 fish, tags them and puts them back in the lake.
The next day she catches 40 fish. 8 of these fish are tagged.
Work out an estimate for the number of fish in the lake.
Show answer
150
153 marks
f(x) = 3x − 4 g(x) = x2
Find f(5)
Find gf(2)
Show answer
a) 11 b) 4
162 marks
Here are four equations.
A: y = 3 × 1.2x B: y = 5 × 0.8x C: y = 0.5 × 4x D: y = 2 × (⅓)x
Which of the graphs show exponential decay (the curve goes down as x increases)? Give a reason.
Show answer
B and D
17
2 marks
A histogram shows the heights of 71 trees. The table gives the frequency density for each class.
| Height (h m) | Frequency density |
|---|---|
| 0 < h ≤ 10 | 1.2 |
| 10 < h ≤ 20 | 2.5 |
| 20 < h ≤ 40 | 1.5 |
| 40 < h ≤ 50 | 0.4 |
Work out the frequency for each class and check that the total is 71.
Show answer
12, 25, 30, 4 (total 71)
182 marks
Here are the first five terms of a quadratic sequence.
2 7 14 23 34
Find an expression, in terms of n, for the nth term of this sequence.
Show answer
n2 + 2n - 1
192 marks
Prove algebraically that the sum of an odd number and an even number is always odd.
Show answer
2n + (2m + 1) = 2(n + m) + 1, which is odd
202 marks
Simplify fully 2x2 + 6x4x
Show answer
(x + 3)/2
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 7 topic worksheets. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.