12 marks
Write x2 + 10x + 7 in the form (x + a)2 + b, where a and b are integers.
Show answer
(x + 5)2 - 18
Weekly check: Higher crossover
20 mixed questions from 20 grades 6 and 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
The line with equation y = 3x + 5 is parallel to the line with equation y = (2k - 1)x + 2
Work out the value of k.
Show answer
k = 2
33 marks
40 students took a typing test. Salma drew a cumulative frequency graph for their times.
Salma plotted each cumulative frequency against the midpoint of its class interval.
- Explain the mistake Salma made.
- Salma redraws the graph correctly. The correct graph shows a cumulative frequency of 34 at a time of 40 seconds. How many students took longer than 40 seconds?
- What percentage of the 40 students took longer than 40 seconds?
Show answer
a) She should plot each cumulative frequency at the upper end (upper class boundary) of the interval, not the midpoint b) 6 c) 15%
42 marks
Lena says, “The graph of y = 3 × 2x goes through the point (2, 36), because 3 × 2 = 6 and 62 = 36.”
Lena is wrong. Explain her mistake and work out the correct y-value when x = 2.
Show answer
She squared the 3 as well: the power applies only to the 2. Correct y = 3 × 22 = 12
53 marks
Dev buys a van for £15 000.
The value of the van depreciates by 12% each year.
Calculate the value of the van at the end of 3 years.
Give your answer to the nearest penny.
Show answer
£10222.08
62 marks
A sector of a circle has radius 9 cm and angle 120°.
Work out the arc length of the sector.
Give your answer in terms of π.
Show answer
6π cm
72 marks
A straight line passes through the points A (2, 5) and B (6, 17).
Work out the gradient of the line.
Show answer
3
83 marks
On the grid, shade the region that satisfies all three of these inequalities.
y ≤ 3
y ≥ x - 1
x > 0
Label the region R.
Show answer
Region bounded by y = 3 (solid, below), y = x - 1 (solid, above) and x = 0 (dashed, right of); vertices (0, -1), (0, 3), (4, 3)
92 marks
y is inversely proportional to x.
When x = 3, y = 20.
Work out the value of y when x = 5.
Show answer
12
102 marks
The curve y = x2 - 6x + 8 crosses the x-axis at x = 2 and at x = 4.
- Write down the solutions of x2 - 6x + 8 = 0
- Write down the x-coordinate of the turning point of the curve.
Show answer
a) x = 2 and x = 4 b) x = 3
113 marks
Without working out the squares, show that
532 - 472 = 600
Show answer
532 - 472 = (53 + 47)(53 - 47) = 100 × 6 = 600
123 marks
Solve 2x2 + 5x - 12 = 0
Show answer
x = 32, x = -4
133 marks
The straight line L has equation y = -x3 + 5
Find the equation of the straight line that is perpendicular to L and passes through the point (2, -1).
Show answer
y = 3x - 7
143 marks
A box contains 12 chocolates: 5 dark and 7 milk. Ravi takes two chocolates at random without replacement.
Work out the probability that at least one of the chocolates is dark.
Show answer
15/22
153 marks
A, B and C are points on a circle with centre O.
AOC is a diameter of the circle.
Angle CAB = 37°.
Work out the size of angle ACB. Give a reason for each stage of your working.
Show answer
53°
162 marks
Prove that n2 + n is even for every integer n.
Show answer
n2 + n = n(n + 1), the product of consecutive integers, so it is even
174 marks
- Using the discriminant, explain why the equation x2 + 3x + 7 = 0 has no real solutions.
- Write down the number of real solutions of the equation x2 - 6x + 9 = 0. Give a reason for your answer.
Show answer
a) b2 - 4ac = 32 - 4(1)(7) = -19, which is negative, so there are no real solutions b) One repeated real solution, because b2 - 4ac = 36 - 36 = 0
18
2 marks
100 students were asked how they travel to school. The two-way table shows the results.
| Walk | Bus | Car | Total | |
|---|---|---|---|---|
| Year 10 | 18 | 22 | 10 | 50 |
| Year 11 | 12 | 14 | 24 | 50 |
| Total | 30 | 36 | 34 | 100 |
A student is chosen at random.
Given that the student travels by bus, work out the probability that they are in Year 11.
Show answer
14/36
192 marks
a = (−2, 5) and b = (3, −1).
Work out 3a − 2b as a column vector.
Show answer
(-12, 17)
202 marks
Triangle P has vertices at (2, 1), (4, 1) and (4, 2).
Triangle P is enlarged by scale factor −1, centre (0, 0), to give triangle Q.
Write down the coordinates of the vertices of triangle Q.
Show answer
(-2, -1), (-4, -1), (-4, -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 grades 6 and 7 topic worksheets. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.