Printable · GCSE Higher · ages 14-16

Algebra worksheet — GCSE Higher

Fifteen questions across the algebra statements at Higher tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.

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Algebra worksheet — GCSE Higher

Maths · GCSE Higher · Algebra · 15 questions

MathsUKwww.geekhero.co.uk

1.Describe the single transformation that maps the graph of y = x² onto the graph of y = x² + 3.
y = x²y = x² + 3
(a)A translation by vector (0, 3)
(b)A translation by vector (0, −3)
(c)A translation by vector (3, 0)
(d)A stretch parallel to the y-axis, scale factor 3
2.A tree is 2 metres tall. Each year its height increases by 10% of its height at the start of that year. Work out the height of the tree after 3 years, giving your answer to 1 decimal place.
(a)2.6
(b)2.9
(c)2.4
(d)2.7
3.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.
(a)10
(b)16
(c)12
(d)13
4.A student claims: 'For every positive integer n, n² + n + 1 is a prime number.' Which value of n shows that this claim is false?
(a)n = 3
(b)n = 1
(c)n = 4
(d)n = 2
5.Make x the subject of the formula y = x/2 − 5.
y = x
(a)x = (y + 5)/2
(b)x = 2y − 10
(c)x = 2y + 10
(d)x = 2y + 5
6.The graph of y = f(x) has a root (an x-intercept) at x = 5. Work out the x-coordinate of the corresponding root on the graph of y = f(x + 2).
(a)3
(b)2
(c)5
(d)7
7.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.
(a)t = 4
(b)t = 8
(c)t = 10
(d)t = 5
8.Solve the simultaneous equations y = 2x − 1 and y = x² − x − 1, giving both pairs of solutions.
y = 2x − 1y = x²
(a)x = 0, y = −1 and x = −3, y = −7
(b)x = 0, y = −1
(c)x = −2, y = −5 and x = 1, y = 1
(d)x = 0, y = −1 and x = 3, y = 5
9.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.
(a)11
(b)4
(c)7.5
(d)22
10.Make x the subject of the formula y = 4(x − 6).
(a)x = 4y + 96
(b)x = (y + 6)/4
(c)x = (y + 24)/4
(d)x = y/4 − 6
11.A ball is dropped and bounces. The height of each bounce after the first is 8 cm less than the bounce before it. The first bounce reaches 60 cm. Work out the height of the 5th bounce.
(a)40
(b)92
(c)20
(d)28
12.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.
(a)500 m
(b)300 m
(c)200 m
(d)400 m
13.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.
(a)(−4, 3)
(b)(4, −9)
(c)(3, 4)
(d)(4, 3)
14.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.
(a)2
(b)5
(c)9
(d)−5
15.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.
(a)12 km/h
(b)9 km/h
(c)8 km/h
(d)0.2 km/h

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