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.The point (18, 24) lies on the circle x² + y² = 900, which has centre (0, 0). The tangent to the circle at (18, 24) crosses the y-axis at the point Q. Work out the y-coordinate of Q.
(a)900
(b)50
(c)37.5
(d)1.25
2.Make x the subject of the formula y = 4x − 3.
y = 4x − 3
(a)x = 4(y + 3)
(b)x = y/4 + 3
(c)x = (y − 3)/4
(d)x = (y + 3)/4
3.By completing the square, find the turning point of the curve y = 2x² − 8x + 3.
y = 2x² − 8x + 3
(a)x = 4, y = −29
(b)x = 2, y = −5
(c)x = −2, y = −5
(d)x = 2, y = 5
4.Write down the expression that means the same as (x + 7) ÷ 4.
(a)4(x + 7)
(b)4/(x + 7)
(c)(x + 7)/4
(d)(x + 7) − 4
5.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.
(a)1
(b)−1
(c)3
(d)4
6.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.
y = 12x + 20
(a)12
(b)3
(c)20
(d)5
7.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.
(a)t = 1 second and t = 4 seconds
(b)t = 1 second and t = −5 seconds
(c)t = 1 second and t = 5 seconds
(d)t = −1 second and t = 5 seconds
8.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.
(a)4
(b)2
(c)16
(d)8
9.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.
(a)18 cm²
(b)6 cm²
(c)12 cm²
(d)36 cm²
10.A student says that (x + 4)² is equivalent to x² + 16. For which value of x do the two expressions give the SAME result, making it look (misleadingly) like the student could be right?
(a)x = 4
(b)x = −4
(c)x = 0
(d)x = 8
11.The table shows some values of f(x): when x = 0, f(x) = 5; when x = 1, f(x) = 8; when x = 2, f(x) = 4; when x = 3, f(x) = 1. Work out the value of f(x − 1) when x = 2.
(a)8
(b)4
(c)1
(d)3
12.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.
y = 4x + 3
(a)y = 3x − 5
(b)y = 4x + 5
(c)y = 4x − 5
(d)y = −4x − 5
13.Work out the value of the discriminant b² − 4ac for the equation 2x² + 3x − 2 = 0.
(a)13
(b)−7
(c)25
(d)22
14.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.
(a)y = x − 1
(b)y = 2x − 1
(c)y = 3x − 1
(d)y = 2x + 1
15.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.
(a)24
(b)35
(c)5
(d)30

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