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 · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.Make x the subject of the formula y = 2x − 9.
y = 2x − 9
(a)x = (y + 9) / 2
(b)x = (y − 9) / 2
(c)x = 2(y + 9)
(d)x = y / 2 + 9
2.Solve 4(x − 3) = 2x + 6.
(a)4.5
(b)−3
(c)3
(d)9
3.The nth term of a sequence is n² − 2n + 5. Work out the 10th term.
(a)68
(b)85
(c)80
(d)125
4.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.
(a)9
(b)7
(c)1
(d)11
5.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.
(a)(n − 5)/2
(b)n/2 − 5
(c)2(n − 5)
(d)(5 − n)/2
6.Which expression means 'add 3 to n, then multiply the result by 4'?
(a)4n + 3
(b)3(n + 4)
(c)4(n + 3)
(d)n + 3 × 4
7.Explain why the equation 4x + 3 = 4x + 10 has no solution for x.
(a)Subtracting 4x gives 3 = 10, which is never true.
(b)x would have to be negative, but x must be positive.
(c)It's true for every x, so there are infinite solutions.
(d)x = 7, since 10 − 3 = 7.
8.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.
y = x² + 1
(a)−3
(b)1
(c)5
(d)4
9.Work out the value of (x − 4)/2 + 3 when x = 10
(a)0
(b)4.5
(c)6
(d)11
10.Line L has equation y = 3x + 1. Which of these lines is perpendicular to L?
y = 3x + 1
(a)y = (1/3)x + 2
(b)y = −(1/3)x + 2
(c)y = −3x + 2
(d)y = 3x − 4
11.A plumber charges a call-out fee plus an hourly rate for a job. The total cost, £C, for a job lasting h hours is given by the formula C = 40 + 25h. What does the number 40 represent in this formula?
(a)The total cost for a job lasting 1 hour.
(b)The hourly rate the plumber charges.
(c)The number of hours worked before charging starts.
(d)The fixed call-out fee, charged before the hourly rate.
12.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?
(a)Yes — the t² coefficient is negative, giving an n-shape.
(b)No — it is U-shaped, since height starts by increasing.
(c)No — the shape comes from the story, not the coefficient.
(d)Yes, but only because the rocket eventually lands.
13.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.
(a)−3
(b)−2
(c)3
(d)6
14.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.
(a)2
(b)−18
(c)−6
(d)−2
15.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.
(a)19
(b)21
(c)22
(d)16

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