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.A curve has equation y = x² − 9. Which statement about its graph is correct?
y = x² − 9
(a)It crosses the x-axis only once, at x = 9.
(b)It does not cross the x-axis, since −9 is negative.
(c)It crosses the x-axis at x = 9 and x = −9.
(d)It crosses the x-axis at x = 3 and x = −3.
2.On a distance-time graph, a horizontal line segment shows a period when the graph's gradient is 0. What does this tell you about the journey during that time?
(a)The object was decelerating
(b)The object was travelling at a constant, non-zero speed
(c)The object was stationary (not moving)
(d)The object was travelling at its maximum speed
3.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.
(a)y = 6x − 4
(b)y = x/3 + 13
(c)y = 3x + 5
(d)y = 3x + 23
4.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
5.A student attempts to prove that the product of two consecutive integers is always even: (i) Let the two consecutive integers be n and n + 1. (ii) Since n(n + 1) is even, one of n and n + 1 must be an even number. (iii) Therefore, n(n + 1) is even. At which statement does the proof first assume the very fact it is trying to prove?
(a)Statement (iii)
(b)Statement (i)
(c)Statement (ii)
(d)The proof does not assume anything it is trying to prove
6.The diagram shows the graph of $y = x^{2} - x - 2$ , together with the horizontal line $y = 3$ . Use the graphs to estimate, to 1 decimal place, the two solutions of $x^{2} - x - 2 = 3$ .
(a)x = −1.8 and x = 2.8
(b)x = −3.0 and x = 4.0
(c)x = 1.8 and x = 2.8
(d)x = −1.0 and x = 2.0
7.Work out the equation of the straight line through the points (−3, 4) and (1, −8).
(a)y = −3x − 5
(b)y = 3x − 11
(c)y = −3x + 5
(d)y = −3x + 11
8.Solve 4x − (2x − 6) = 18
(a)x = 6
(b)x = 3
(c)x = 12
(d)x = 24
9.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.
(a)720
(b)184
(c)176
(d)45
10.The point (6, 8) lies on the circle x² + y² = 100. Work out the gradient of the tangent to the circle at (6, 8).
(a)−3/4
(b)−4/3
(c)3/4
(d)4/3
11.x = 5. Work out the value of 3x² − 4.
(a)221
(b)75
(c)71
(d)3
12.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.
(a)6 years
(b)12 years
(c)14 years
(d)28 years
13.Expand and simplify (2x − 1)(x + 5)(x − 2). Write down the coefficient of x in your answer.
(a)−13
(b)−23
(c)−20
(d)10
14.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
15.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.
(a)9n + 5
(b)5n + 9
(c)5n
(d)5n + 4

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