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.Which of these is a formula, rather than an expression, an equation, or an identity?
(a)lwh
(b)lwh = 60
(c)2(l + w) ≡ 2l + 2w
(d)V = lwh
2.A geometric sequence has first term 3 and common ratio √3. Work out the position of the first term of the sequence that exceeds 30.
(a)5th term
(b)4th term
(c)7th term
(d)6th term
3.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
4.A number, n, is tripled and then 4.5 is added. The result is 22.5. Form an equation and solve it to find n.
(a)12
(b)6
(c)7.5
(d)9
5.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.
(a)7
(b)17
(c)12
(d)2
6.By completing the square, show that the curve y = x² − 14x + 50 never crosses the x-axis. Which statement gives the correct reason?
y = x² − 14x + 50
(a)The turning point is above the x-axis at (7, −1)
(b)50 is positive, so y is always positive
(c)The discriminant is positive, so y is never zero
(d)(x − 7)² + 1 is at least 1 for every x, so y is never 0
7.The graph of y = 60 × (0.5)ˣ is sketched for x ≥ 0. Which statement correctly describes what happens to the curve as x increases?
(a)It gets closer to zero but never actually reaches it.
(b)It decreases steadily and reaches zero when x = 60.
(c)It levels off at y = 0.5 as x increases.
(d)It decreases at first, then becomes negative for large x.
8.Work out the smallest positive value of x, in degrees, for which y = tan x is undefined.
y = tan(x)
(a)270°
(b)0°
(c)90°
(d)45°
9.The point (9, 40) lies on the circle x² + y² = 1681, which has centre (0, 0). Work out the equation of the tangent to the circle at (9, 40), giving your answer in the form ax + by = c.
(a)9x − 40y = 1681
(b)9x + 40y = 1681
(c)40x + 9y = 1681
(d)9x + 40y = 41
10.Which of these values of x is a solution of x² + 2x − 15 = 0?
(a)x = 3
(b)x = 5
(c)x = 15
(d)x = −3
11.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?
(a)3 and 2n + 5 are the two terms of 6n + 15
(b)6n and 15 are the factors of 6n + 15
(c)3 and 2n + 5 are both factors of 6n + 15
(d)3 is the only factor of 6n + 15
12.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.
(a)9n + 6
(b)6n
(c)6n + 9
(d)6n + 3
13.The diagram shows the graph of a quadratic function. Which equation could it represent?
(a) $y = x^{2} - x - 6$
(b) $y = x^{2} - x - 2$
(c) $y = x^{2} + 2 x - 3$
(d) $y = x^{2} - 2 x - 3$
14.The simultaneous equations kx + 2y = 4 and 3x + y = 5 have no solution. Work out the value of k.
(a)k = −6
(b)k = 6
(c)k = 2/3
(d)k = 3
15.Solve x² − 2x − 24 = 0.
(a)x = 6 or x = −4
(b)x = −6 or x = 4
(c)x = −8 or x = 3
(d)x = −6 or x = −4

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