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.f(x) = x + 3 and g(x) = 2x. Work out fg(x).
y = x + 3
(a)2x² + 6x
(b)2x + 3
(c)3x + 3
(d)2x + 6
2.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.
(a)55 − 5n
(b)n − 5
(c)−5n − 5
(d)50n − 5
3.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.
(a)r = A/π
(b)r = √A/π
(c)r = √(A/π)
(d)r = (A/π)²
4.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.
(a)16 cm
(b)24 cm
(c)84 cm
(d)28 cm
5.The graph of y = f(x) has a maximum turning point at (5, 8). Which of these correctly gives the corresponding turning point on the graph of y = −f(x + 1), and its type?
(a)(4, −8), a minimum point
(b)(4, 8), a minimum point
(c)(6, −8), a minimum point
(d)(4, −8), a maximum point
6.A circle has centre O(0, 0) and equation x² + y² = 169. The point Q has coordinates (10, 11). Work out which of these gives the correct position of Q together with correct working.
(a)Outside: OQ² = 221 > r² = 169
(b)Outside: OQ = 21 (10 + 11) > r = 13
(c)Inside: OQ ≈ 14.87 < r² = 169
(d)Inside: OQ² = 221 < (2r)² = 676
7.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.
(a)12
(b)8
(c)36
(d)6
8.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
9.Work out the coordinates of the reflection of (6, −3) in the y-axis.
(a)(−6, −3)
(b)(6, −3)
(c)(−6, 3)
(d)(6, 3)
10.Which of these is a factor of 15x + 20?
(a)5
(b)3
(c)4
(d)10
11.The equation x² − 6x + k = 0 has exactly one solution. Work out the value of k.
(a)k = −9
(b)k = 9
(c)k = 3
(d)k = 36
12.A population of bacteria doubles every 3 hours. It starts at 800. Work out the population after 9 hours.
(a)409,600
(b)8
(c)6,400
(d)3,200
13.Work out the integer values of x that satisfy x² − 2x − 8 ≤ 0.
(a)−1, 0, 1, 2, 3
(b)−2, −1, 0, 1, 2, 3, 4
(c)−2, −1, 0, 1, 2, 3, 4, 5
(d)−3, −2, −1, 0, 1, 2, 3
14.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
15.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).
(a)y = −2x − 1
(b)y = −2x + 1
(c)y = −(1/2)x + 2
(d)y = 2x + 7

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