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.A square tile has an area of 144 cm². Work out the side length of the tile.
(a)12 cm or −12 cm
(b)72 cm
(c)12 cm
(d)36 cm
2.Solve (3x + 2)/5 = (x + 4)/3
(a)x = 3.5
(b)x = 4.5
(c)x = 10
(d)x = 1
3.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)
4.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.
(a)(L − 4)/6
(b)L/6 + 4
(c)4 − L/6
(d)L/6 − 4
5.Simplify 2/(x + 1) + 3/(x − 2), giving your answer as a single fraction.
(a)5/(2x − 1)
(b)(5x + 1)/(x² − x − 2)
(c)(5x − 1)/(x² + x − 2)
(d)(5x − 1)/(x² − x − 2)
6.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
7.Solve x² − 100 = 0.
(a)x = 10 or x = −10
(b)x = 10
(c)x = 100 or x = −100
(d)x = 50
8.The graph of y = 2x² + 6x − 1 is translated by the vector (−2, 0). Work out the equation of the image, giving your answer in the form y = 2x² + bx + c.
y = 2x² + 6x − 1y = 2x²
(a)y = 2x² + 10x + 15
(b)y = 2x² + 14x + 19
(c)y = 2x² − 2x − 5
(d)y = 2x² + 14x + 20
9.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?
(a)A formula, relating two quantities
(b)An identity, true for all values of x
(c)An expression, with x terms and numbers
(d)An equation, true for one value of x
10.Line L has equation y = 3x − 2. Work out the gradient of a line perpendicular to L.
y = 3x − 2
(a)−1/3
(b)1/3
(c)3
(d)−3
11.The graph of y = x³ − 5x is reflected in the y-axis. Work out the equation of the image.
y = x
(a)y = −x³ + 5x
(b)y = x³ − 5x
(c)y = x³ + 5x
(d)y = −x³ − 5x
12.A car accelerates uniformly from rest at 2.5 m/s² until it reaches a speed of 20 m/s, then travels at this constant speed for a further 30 seconds. Work out the total distance travelled.
(a)900 m
(b)760 m
(c)240 m
(d)680 m
13.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.
(a)16
(b)9
(c)8
(d)12
14.The graph of y = sin x is transformed onto the graph of y = sin x + 1. Which statement correctly describes the transformation and the new range of the graph?
y = sin(x)
(a)Reflect in the x-axis; range unchanged, −1 ≤ y ≤ 1
(b)Translate +1 in x; range unchanged, −1 ≤ y ≤ 1
(c)Translate +1 in y; new range 0 ≤ y ≤ 2
(d)Translate +1 in y; new range −2 ≤ y ≤ 0
15.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

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