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 circle has centre (0, 0) and equation x² + y² = 64. Write down the radius of the circle.
(a)64
(b)8
(c)16
(d)32
2.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.
(a)3.5 km/h
(b)4.75 km/h
(c)4.67 km/h
(d)2.25 km/h
3.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?
(a)y stays the same however large x becomes
(b)y decreases towards zero but never reaches it
(c)y increases towards a limit but never reaches it
(d)y decreases at a steady rate and reaches zero
4.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
5.The graph of y = f(x) passes through the point (2, 5). Write down the coordinates of the corresponding point on the graph of y = f(x − 4) + 1.
(a)(−2, 6)
(b)(−2, 4)
(c)(2, 6)
(d)(6, 6)
6.Solve 4(x − 3) = 2x + 6.
(a)4.5
(b)−3
(c)3
(d)9
7.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.
(a)18 cm²
(b)6 cm²
(c)12 cm²
(d)36 cm²
8.By completing the square, find the turning point of the curve y = 2x² − 8x + 3.
y = 2x² − 8x + 3
(a)x = 4, y = −29
(b)x = 2, y = −5
(c)x = −2, y = −5
(d)x = 2, y = 5
9.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.
10.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
11.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
12.Solve (3x + 2)/5 = (x + 4)/3
(a)x = 3.5
(b)x = 4.5
(c)x = 10
(d)x = 1
13.The tangent to a curve at the point (5, 2) is the line y = mx + c. This tangent crosses the y-axis at (0, −8). Work out the gradient, m, of the tangent.
(a)0.5
(b)−1.2
(c)−2
(d)2
14.Solve 6x − 5 = 3x + 13.
(a)18
(b)2
(c)2.67
(d)6
15.A circle has equation x² + y² = 25. Does the point (3, 4) lie on this circle?
(a)No, because (3 + 4)² = 49, not 25.
(b)Yes, because 3 + 4 = 7, and 7 is less than 25.
(c)No, because 3² + 4² = 17, not 25.
(d)Yes, because 3² + 4² = 25.

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