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.Solve x² − 8x + 3 = 0 by completing the square. Give your answers in surd form.
(a)x = 4 ± √13
(b)x = −4 ± √13
(c)x = 8 ± √13
(d)x = 4 ± √19
2.The point (9, 12) lies on the circle x² + y² = 225, which has centre (0, 0). The tangent to the circle at (9, 12) crosses the x-axis at the point P. Work out the x-coordinate of P.
(a)9
(b)25
(c)18.75
(d)15
3.A line has equation y = −4x + 1. Work out the equation of the line perpendicular to it that passes through the point (0, 3).
y = -4x + 1
(a)y = −4x + 3
(b)y = (−1/4)x + 3
(c)y = 4x + 3
(d)y = (1/4)x + 3
4.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
5.Describe the single transformation that maps the graph of y = x² onto the graph of y = x² + 3.
y = x²y = x² + 3
(a)A translation by vector (0, 3)
(b)A translation by vector (0, −3)
(c)A translation by vector (3, 0)
(d)A stretch parallel to the y-axis, scale factor 3
6.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
7.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
8.Solve x² − x − 12 = 0.
(a)x = 4 or x = −3
(b)x = −4 or x = 3
(c)x = 12 or x = −1
(d)x = 4 or x = 3
9.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.
y = 12x + 20
(a)12
(b)3
(c)20
(d)5
10.The first five terms of a quadratic sequence are 6, 11, 18, 27, 38. Work out an expression, in terms of n, for the nth term.
(a)2n² + 2n + 3
(b)n² + 2n + 3
(c)n² + 3
(d)n² + 2n
11.An allotment is in the shape of a rectangle. Its length is 5 m more than its width, x metres, and its area is 20 m². This gives x² + 5x − 20 = 0, which can be solved using the iterative formula xₙ₊₁ = 20 ÷ (xₙ + 5). Taking x₀ = 2, so that x₁ is the value found after the formula has been used once, work out x₂ correct to 2 decimal places.
(a)2.55
(b)−1.71
(c)2.00
(d)2.86
12.Describe the single transformation that maps the graph of y = f(x) onto the graph of y = f(−x).
(a)A rotation of 180° about the origin
(b)A reflection in the x-axis
(c)A reflection in the y-axis
(d)A reflection in the line y = x
13.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
14.Solve the inequality 3x + 6 ≤ 0.
(a)x ≤ 2
(b)x ≤ −2
(c)x ≥ −2
(d)x ≤ −18
15.The braking distance of a car, in metres, is estimated using the formula d = 0.4v² + 6, where v is the speed in mph. A car travelling at 35 mph brakes. Work out the estimated braking distance.
(a)202
(b)490
(c)496
(d)20

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