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.Simplify (2x² + 7x + 3) ÷ (x² − 9), giving your answer as a single fraction.
(a)(2x + 1)/(x + 3)
(b)(2x + 1)/(x − 3)
(c)2x + 1
(d)(2x + 3)/(x − 3)
2.A sequence begins at 50, and each term after that is found by subtracting 8 from the term before it. Priya says the 8th term of the sequence is negative. Is Priya correct?
(a)No: the 8th term is 50 − 8 × 6 = 2, which is positive.
(b)Yes, but the 8th term is 50 − 8 × 8 = −14.
(c)No: repeated subtraction from 50 can never go negative.
(d)Yes: the 8th term is 50 − 8 × 7 = −6, which is negative.
3.The first four terms of a sequence are 2, 2√3, 6, 6√3, ... Work out the next term.
(a)18
(b)12
(c)18√3
(d)12√3
4.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
5.The graph of y = f(x) has roots at x = −1 and x = 4, and crosses the y-axis at (0, −8). Which statement about the graph of y = f(x − 3) is correct?
(a)x = 2, x = 7; y-intercept cannot be found here
(b)x = 2, x = 7; y-intercept stays at (0, −8)
(c)x = −4, x = 1; y-intercept stays at (0, −8)
(d)x = −4, x = 1; y-intercept cannot be found here
6.Factorise fully 5x + 5y − 5
(a)5(xy − 1)
(b)5(x + y + 1)
(c)5(x + y − 1)
(d)5(x + y − 5)
7.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.
(a)40
(b)11
(c)20
(d)80
8.An exponential graph y = A × rˣ passes through the points (0, 8) and (2, 18). Work out the value of r, correct to 2 decimal places.
(a)1.13
(b)1.50
(c)0.44
(d)2.25
9.The graph of y = f(x) passes through the point (0, 4). Work out the y-coordinate of the point where the graph of y = f(x) − 6 crosses the y-axis.
(a)10
(b)−6
(c)4
(d)−2
10.A graph has equation y = −2x² + 5. Which statement about its shape is correct?
y = -2x² + 5
(a)It is U-shaped, since x² is always positive.
(b)It is a straight line, because of the constant term +5.
(c)It repeatedly rises and falls, like a wave shape.
(d)It is n-shaped, since the x² coefficient is negative.
11.For 0 ≤ x ≤ 360, the equation sin x = 0.5 has two solutions. What are they?
(a)30° and 120°
(b)30° and 210°
(c)45° and 135°
(d)30° and 150°
12.The graph of y = f(x) has a root (an x-intercept) at x = 5. Work out the x-coordinate of the corresponding root on the graph of y = f(x + 2).
(a)3
(b)2
(c)5
(d)7
13.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
14.A company's weekly profit, P thousand pounds, when it makes x thousand items is modelled by P = x² − 8x + 12, for x ≥ 0. Work out the values of x for which the company makes a loss.
(a)x < 2 or x > 6
(b)2 < x < 6
(c)−6 < x < −2
(d)2 ≤ x ≤ 6
15.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

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