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.A cup of tea cools after being made. Its temperature-time graph is a curve. Three tangents are drawn on the graph: at t = 2 minutes the tangent has gradient −8; at t = 10 minutes the tangent has gradient −3; at t = 20 minutes the tangent has gradient −0.5. Which of these statements about the tea's cooling is correct?
(a)Fastest at t = 20 min — largest gradient.
(b)Cools at the same rate throughout.
(c)Fastest at t = 2 min — steepest gradient.
(d)Fastest at t = 10 min — the middle reading.
2.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
3.A taxi company charges a £2.50 booking fee plus £1.80 per mile. A journey costs £15.10 in total. Work out the number of miles travelled.
(a)9.78
(b)8.39
(c)5.32
(d)7
4.The curve y = −x² + 6x − 5 has a maximum point. Use completing the square to find its coordinates.
y = −x² + 6x − 5
(a)x = 3, y = −4
(b)x = 3, y = 4
(c)x = 6, y = 31
(d)x = −3, y = 4
5.Which of these rules generates the sequence 6, 11, 16, 21, …?
(a)6n
(b)5n − 1
(c)5n + 1
(d)n + 5
6.The graph of y = f(x) has a minimum turning point at (2, −3). The graph of y = −f(x) + a has a maximum turning point at (2, 9). Work out the value of a.
(a)12
(b)6
(c)−12
(d)−6
7.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.
(a)5
(b)8
(c)7
(d)28
8.The diagram shows the graph of $y = x^{2} - x - 2$ , together with the horizontal line $y = 3$ . Use the graphs to estimate, to 1 decimal place, the two solutions of $x^{2} - x - 2 = 3$ .
(a)x = −1.8 and x = 2.8
(b)x = −3.0 and x = 4.0
(c)x = 1.8 and x = 2.8
(d)x = −1.0 and x = 2.0
9.A car's fuel tank contains 50 litres when it starts a journey. After travelling for 2 hours, it contains 38 litres, and fuel is used at a constant rate. Work out the rate at which fuel is used, in litres per hour.
(a)44
(b)19
(c)6
(d)12
10.Solve the simultaneous equations y = 3 − x and x² + y² = 9, giving both pairs of solutions.
(a)x = 0, y = 3 and x = 6, y = −3
(b)x = 0, y = 3 and x = −3, y = 6
(c)x = 0, y = 3 and x = 3, y = 0
(d)x = 0, y = 3
11.A student attempts to prove that the sum of any three consecutive integers is a multiple of 3. Line 1: Let the three consecutive integers be n, n + 1 and n + 2. Line 2: Their sum is n + (n + 1) + (n + 2) = 3n + 2. Line 3: 3n + 2 leaves a remainder of 2 when divided by 3, so it is not a multiple of 3. Line 4: So the sum of three consecutive integers is not always a multiple of 3. Which line contains the FIRST error?
(a)line 3
(b)line 4
(c)line 1
(d)line 2
12.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.
(a)x = 2, y = 5
(b)x = 3, y = 2
(c)x = 2, y = 3
(d)x = −2, y = 11
13.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.
(a)x = −8
(b)x = 5
(c)x = 5 or x = −8
(d)x = 4
14.The mass of a chemical sample decays by 15% every hour. It starts at 500 g. Work out the mass remaining after 3 hours, correct to 1 decimal place.
(a)192.9 g
(b)275.0 g
(c)307.1 g
(d)361.3 g
15.The graph of y = x² − 4x is translated by the vector (3, 0). Work out the equation of the image, giving your answer in the form y = x² + bx + c.
y = x² − 4xy = x²
(a)y = x² − 7x + 21
(b)y = x² + 2x − 3
(c)y = x² − 4x + 3
(d)y = x² − 10x + 21

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