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 plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.
(a)4
(b)7.5
(c)5.75
(d)2.71
2.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
3.The graph of y = sin x is reflected in the x-axis to give the graph of y = g(x). Work out the value of g(90), where x is measured in degrees.
y = sin(x)
(a)−1
(b)1
(c)−0.5
(d)0
4.Solve the inequality 6.3x + 1.8 ≤ 40. Hence write down the greatest number with exactly one decimal place that satisfies the inequality.
(a)6.6
(b)6.1
(c)6.3
(d)6.0
5.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.
y = x² − 2x − 8
(a)x = −2
(b)x = −1 or x = 3
(c)x = −2 or x = 4
(d)x = 0 or x = −8
6.f(x) = x³ − 3x² − 4. Work out the pair of consecutive integers between which the solution of f(x) = 0 lies.
y = x
(a)4 and 5
(b)2 and 3
(c)0 and 1
(d)3 and 4
7.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.
(a)y = 2x
(b)y = 3x
(c)y = x²
(d)y = 3x − 2
8.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.
(a)68, and it is an equation
(b)36, and it is a formula
(c)52, and it is a formula
(d)68, and it is a formula
9.The trapezium rule is used to estimate the area under a curve between x = 2 and x = 6. The curve is concave up (it curves upwards, like the inside of a bowl) throughout this interval. Which statement about the estimate is correct?
(a)Overestimates — trapezium edges lie above the curve.
(b)Underestimates — trapezium edges lie below the curve.
(c)Exact — straight lines model any curve with no error.
(d)Overestimates, because more strips always increase it.
10.Which of these statements is an equation with exactly one solution?
(a)5x − 3 = 12
(b)5x − 3 = 5x − 3
(c)5x − 3 > 12
(d)5x − 3 = 5x + 2
11.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.
(a)(1, 3)
(b)(−1, 3)
(c)(9, 4)
(d)(−1, 4)
12.How many turning points does the graph of y = x² − 7x + 10 have?
y = x² − 7x + 10
(a)Four turning points.
(b)One turning point.
(c)Two turning points.
(d)No turning points.
13.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
14.The point (3, 4) lies on the circle x² + y² = 25, which has centre (0, 0). Work out the gradient of the tangent to the circle at (3, 4).
(a)−4/3
(b)−3/4
(c)4/3
(d)3/4
15.Solve the inequality x² ≥ 16, giving your answer using set notation.
(a){x : x ≤ 4}
(b){x : x ≥ 4}
(c){x : x ≤ −4} ∪ {x : x ≥ 4}
(d){x : −4 ≤ x ≤ 4}

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