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
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- 1.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.
- 2.Solve 7x − 5 = 3x + 11
- 3.Solve the simultaneous equations x + y = 1 and 2x + y = 5.
- 4.The curve y = x² − 3x. Use the chord between x = 1 and x = 4 to estimate the gradient of the curve at x = 2.5.y = x² − 3x
- 5.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.
- 6.The discriminant of a quadratic equation is greater than zero. Which statement about the solutions of that equation is correct?
- 7.A sequence is defined by aₙ = aₙ₋₁ + aₙ₋₂ for n ≥ 3. Given that a₃ = 11 and a₅ = 29, work out a₁.
- 8.Which of these is a formula, rather than an expression, an equation, or an identity?
- 9.Write down the gradient of the line with equation y = −x + 3.y = −x + 3
- 10.Solve 5(x + 3) = 40
- 11.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.
- 12.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.
- 13.Work out the value of a² − 2b when a = −3 and b = 4.
- 14.Which of these statements is an equation with exactly one solution?
- 15.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.
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