Algebra worksheet — GCSE Higher

1.Solve 7x − 5 = 3x + 11

2.Expand and simplify 2(a + 6) − 2(a − 7)

3.The tangent to a curve at the point where x = 4 passes through the points (2, 5) and (6, 21). Use these two points to estimate the gradient of the curve at x = 4.

4.Which of these quadratic graphs does NOT cross the x-axis at all?

5.Work out the value of 5m² + 3m when m = −2.4

6.A graph passes through the point (0, 1). As x increases through positive values, the graph rises more and more steeply, and as x decreases through negative values, the graph gets closer and closer to the x-axis without ever reaching it. Which of these could be the equation of the graph?

7.The point (3, 6) lies on the circle x² + y² = 45. The tangent to the circle at (3, 6) crosses the x-axis at the point P. Work out the coordinates of P.

8.Solve the inequality 2(x − 1) ≤ 8.

9.Which of these statements is an equation with exactly one solution?

10.A car's speed, in m/s, during a journey is: 0 at t = 0 s, 8 at t = 4 s, and 8 (constant) from t = 4 s to t = 10 s, increasing at a constant rate between t = 0 and t = 4. Estimate the total distance the car travels, using the areas of a triangle and a rectangle.

11.Solve the inequality x² + 6x + 9 > 0.

12.Factorise 6x² − 7x − 3.

13.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

14.The table shows some values of f(x): when x = 0, f(x) = 5; when x = 1, f(x) = 8; when x = 2, f(x) = 4; when x = 3, f(x) = 1. Work out the value of f(x − 1) when x = 2.

15.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?