Algebra worksheet — GCSE Higher

1.Which of these pairs of lines are perpendicular to each other?

2.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

3.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

4.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

5.Solve x² + 7x = 0.

6.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.

7.Solve the inequality x² − 5x + 6 < 0.

8.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

9.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.

10.Solve x² − x − 12 = 0.

11.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

12.The curve y = x² − 6 and the line y = 2x − 3 intersect at two points. Which pair of points is correct?

13.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

14.The point (9, 12) lies on the circle x² + y² = 225, which has centre (0, 0). The tangent to the circle at (9, 12) crosses the x-axis at the point P. Work out the x-coordinate of P.

15.Work out the value of the discriminant b² − 4ac for the equation 2x² + 3x − 2 = 0.