Algebra worksheet — GCSE Higher

1.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

2.Which of these values of x is a solution of x² + 2x − 15 = 0?

3.Solve the inequality 2(3x − 1) ≥ 4x + 8.

4.A circle has centre (0, 0) and equation x² + y² = 100. A straight line is drawn from the origin through the point P(8, 9). Work out whether P lies inside, on, or outside the circle.

5.A company's weekly profit, P thousand pounds, when it makes x thousand items is modelled by P = x² − 8x + 12, for x ≥ 0. Work out the values of x for which the company makes a loss.

6.Line P has equation y = −2x + 5 and line Q has equation 2y = x + 6. Are lines P and Q perpendicular to each other?

7.Which of these equations is equivalent to 5x − 2 = 3x + 8?

8.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

9.A circle has centre (0, 0) and equation x² + y² = 100. Work out which one of these points lies on the circle.

10.Make x the subject of the formula y = (x − 4)/5.

11.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.

12.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.

13.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

14.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.

15.The point (4, 2) lies on the circle x² + y² = 20. Work out the equation of the tangent to the circle at (4, 2).