Algebra worksheet — GCSE Higher

1.A cyclist's speed rises from rest to a maximum — quickly at first, then more and more slowly — so her speed-time graph is a curve that is concave down (its gradient decreases as time goes on). A trapezium estimate is made for the distance travelled during this phase, using two points on the curve. Is the trapezium estimate an overestimate or an underestimate of the true distance, and why?

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

3.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.

4.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?

5.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

6.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

7.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

8.y = 5 − 2x. Work out the value of x when y = 11.

9.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

10.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

11.Using the table of values of f(x) (x = 0, 1, 2, 3 gives f(x) = 5, 8, 4, 1), work out the value of −f(x) when x = 1.

12.The tangent to a curve at the point (6, 1) has gradient −3. Work out the y-coordinate of the point where this tangent crosses the y-axis.

13.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

14.Points A(−1, 2) and B(5, 8) are the endpoints of a line segment. Work out the equation of the perpendicular bisector of AB.

15.A sequence begins at 50, and each term after that is found by subtracting 8 from the term before it. Priya says the 8th term of the sequence is negative. Is Priya correct?