Algebra worksheet — GCSE Foundation

1.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?

2.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?

3.Solve the inequality 5 − x ≤ 2.

4.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

5.Work out the distance of the point (−6, 4) from the x-axis.

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

7.A straight line has gradient −2 and passes through the point (3, 1). Work out the equation of the line.

8.A curve has equation y = x² − 9. Which statement about its graph is correct?

9.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.

10.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.

11.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

12.A number machine adds 5 to its input. Work out the output when the input is 0.

13.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

14.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.

15.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?