Algebra worksheet — GCSE Foundation

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

2.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.

3.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

4.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.

5.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.

6.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

7.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

8.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

9.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

10.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

11.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.

12.y = 5x − 1. Work out the value of y when x = 3.

13.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

14.Solve the inequality 3x + 6 ≤ 0.

15.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.