Algebra worksheet — GCSE Foundation

1.Expand and simplify 2(a + 6) − 2(a − 7)

2.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

3.The point B has coordinates (−2, −2). In which quadrant is B?

4.Write down the expression that means the same as (x + 7) ÷ 4.

5.Solve the inequality x − 10 < −3.

6.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

7.Simplify 2b − 1 + 2b − 4 + 2b

8.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

9.A number machine multiplies its input by 3. The output is 15. Work out the input.

10.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.

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

12.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

13.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.

14.Solve the inequality 4x + 1 > 2x + 9.

15.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.