Algebra worksheet — GCSE Foundation

1.Write down the number of terms in the expression 4x² − 7x + 3.

2.Solve x² − 6x = 0.

3.Solve the inequality x − 10 < −3.

4.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.

5.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.

6.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

7.The nth term of a sequence is 2n − 1. Work out the 6th term of the sequence.

8.The nth term of a sequence is 3n + 2. Work out the 4th term of the sequence.

9.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.

10.Solve the inequality x + 5 < 12.

11.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

12.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.

13.A person's body mass index is given by the formula B = m ÷ h², where m is the mass in kg and h is the height in metres. Work out B, to 1 decimal place, when m = 68 and h = 1.6.

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

15.Solve 5(x + 3) = 40