Algebra worksheet — GCSE Foundation

1.Expand 7(a + 8)

2.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.

3.How many turning points does the graph of y = x² − 7x + 10 have?

4.y = x + 4. Work out the value of y when x = 3.

5.Which expression means the same as 3 × a × b?

6.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

7.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

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

9.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

10.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?

11.Work out the value of m² + 3m when m = −2

12.The point A is at (5, −3). In which quadrant does A lie?

13.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.

14.Which of these is a factor of 15x + 20?

15.Factorise x² − 3x − 10.