Free Year 10 Algebra Diagnostic Worksheet

Diagnostic questions

1. 1. Expand and simplify 3(x + 4) - 2x.

   Answer

   x + 12

   Explanation

   Expand the brackets first: 3x + 12 - 2x. Combine like terms to get x + 12.

2. 2. Solve 2x + 5 = 17.

   Answer

   x = 6

   Explanation

   Subtract 5 from both sides to get 2x = 12, then divide by 2.

3. 3. Factorise x^2 + 7x + 12.

   Answer

   (x + 3)(x + 4)

   Explanation

   Find two numbers that multiply to 12 and add to 7. The numbers are 3 and 4.

4. 4. Solve (x - 2)(x + 5) = 0.

   Answer

   x = 2 or x = -5

   Explanation

   A product is zero when at least one factor is zero, so x - 2 = 0 or x + 5 = 0.

5. 5. Rearrange A = 1/2 bh to make h the subject.

   Answer

   h = 2A / b

   Explanation

   Multiply both sides by 2 to get 2A = bh, then divide by b.

6. 6. Solve the simultaneous equations x + y = 11 and x - y = 3.

   Answer

   x = 7 and y = 4

   Explanation

   Add the equations to get 2x = 14, so x = 7. Substitute into x + y = 11 to get y = 4.

7. 7. Find the gradient of the line through (2, 3) and (6, 11).

   Answer

   2

   Explanation

   The gradient is change in y divided by change in x: (11 - 3) / (6 - 2) = 8 / 4 = 2.

8. 8. Solve x/3 + 4 = 9.

   Answer

   x = 15

   Explanation

   Subtract 4 from both sides to get x/3 = 5, then multiply by 3.

9. 9. Expand (x + 5)^2.

   Answer

   x^2 + 10x + 25

   Explanation

   (x + 5)^2 means (x + 5)(x + 5). Expanding gives x^2 + 5x + 5x + 25.

10. 10. A number pattern has nth term 3n + 2. What is the 10th term?

    Answer

    32

    Explanation

    Substitute n = 10: 3 x 10 + 2 = 32.