Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
15 questions · official format, shuffled order
1 Expand and simplify 3(2p − 5) − 2(p − 4).
Show worked solution
6p − 15 − 2p + 8 = 4p − 7. (4p − 23 writes −2 × −4 as −8.)
2 Expand (3x − 2)(2x + 5).
Show worked solution
6x2 + 15x − 4x − 10 = 6x2 + 11x − 10. (6x2 − 10 multiplies only first and last terms.)
3 Expand (2a − 7)2.
Show worked solution
(2a)2 + 2(2a)(−7) + (−7)2 = 4a2 − 28a + 49. (4a2 + 49 forgets the middle term.)
4 Use a special product to work out 63 × 57 without a calculator.
Show worked solution
602 − 32 = 3600 − 9 = 3591.
5 Factorise fully: 18x2y − 12xy2.
Show worked solution
The HCF is 6xy, leaving 6xy(3x − 2y). The others are equal in value but not fully factorised — a common factor is still left inside the bracket.
6 Factorise ab − 4a + 3b − 12.
Show worked solution
a(b − 4) + 3(b − 4) = (b − 4)(a + 3). Check: expanding gives ab + 3b − 4a − 12. ✓
7 Simplify (x + 2)/4 − (x − 3)/6.
Show worked solution
3(x + 2) − 2(x − 3) = 3x + 6 − 2x + 6 = x + 12, so (x + 12)/12. (x/12 writes −2 × −3 as −6; (5x + 12)/12 adds the fractions instead of subtracting.)
8 (x + a)(x + 4) = x2 + 9x + b for every value of x. What is b?
Show worked solution
a + 4 = 9 gives a = 5, and b = 4a = 20. (5 is a, not b.)
9 Work out 472 − 432 without a calculator.
Show worked solution
90 × 4 = 360.
10 Expand and simplify (x + 3)(x2 − 2x + 1).
Show worked solution
x3 − 2x2 + x + 3x2 − 6x + 3 = x3 + x2 − 5x + 3.
11 1 (x − 5)2 = x2 − 25.
2 (x + 2)(x − 2) = x2 − 4.
3 −(3 − x) = x − 3.
Which statements are correct?
2 (x + 2)(x − 2) = x2 − 4.
3 −(3 − x) = x − 3.
Which statements are correct?
Show worked solution
(x − 5)2 = x2 − 10x + 25, not x2 − 25 (1 ✗). The middle terms cancel in (x + 2)(x − 2) (2 ✓). −3 + x = x − 3 (3 ✓). 2 and 3.
12 A square of side (2x + 1) has a square of side (x − 1) cut out of one corner. Which expression gives the area that is left?
Show worked solution
(4x2 + 4x + 1) − (x2 − 2x + 1) = 3x2 + 6x. (3x2 + 2x subtracts −2x as if it were +2x.)
13 What is the coefficient of x in (2x − 3)(4x + 5) − (x − 1)2?
Show worked solution
The first product has 10x − 12x = −2x. The square has −2x, which is subtracted: −2x − (−2x) = 0. The coefficient is 0.
14 Simplify (10x + 15)/5 − (6x − 21)/3.
Show worked solution
(2x + 3) − (2x − 7) = 10. (−4 comes from −(2x − 7) written as −2x − 7.)
15 1 12a2 − 27 = 3(4a2 − 9).
2 12a2 − 27 = 3(2a − 3)(2a + 3).
3 12a2 − 27 = (6a − 9)(2a − 3).
Which statements are correct?
2 12a2 − 27 = 3(2a − 3)(2a + 3).
3 12a2 − 27 = (6a − 9)(2a − 3).
Which statements are correct?
Show worked solution
3 × 4a2 − 3 × 9 (1 ✓). 3(4a2 − 9) is the same as statement 1 (2 ✓). (6a − 9)(2a − 3) = 12a2 − 36a + 27 (3 ✗). 1 and 2.