This checkpoint assesses your understanding of variables, substitution, simplifying expressions, expanding brackets and factorising. It covers Lessons 1–5.
❓ Multiple Choice (10 questions)
1. In the expression $4x - 5y + 7$, what is the constant term?
2. Evaluate $3a + 2$ when $a = 4$.
3. Simplify $5x + 3y - 2x + 4y$.
4. Expand $-3(x - 2)$.
5. Expand $(x + 3)(x + 4)$.
6. Factorise $6x + 9$.
7. Expand and simplify $2(x + 3) + 3(x - 1)$.
8. Factorise $x^2 - 16$.
9. Simplify $3(2a + b) - 2(a - 3b)$.
10. Expand $(2x - 1)^2$.
✍ Short Answer (4 questions)
11. Evaluate the following expressions.
(a) $4m - 3n + 2$ when $m = 3$ and $n = -1$ (1 mark)
(b) $p^2 - 2q + 5$ when $p = -2$ and $q = 4$ (1 mark)
(c) $\dfrac{2a + b}{3}$ when $a = 5$ and $b = 4$ (1 mark)3 MARKS
12. Simplify fully.
(a) $7x + 3y - 4x + 2y$ (1 mark)
(b) $3a^2 + 5a - a^2 + 2a - 4$ (1 mark)
(c) $5(m + 2n) - 2(3m - n)$ (2 marks)4 MARKS
13. Expand and simplify.
(a) $(x + 2)(x + 5)$ (1 mark)
(b) $(2a - 1)(a + 3)$ (2 marks)
(c) $(x + 3)^2 - (x + 2)(x - 2)$ (2 marks)5 MARKS
14. Factorise fully.
(a) $8x + 12$ (1 mark)
(b) $5a^2 - 15a$ (1 mark)
(c) $9m^2 - 25n^2$ (2 marks)
(d) $2x^2 + 8x$ (1 mark)5 MARKS
1. B — The constant term is $7$ (the term with no variables).
2. C — $3(4) + 2 = 12 + 2 = 14.
3. A — $(5x - 2x) + (3y + 4y) = 3x + 7y.
4. B — $-3(x - 2) = -3x + 6 = -3x + 6.
5. B — $(x + 3)(x + 4) = x^2 + 4x + 3x + 12 = x^2 + 7x + 12.
6. A — HCF is $3$, so $6x + 9 = 3(2x + 3).
7. A — $2x + 6 + 3x - 3 = 5x + 3.
8. D — $x^2 - 16 = (x + 4)(x - 4) (difference of two squares).
9. B — $6a + 3b - 2a + 6b = 4a + 9b.
10. B — $(2x - 1)^2 = 4x^2 - 4x + 1 = 4x^2 - 4x + 1.
Q11 (3 marks): (a) $4(3) - 3(-1) + 2 = 12 + 3 + 2 = 17 [1]. (b) $(-2)^2 - 2(4) + 5 = 4 - 8 + 5 = 1 [1]. (c) $\dfrac{2(5) + 4}{3} = \dfrac{14}{3} = 4\frac{2}{3}$ [1].
Q12 (4 marks): (a) $7x - 4x + 3y + 2y = 3x + 5y [1]. (b) $3a^2 - a^2 + 5a + 2a - 4 = 2a^2 + 7a - 4 [1]. (c) $5m + 10n - 6m + 2n = -m + 12n [2].
Q13 (5 marks): (a) $x^2 + 5x + 2x + 10 = x^2 + 7x + 10 [1]. (b) $2a^2 + 6a - a - 3 = 2a^2 + 5a - 3 [2]. (c) $(x^2 + 6x + 9) - (x^2 - 4) = x^2 + 6x + 9 - x^2 + 4 = 6x + 13 [2].
Q14 (5 marks): (a) $4(2x + 3)$ [1]. (b) $5a(a - 3)$ [1]. (c) $(3m + 5n)(3m - 5n)$ [2]. (d) $2x(x + 4)$ [1].
Tick when you have finished all questions and checked your answers.