Checkpoint 1
Algebraic expressions, expanding single and double brackets, factorising common factors, difference of squares and monic quadratics.
Multiple Choice Questions
Which expression is equivalent to $5x + 3y - 2x + 7y$?
If $a = 3$ and $b = -2$, what is the value of $2a^2 - 5b$?
Expand and simplify $4(2x - 3)$.
Expand and simplify $(x + 3)(x - 4)$.
Factorise $6x + 15$ completely.
Factorise $x^2 - 49$.
Factorise $x^2 + 9x + 20$.
Factorise $x^2 - 2x - 15$.
Expand and simplify $2(x + 5) + 3(x - 2)$.
Which method is most efficient to simplify $3x(x + 4) - 2(x^2 - 5)$?
Short Answer Questions
Mixed algebraic simplification.
(a) Simplify $3(x + 4) - 2x$. 1 mark
(b) Expand and simplify $(x + 2)(x + 5)$. 2 marks
(c) Factorise $x^2 - 9x + 20$. 1 mark
A rectangular garden has length $(2x + 5)$ metres and width $(x + 3)$ metres.
(a) Write an expression for the area of the garden in expanded form. 2 marks
(b) Find the area when $x = 4$. 2 marks
Quick Review — Block A: Algebraic Techniques
Like terms
Same variables and powers can be combined
Substitution
Replace variables with given values and evaluate
Expand single brackets
$a(b + c) = ab + ac$
Expand double brackets
$(a + b)(c + d) = ac + ad + bc + bd$
Factorise common factor
Find HCF of all terms and place outside brackets
Difference of squares
$a^2 - b^2 = (a + b)(a - b)$
Monic quadratics ($+c$)
Find two positive numbers: product $= c$, sum $= b$
Monic quadratics ($-c$)
Find two numbers of opposite sign: product $= c$, sum $= b$
Mixed techniques
Expand first, then collect like terms
Area of rectangle
$A = \text{length} \times \text{width}$