Section A
Substituting into Expressions
Method: Replace each letter with its given value, then follow the order of operations (BIDMAS/BODMAS) — powers before multiplying, multiplying before adding or subtracting.
Example: If x = 3, evaluate 2x + 5 → 2(3) + 5 = 6 + 5 = 11
Q1
If x = 5, evaluate 2x + 3.
1 mark
Q2
If a = 4, evaluate a² − 5.
1 mark
Q3
If p = −2, evaluate 3p + 8.
1 mark
Q4
If x = 3 and y = 4, evaluate 2x² − y.
2 marks
SUBSTITUTING — SECTION SCORE
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Section B
Constructing Expressions
Method: Turn a word description into an algebraic expression by choosing a letter for the unknown, then translating each phrase in order.
Example: "A number, n, decreased by 6" → n − 6
Q5
Write an expression for: "A number, n, increased by 7."
1 mark
Q6
Write an expression for: "Three times a number, x, decreased by 4."
1 mark
Q7
Write an expression for: "The cost, in dollars, of n tickets at $8 each, plus a $5 booking fee."
1 mark
Q8
A rectangle has length (x + 3) and width x. Write an expression for its perimeter, fully simplified.
2 marks
CONSTRUCTING — SECTION SCORE
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Section C
Expressions and Indices
Method: Multiply/divide the coefficients (number parts) separately from the letters, then apply the index laws to the letters — add powers when multiplying, subtract when dividing, multiply powers when raising a power to a power.
Example: 3x² × 4x³ = (3 × 4)x^(2+3) = 12x⁵
Q9
Simplify: 3x² × 4x³
1 mark
Q10
Simplify: 10y⁵ ÷ 2y²
1 mark
Q11
Simplify: (2a³)²
1 mark
Q12
Simplify: 6x⁴y² ÷ 3xy
2 marks
INDICES — SECTION SCORE
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Section D
Expanding Products of Linear Expressions
Method: For a single bracket, multiply everything inside by the term outside: a(b + c) = ab + ac. For two brackets, multiply every term in the first bracket by every term in the second (FOIL), then collect like terms.
Example: (x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6
Q13
Expand: 3(x + 4)
1 mark
Q14
Expand: −2(x − 5)
1 mark
Q15
Expand: x(x + 6)
1 mark
Q16
Expand and simplify: (x + 2)(x + 3)
2 marks
Q17
Expand and simplify: (x − 4)(x + 2)
2 marks
BRACKETS — SECTION SCORE
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Section E
Simplifying Algebraic Fractions
Method: Divide the numerator and denominator by their highest common factor — a shared number, a shared letter, or both.
Example: (6x + 9) / 3 = 2x + 3
Q18
Simplify: 8x / 4
1 mark
Q19
Simplify: (6x + 9) / 3
1 mark
Q20
Simplify: (x² + 5x) / x
1 mark
Q21
Simplify: 10x²y / 5xy
2 marks
FRACTIONS — SECTION SCORE
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Section F
Deriving and Using Formulae
Method: To rearrange a formula, use inverse operations to isolate the letter you want as the subject — undo addition/subtraction first, then multiplication/division. To use a formula, substitute the given values and evaluate.
Example: A = ½bh, rearranged to make h the subject → h = 2A / b
Q22
The formula for the area of a triangle is A = ½bh. Rearrange to make h the subject.
1 mark
Q23
Using A = ½bh, find A when b = 8 and h = 5.
1 mark
Q24
The formula v = u + at gives final velocity. Rearrange to make a the subject.
1 mark
Q25
Using v = u + at, find v when u = 10, a = 2 and t = 4.
2 marks
Q26
The perimeter of a rectangle is P = 2l + 2w. Rearrange to make w the subject.
2 marks
FORMULAE — SECTION SCORE
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