Think First
warm-up

Before diving into the practice questions, take a moment to think about what you already know about this topic.

Record in workbook.
1
Unit 2 — Module Summary
overview

Here is a snapshot of every key idea from Unit 2. Use it as a reference as you work through today's review.

Topic Key Idea Example
Algebraic expressions Letters represent unknown numbers $3x$ means $3 \times x$
Like terms Same variable and power can be combined $2x + 5x = 7x$; but $2x + 3y$ cannot simplify
Expanding brackets Multiply each term inside by the factor outside $3(x + 4) = 3x + 12$
Factorising Find the highest common factor and place it outside $6x + 9 = 3(2x + 3)$
One-step equations Apply one inverse operation to both sides $x + 7 = 12 \Rightarrow x = 5$
Two-step equations Apply two inverse operations (reverse order of operations) $2x + 3 = 11 \Rightarrow x = 4$
Word problems Define a variable, write an equation, then solve $2n + 5 = 17 \Rightarrow n = 6$
2
Self-Assessment Checklist
objectives

Rate yourself honestly on each skill. Use this to guide which topics need more practice.

Know

  • I can write and simplify algebraic expressions
  • I can collect like terms correctly

Understand

  • I can expand single brackets using the distributive law
  • I can factorise expressions by finding the highest common factor

Can Do

  • I can solve one-step linear equations
  • I can solve two-step linear equations
  • I can translate a word problem into an equation and solve it

Watch Me Solve It · Expressions & Like Terms

Expressions, Expanding & Factorising — Worked Examples
+15 XP per step
A
EXAMPLE A — Collecting Like Terms
Simplify: $5x + 3y - 2x + y$
  1. 1
    Identify and group like terms
    $x$ terms: $5x$ and $-2x$  |  $y$ terms: $3y$ and $y$
    Like terms share the same variable and power. $x$ and $y$ terms cannot be combined with each other.
  2. 2
    Combine the $x$ terms
    $5x - 2x = 3x$
    Subtract the coefficients: $5 - 2 = 3$.
  3. 3
    Combine the $y$ terms
    $3y + y = 4y$
    $y$ has an invisible coefficient of 1, so $3y + 1y = 4y$.
  4. 4
    Write the simplified answer
    $5x + 3y - 2x + y = 3x + 4y$
    This cannot simplify further — $x$ and $y$ terms are unlike.
Answer A $3x + 4y$
B
EXAMPLE B — Expanding
Expand: $4(2x - 3)$
  1. 1
    Multiply the factor by the first term inside the bracket
    $4 \times 2x = 8x$
    Multiply coefficients: $4 \times 2 = 8$. Variable stays as $x$.
  2. 2
    Multiply the factor by the second term (watch the sign!)
    $4 \times (-3) = -12$
    Positive times negative gives a negative result.
  3. 3
    Write the final expanded expression
    $4(2x - 3) = 8x - 12$
    Check: no more brackets and no like terms to collect.
Answer B $8x - 12$
C
EXAMPLE C — Factorising
Factorise: $10x + 15$
  1. 1
    Find the HCF of the coefficients
    HCF(10, 15) = 5
    Factors of 10: {1, 2, 5, 10}. Factors of 15: {1, 3, 5, 15}. Largest shared factor is 5.
  2. 2
    Check for a variable HCF
    $10x$ has $x$; but $15$ has no $x$
    Since $x$ is not in every term, it cannot be part of the HCF.
  3. 3
    Divide each term by 5 and write the factorised form
    $10x \div 5 = 2x \qquad 15 \div 5 = 3$
    These remainders go inside the brackets.
  4. 4
    Write the answer and verify by expanding
    $10x + 15 = 5(2x + 3)$
    Check: $5 \times 2x = 10x$ and $5 \times 3 = 15$. So $5(2x + 3) = 10x + 15$ ✓
Answer C $5(2x + 3)$

Watch Me Solve It · Equations

Solving Equations — Worked Examples
+15 XP per step
A
EXAMPLE A — One-Step Equation
Solve: $x + 9 = 14$
  1. 1
    Identify the operation being applied to $x$
    $x$ has 9 added to it
    To isolate $x$, apply the inverse operation — subtraction.
  2. 2
    Subtract 9 from both sides
    $x + 9 - 9 = 14 - 9$
    Whatever you do to one side, you must do to the other.
  3. 3
    State the answer and check
    $x = 5$  |  Check: $5 + 9 = 14$ ✓
    Always substitute back to verify.
Answer A $x = 5$
B
EXAMPLE B — Two-Step Equation
Solve: $3x - 4 = 11$
  1. 1
    Add 4 to both sides (undo the subtraction first)
    $3x - 4 + 4 = 11 + 4$
    Reverse order of operations: addition/subtraction is undone before multiplication/division.
  2. 2
    Simplify
    $3x = 15$
    $-4 + 4 = 0$, so that term disappears.
  3. 3
    Divide both sides by 3
    $x = 15 \div 3 = 5$
    Division is the inverse of multiplication.
  4. 4
    Check by substituting $x = 5$
    $3(5) - 4 = 15 - 4 = 11$ ✓
    Left-hand side equals right-hand side, so the answer is correct.
Answer B $x = 5$
C
EXAMPLE C — Word Problem
A number is doubled and 7 is added, giving 19. Find the number.
  1. 1
    Define the variable
    Let $n$ = the unknown number
    Always name your variable before writing the equation.
  2. 2
    Translate words into an equation
    "doubled and 7 added, giving 19" → $2n + 7 = 19$
    "doubled" = multiply by 2; "7 is added" = add 7; "giving 19" = equals 19.
  3. 3
    Subtract 7 from both sides
    $2n = 19 - 7 = 12$
    Undo addition first (reverse order of operations).
  4. 4
    Divide both sides by 2 and check
    $n = 6$  |  Check: $2(6) + 7 = 12 + 7 = 19$ ✓
    The solution satisfies the original condition.
Answer C $n = 6$
5
Common Errors to Avoid
heads-up

These are the most frequent mistakes students make in this unit. Read each one carefully so you do not repeat them.

Adding unlike terms together
Writing $2x + 3y = 5xy$. These are unlike terms — they have different variables and cannot be combined.
Fix: only combine terms that have exactly the same variable and power. $2x + 3y$ is already fully simplified.
Forgetting to multiply ALL terms inside the bracket
Writing $3(x + 4) = 3x + 4$. The 3 must multiply both $x$ AND 4.
Fix: $3(x + 4) = 3 \times x + 3 \times 4 = 3x + 12$. Check by expanding every term.
Sign errors when solving equations
For $x - 5 = 8$, writing $x = 3$ by subtracting 5 again. You need to ADD 5 to both sides to undo the subtraction.
Fix: $x - 5 + 5 = 8 + 5$, so $x = 13$. Always apply the inverse operation.
Factorising without using the full HCF
Writing $6x + 9 = 3(2x) + 9$ instead of taking out the full common factor. The 9 must also be inside the bracket.
Fix: $6x + 9 = 3(2x + 3)$. Check: $3 \times 2x = 6x$ and $3 \times 3 = 9$ ✓. Every term must be divided by the HCF.
6
Exam Strategy
tips

Use these strategies on every algebra question to maximise your marks.

Always check by substituting back
After solving an equation, substitute your answer into the original equation. If both sides are equal, you are correct.
Define your variable first
In word problems, always write "Let $x$ = ..." before writing any equation. This earns a mark and keeps your work clear.
Show all working steps
Partial marks are awarded for correct working even if your final answer is wrong. Never skip steps.
Circle same-type terms
When collecting like terms, physically circle or underline matching terms before combining them — this prevents mixing up $x$ and $y$ terms.

Quick Check · 5 questions

1
Simplify $3x + 5y - 2x + y$.
+10 XP
2
Expand and simplify: $2(3x - 4) + 5(x + 2)$.
+10 XP
3
Solve $\frac{x + 5}{3} = 4$.
+10 XP
4
The $n$th term of a sequence is $4n - 1$. What is the sum of the 5th and 10th terms?
+10 XP
5
A line has equation $y = 3x - 2$. Which point is NOT on the line?
+10 XP
Apply Easy 2 MARKS

Q1. Factorise fully: $12x^2 + 8x$.

Answer in your workbook.
Apply Medium 3 MARKS

Q2. "Three consecutive even numbers add to 48. Find the numbers." Write and solve an equation.

Answer in your workbook.
Apply Hard 4 MARKS

Q3. A car travels at 80 km/h. Write a rule for distance $d$ in terms of time $t$. How long does it take to travel 300 km? Draw a graph showing the relationship for the first 5 hours.

Answer in your workbook.
Stretch Challenge · +25 XP, +10 coins

Extension Problems

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R
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Unit overview · Maths subject page · Unit quiz

Brain Trainer

⚡
Speed Drills — Mixed Revision!

Set a timer for 5 minutes. Solve as many as you can!

Simplify: $5a + 3b - 2a + b$
Expand: $3(2x - 5)$
Factorise: $8x + 12$
Solve: $3x + 7 = 22$
Solve: $\frac{x}{4} - 3 = 2$
$n$th term: 5, 8, 11, 14, ...
If $y = 2x + 3$, find $y$ when $x = 4$
Expand: $2(x + 3) + 4(x - 1)$
Solve: $5(x - 2) = 20$
Factorise: $6x^2 + 9x$