Part A: Numeracy
4
Algebra & Patterns
Master linear equations, sequences, algebraic expressions, and function rules
Learning Objectives
- Identify arithmetic and geometric number patterns in real-world teaching data
- Simplify algebraic expressions by combining like terms correctly
- Apply the distributive law to expand brackets
- Solve linear equations using inverse operations step-by-step
- Formulate algebraic equations from written school scenarios
Chapter Progress: 0%
1. Number Patterns & Sequences
Arithmetic vs Geometric Sequences
A number sequence is an ordered list of numbers following a mathematical rule. An arithmetic sequence adds or subtracts a constant common difference (d) between terms. A geometric sequence multiplies or divides by a constant common ratio (r).
Example 1
Finding the Next Term in an Arithmetic Sequence
❓ Question: A teacher records test score improvements across 4 terms: 12, 19, 26, 33. If this linear pattern continues, what is the expected score in Term 5?
📝 Step-by-Step Method:
1
Determine the common difference (d) between consecutive terms.
2
Add the common difference to the last known term (33).
🎯 Final Answer: 40
💡 Why It Is Correct: The sequence increases by a constant common difference of +7 each term. 33 + 7 = 40.
2. Simplifying Algebraic Expressions
Distributive Law
a(b + c) = ab + ac
a = Multiplier outside brackets
b, c = Terms inside brackets
Example
3(2x + 4) = 3(2x) + 3(4) = 6x + 12
Example 2
Simplifying Classroom Inventory Expressions
❓ Question: Simplify the algebraic expression representing classroom supplies: 3x + 2y + 4x - y (where x = exercise books and y = pens).
📝 Step-by-Step Method:
1
Group like terms containing x and like terms containing y.
2
Combine the coefficients of each set of like terms.
🎯 Final Answer: 7x + y
💡 Why It Is Correct: Combining like terms yields 7x for books and y for pens. Unlike terms cannot be combined.
3. Solving Linear Equations
Example 3
Solving Two-Step Linear Equations
❓ Question: Solve for x in the equation representing classroom desk allocations: 2x + 5 = 11.
📝 Step-by-Step Method:
1
Isolate the variable term (2x) by subtracting 5 from both sides.
2
Divide both sides by 2 to solve for x.
🎯 Final Answer: x = 3
💡 Why It Is Correct: Subtracting 5 gives 2x = 6, and dividing by 2 yields x = 3. Check: 2(3) + 5 = 11 (Verified!).
4. Setting Up Equations from Word Problems
Translating Words to Algebraic Symbols
Key translation rules: "sum" or "more than" = addition (+); "difference" or "less than" = subtraction (-); "times" or "product" = multiplication (×); "per" or "divided equally" = division (÷); "is" or "equals" = =.
Example 4
Setting Up Equations for Resource Quantities
❓ Question: A school bus fuel tank contains an unknown volume of diesel (x litres). After adding 15 litres, the tank holds 40 litres. Find the initial fuel volume.
📝 Step-by-Step Method:
1
Define variable and write equation based on scenario.
2
Solve for x by subtracting 15 from both sides.
🎯 Final Answer: 25 litres
💡 Why It Is Correct: Subtracting the 15 added litres from the total 40 litres reveals an initial volume of 25 litres.