Algebra
Using letters to represent unknowns, simplifying linear expressions, evaluating by substitution, and solving simple linear equations.
Stage 1 of 5
What is algebra? Using a letter for an unknown
In PSLE algebra, we use a letter (usually n, x, or a) to represent a number we don't know yet.
Instead of saying "some number", we write n. Instead of "3 times some number", we write 3n.
Instead of saying "some number", we write n. Instead of "3 times some number", we write 3n.
Writing expressions
n + 3 → 3 more than nn − 5 → 5 less than n
3n → 3 times n
n ÷ 4 → n divided by 4
Note on notation
3n means 3 × n(the × sign is dropped)
n/4 means n ÷ 4
(fraction bar = divide)
Write an expression: "Sam has n stickers. He gets 8 more. How many does he have now?"
Expressionn + 8
Meaningoriginal stickers + 8 new ones
Write an expression: "A box has n apples. 4 boxes altogether."
Expression4n
Meaning4 groups of n apples each
Stage 2 of 5
Simplifying expressions — collecting like terms
Like terms have the same letter (or are both plain numbers). You can add or subtract like terms. You cannot add unlike terms together.
3n + 5n = 8n ✓ (both have n)
3n + 5 → stays as 3n + 5 ✗ (cannot combine)
3n + 5n = 8n ✓ (both have n)
3n + 5 → stays as 3n + 5 ✗ (cannot combine)
Simplify: 5a + 3 + 2a − 1
Group terms= (5a + 2a) + (3 − 1)
Simplify= 7a + 2
Simplify: 10n − 4n + 6
Group terms= (10n − 4n) + 6
Simplify= 6n + 6
Brackets are NOT used at P6. The syllabus only covers simplifying without brackets — e.g. 3(n + 2) will not appear. If you see it, it is above syllabus.
Stage 3 of 5
The balance method — solving equations
An equation is like a balance scale. Both sides are equal. Whatever you do to one side, you must do to the other — keeping it balanced.
Goal: get the letter alone on one side.
Goal: get the letter alone on one side.
Solve: 3n + 5 = 20
3n + 5 = 20
− 5 from both sides
3n = 15
÷ 3 on both sides
n = 5
n = 5Check: 3(5) + 5 = 15 + 5 = 20 ✓
Solve: 40 − 2n = 12
40 − 2n = 12
− 40 from both sides
−2n = −28
÷ (−2) on both sides
n = 14
n = 14Check: 40 − 2(14) = 40 − 28 = 12 ✓
Stage 4 of 5
Substitution — evaluating expressions
Substitution means replacing the letter with a given number and computing the result. This is tested directly in Paper 1 (no calculator) and Paper 2.
If n = 4, find the value of 5n − 3
Replace n= 5 × 4 − 3
Calculate= 20 − 3 = 17
If a = 6 and b = 2, find the value of 3a + 4b
Replace= 3 × 6 + 4 × 2
Calculate= 18 + 8 = 26
Order of operations matters. Always multiply and divide before adding and subtracting — even after substituting. 5n − 3 with n = 4 is (5 × 4) − 3 = 17, NOT 5 × (4 − 3) = 5.
Stage 5 of 5
Word problem → equation (the full PSLE method)
The 4-step method for every PSLE algebra word problem:
1. Let n = the unknown quantity (state the unit)
2. Form an equation using the information given
3. Solve the equation
4. State the answer with a unit
1. Let n = the unknown quantity (state the unit)
2. Form an equation using the information given
3. Solve the equation
4. State the answer with a unit
Mary is 3 times as old as her son. The sum of their ages is 48. How old is her son?
Letn = son's age (years)
Mary's age= 3n
Equationn + 3n = 48
Simplify4n = 48
Solven = 48 ÷ 4 = 12
Son is 12 years old
A pen costs $n. A book costs $5 more than 2 pens. Together they cost $23. Find n.
Book= 2n + 5
Equationn + (2n + 5) = 23
Simplify3n + 5 = 23
Solve3n = 18 → n = 6
Pen costs $6