Sec 1
Sec 1 algebra
The one-page cheat sheet
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Sec 1 Math · Singapore MOE syllabus
1Notation you must read correctly
3a means 3 × a
If a = 4, then 3a = 12, not 34.
a² means a × a
If a = 5, then a² = 25, not 10.
a/b means a ÷ b
"Half of x" is written x/2 or ½x.
−a is "negative a"
If a = −3, then −a = 3.
2Like terms — what you can combine
Same letter, same power → like terms. Different → unlike.
| ✓ Like | 5x and 2x | → 7x |
| ✓ Like | 3y² and −y² | → 2y² |
| ✗ Unlike | 3x and 3y | → stays as 3x + 3y |
| ✗ Unlike | 2x and 2x² | → stays as 2x + 2x² |
3Worked example — simplifying
Simplify: 5x + 3 − 2x + 7
Step 1. Group like terms → (5x − 2x) + (3 + 7)
Step 2. Combine each group → 3x + 10
4Expanding brackets
The number outside multiplies every term inside.
3(x + 4) = 3x + 12
−2(x − 5) = −2x + 10
4(2a − 3b) = 8a − 12b
−2(x − 5) = −2x + 10
4(2a − 3b) = 8a − 12b
5Substitution
If x = 5, find 2x² − 3x + 1
Step 1. Replace x with (5) — use brackets
= 2(5)² − 3(5) + 1
Step 2. Powers first → = 2(25) − 3(5) + 1
Step 3. Multiply → = 50 − 15 + 1
Step 4. Add and subtract → = 36
⚠The 4 mistakes that cost the most marks
1. The negative-sign trap
−3(x − 4) = −3x + 12, not −3x − 12
2. The 2x² trap
2x² means 2 × (x²), not (2x)². If x = 5, 2x² = 50, not 100.
3. Forgetting to distribute the second term
5(x + 2) = 5x + 10, not 5x + 2
4. Combining unlike terms
3x + 2y ≠ 5xy. They stay separate.
Self-check before moving on
Can you simplify 7a − 3 + 2a − 5, expand −4(2x − 3), and find 3x² − x when x = 4? If yes, you're solid. If no, redo the worked example for that section.
Answers: 9a − 8 · −8x + 12 · 44