§1 Order of operations
Parentheses, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right. Multiplication does not come before division — they share a level.
§2 Fractions, decimals and percents
| Fraction | Decimal | Percent |
|---|---|---|
| 1/8 | 0.125 | 12.5% |
| 1/5 | 0.2 | 20% |
| 1/4 | 0.25 | 25% |
| 1/3 | 0.333… | 33⅓% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 2/3 | 0.666… | 66⅔% |
| 3/4 | 0.75 | 75% |
§3 Number sequences — what to test, in order
§4 Word-problem formulas worth memorising
| Type | Relationship |
|---|---|
| Distance | distance = rate × time |
| Work | combined rate = 1/a + 1/b; time = 1 ÷ combined rate |
| Simple interest | I = P × r × t (t in years) |
| Average | sum = average × count |
| Ratio a : b of total T | one part = T ÷ (a + b) |
| Consecutive integers | n, n + 1, n + 2 (even/odd: n, n + 2, n + 4) |
§5 Worked examples
Example 1
A printer does a job in 4 hours; a second printer does it in 12 hours. How long together?
- Rates: 1/4 + 1/12 = 3/12 + 1/12 = 4/12 = 1/3 job per hour.
- Time = 1 ÷ (1/3) = 3 hours.
Answer 3 hours
Example 2
A price rose from ₱250 to ₱300, then fell back to ₱250. What were the percent changes?
- Rise: (300 − 250) ÷ 250 = 50/250 = 20%.
- Fall: (250 − 300) ÷ 300 = −50/300 ≈ −16.7%.
- The base changes, so the percentages differ even though the peso amount is the same.
Answer +20%, then about −16.7%
Example 3
Next term: 7, 10, 8, 11, 9, 12, ___
- Odd positions: 7, 8, 9 (+1).
- Even positions: 10, 11, 12 (+1).
- The 7th term is an odd position: 10.
Answer 10
! Common traps
- Averaging rates or times in work problems — add rates instead.
- Forgetting to convert months to years in interest, or minutes to hours in speed.
- Computing the answer to a different question, e.g. the discount instead of the sale price. Re-read the last line.
Coverage sources: Examination Announcement No. 03, s. 2026; Examination Advisory No. 10, s. 2026