Mathematical and Problem-Solving Skills
What to master
Core areas: operations on fractions, decimals, and percentages; ratio and proportion; integer rules; algebraic expressions and simple equations; geometry (perimeter, area, volume, angles); statistics (mean, median, mode); and word problems involving money, time, and rates. Percent problems (discount, tax, interest, increase/decrease) appear often.
Common traps
- Percent of what? A 20% discount then a 10% discount is not 30% off; the second discount applies to the reduced price.
- Mixing units (minutes vs. hours, cm vs. m) before computing.
- Sign errors with negative numbers: subtracting a negative adds.
- Confusing mean with median when one outlier skews the data.
- Solving for x but answering the wrong quantity (the question asks for the other number).
Rule of thumb
For word problems: (1) underline what is asked, (2) list given values with units, (3) choose a formula or set up an equation, (4) estimate the answer first, then compute, (5) check whether the result is reasonable.
Worked example
A shirt costs ₱800 and is discounted 25%. What is the sale price?
- Discount = 0.25 × 800 = ₱200.
- Sale price = 800 − 200 = ₱600. Shortcut: pay 75% of the price → 0.75 × 800 = ₱600. Estimate check: 25% is a quarter, so the price should drop by about ₱200 - reasonable.