Mathematics
What the exam tests
Kankor mathematics rewards clean fundamentals: arithmetic with fractions and decimals, ratio and proportion, percentages, exponents and roots, linear equations and inequalities, simple quadratics, basic geometry (angles, triangles, circles, area and volume), and elementary probability and statistics (mean, median, mode).
Concepts to master
- Percentage change and successive discounts: a 20% rise then a 20% fall does not return to the original value.
- Ratio and rate problems, including work-rate and mixture questions.
- Algebraic manipulation: factoring, the difference of squares, and solving linear systems by substitution or elimination.
- Geometry formulas: area of triangle and circle, Pythagorean theorem, sum of interior angles of a polygon.
- Averages: total = mean × count is the fastest route through most statistics questions.
Common traps
- Unit mismatches (minutes vs hours, cm vs m) hidden in word problems.
- Reading "percent of" as "percent increase".
- Forgetting that the square root sign returns only the non-negative value.
- Rounding too early; carry full precision and round at the end.
- In inequalities, forgetting to flip the sign when multiplying or dividing by a negative number.
Worked example
A shirt costs 800 afghanis. Its price rises 25%, then the new price is discounted 20%. Final price? Rise: 800 × 1.25 = 1000. Discount: 1000 × 0.80 = 800. The final price equals the original - a good rule of thumb: a rise of p% followed by a fall of the same p% always lands below the start, but here the percentages apply to different bases, so check each step on its own base.