Mathematics
What this domain tests
Mathematics tests number sense, arithmetic, ratio and proportion, percentage, average, simple interest, mensuration and data interpretation at upper-primary level. Speed matters, but accuracy comes from choosing the right unitary base.
Core rules and concepts
- Divisibility: a number is divisible by 3 if its digit sum is divisible by 3; by 9 if the digit sum is divisible by 9; by 8 if the last three digits form a multiple of 8.
- HCF × LCM = product of two numbers (for two positive integers).
- Percentage change uses the original quantity as base. Successive changes of a% and b% give a net change of a + b + ab/100, with signs.
- Average speed for equal distances is the harmonic mean: 2xy/(x+y), not (x+y)/2.
Worked example
A shopkeeper marks an article 40% above cost and allows a 25% discount. Find the profit percentage. Reasoning: Let cost price = 100. Marked price = 140. Discount is 25% of 140 = 35, so selling price = 105. Profit = 105 − 100 = 5 on cost 100, so profit = 5%. The discount must be applied to the marked price, not the cost price.
Traps that cost marks
- Applying a discount to cost price instead of marked price.
- Treating successive percentage changes as simple addition.
- Using the arithmetic mean for average speed when distances are equal.
- Forgetting unit conversion in mensuration, such as cm² to m².
Quick check
Estimate before calculating: if marked price is 140 and discount is one-fourth, the answer must be near 105, not near 115.