Chartered Accountancy, Institute of Chartered Accountants of Pakistan (Scheme 2025) · Quantitative Analysis for Business
ICAP PRC-2 Basic mathematics: practice questions with answers
3 free exam-style questions on Basic mathematics for ICAP PRC-2 Quantitative Analysis for Business. Try each one, then open the answer to read the explanation. Fincora has 36 original questions on this syllabus area.
Question 1
Latifabad Biscuits of Hyderabad models its monthly total cost as C = 240,000 + 175Q, where C is in rupees and Q is the number of biscuit boxes made in the month. Which interpretation of this equation is correct?
- A Variable costs are Rs 240,000 a month and fixed costs are Rs 175 per box
- B Average cost is Rs 175 per box at every level of monthly output
- C Fixed costs are Rs 240,000 a month and each extra box adds Rs 175 to total cost
- D Total cost doubles whenever monthly output doubles, from any starting level
Show the answer
Answer: C. For a straight line C = a + bQ, the intercept a is the value of C when Q = 0 and the slope b is the change in C for a one-unit increase in Q.
- a = Rs 240,000: the cost incurred even if no boxes are made, i.e. fixed cost per month.
- b = Rs 175: each additional box adds Rs 175, i.e. variable cost per box.
For example, at Q = 2,000 boxes, C = 240,000 + 175 x 2,000 = Rs 590,000, an average of Rs 295 per box, not Rs 175. At Q = 4,000, C = Rs 940,000, which is less than double Rs 590,000.
Question 2
Which of the following quadratic equations has exactly one (repeated) real root?
- A 2x^2 + 5x - 3 = 0
- B 3x^2 - 4x + 5 = 0
- C x^2 + 6x + 8 = 0
- D 4x^2 - 12x + 9 = 0
Show the answer
Answer: D. The number of real roots of ax^2 + bx + c = 0 depends on the discriminant b^2 - 4ac: positive gives two distinct real roots, zero gives one repeated root, negative gives no real roots.
| Equation | b^2 - 4ac | Real roots |
|---|---|---|
| 4x^2 - 12x + 9 = 0 | 0 | one (repeated) |
| 2x^2 + 5x - 3 = 0 | 49 | two |
| 3x^2 - 4x + 5 = 0 | -44 | none |
| x^2 + 6x + 8 = 0 | 4 | two |
Only 4x^2 - 12x + 9 = 0 has a zero discriminant; it factorises as (2x - 3)^2 = 0, so x = 1.5.
Question 3
Kamalia Hosiery exported 20,000 pairs of socks in year 1 and expects export volume to grow by 8% a year. What is total expected export volume over years 1 to 5 (to the nearest pair)?
- A 90,122 pairs
- B 126,719 pairs
- C 117,332 pairs
- D 116,000 pairs
Show the answer
Answer: C. Volumes form a GP: a = 20,000, r = 1.08, n = 5.
S = a(r^n - 1)/(r - 1) = 20,000 x (1.08^5 - 1) / 0.08 = 20,000 x (1.469328 - 1) / 0.08 = 117,332 pairs.
Check by listing the terms: 20,000, 21,600, 23,328, 25,194, 27,210 (total 117,332).
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