Exam prep

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The exam

Final examination / assessment, as stated in the official syllabus. Ask a senior or your exam office for a past paper to confirm the question pattern.

Graded A+ (85-100) to E (0-24) on a 12-step scale; GPA is credit-weighted (5 credits per course unit).

Practice

Until we have a past paper, practise with the topic quizzes and the likely questions below. Write each essay answer by hand, then check it against its frame.

Mixed quiz and flashcards

Likely questions

Written by us from your syllabus, not copied from any exam paper. Tap one to open its sheet.

Short calculations

Distinguish rational and irrational numbers with two examples of each.Unit I Express 0.272727… as a fraction in its lowest terms.Unit I Evaluate 27^(2/3) × 9^(−1/2) without a calculator.Unit I Factorise 6x² + x − 2.Unit I If n(A) = 25, n(B) = 18 and n(A ∩ B) = 7, find n(A ∪ B).Unit II Evaluate 8C3 and 8P3, and explain why they differ.Unit II Write rows 0 to 6 of Pascal's triangle.Unit II Find the 12th term of the AP 5, 9, 13, …Unit II Find the simple interest on Rs. 60,000 at 9% a year for 146 days.Unit III Explain the terms 2/10, n/30 on an invoice.Unit III Find the effective annual rate of 12% compounded quarterly.Unit III Distinguish an ordinary annuity from an annuity due.Unit III State the domain and range of f(x) = √(x − 2).Unit IV Find the slope of the line through (2, 3) and (6, 11).Unit IV Define the break-even point and contribution per unit.Unit IV Find the inverse of f(x) = 5x + 2.Unit IV Evaluate lim (x → 2) (x² − 4)/(x − 2).Unit V Differentiate y = 3x⁴ − 2x + 7.Unit V Find ∫(4x³ + 6x) dx.Unit V Define marginal cost and marginal revenue.Unit V Find the determinant of [5 2; 3 4].Unit VI When can two matrices be multiplied? Give the order of the product of a 2 × 3 and a 3 × 4 matrix.Unit VI State the three elementary row operations.Unit VI For A = [2 5; 1 3] and B = [4 0; −2 6], find 2A − B.Unit VI

Structured problems

Solve 3x + 2y = 18 and 5x − 2y = 14, and check your answer.Unit I Solve 3x² − 5x − 2 = 0 by factorising, and confirm with the quadratic formula.Unit I Using logarithms, find how many years Rs. 100,000 takes to double at 8% a year compounded yearly.Unit I In a survey of 120 customers, 70 buy tea, 55 coffee and 25 both. Draw a Venn diagram and find how many buy neither.Unit II Expand (x − 2)⁵ by the binomial theorem.Unit II Find the sum to infinity of 12 + 6 + 3 + … and the sum of its first 6 terms.Unit II Find the amount of Rs. 200,000 at 10% a year compounded half-yearly for 3 years.Unit III Find the present value of Rs. 500,000 due in 4 years at 10% compounded yearly.Unit III Find the yearly deposit into a sinking fund to reach Rs. 5,000,000 in 5 years at 10%.Unit III Demand is Qd = 1,000 − 4p and supply Qs = 6p − 200. Find the equilibrium price and quantity.Unit IV Cost is Rs. 16,000 for 100 cards and Rs. 22,000 for 250 cards. Find the linear cost function and the cost of 400 cards.Unit IV Demand is p = 80 − q. Find the revenue function and the maximum revenue.Unit IV Find and classify the stationary points of y = x³ − 3x² − 9x + 5.Unit V A shop sells 2,000 units a year; each order costs Rs. 400 and holding costs Rs. 10 a unit a year. Find the economic order quantity.Unit V Demand is p = 120 − 2q and supply p = 20 + 0.5q. Find the consumer and producer surplus at equilibrium.Unit V For A = [2 5; 1 3] and B = [4 0; −2 6], find AB and BA and comment.Unit VI Solve x + 2y = 8 and 3x − y = 3 by row reduction.Unit VI Find the inverse of [4 7; 2 6] and use it to solve 4x + 7y = 220, 2x + 6y = 160.Unit VI

Long problems

A firm's profit (Rs. '000) is P = −x² + 120x − 2,000. Find the break-even outputs, the profitable range, and the profit at 60 units.Unit I A factory must make 500 garments using exactly 18,000 machine minutes; a shirt takes 30 minutes and trousers 45. Form and solve equations for the plan.Unit I Explain the real number system with a diagram, and find the HCF and LCM of 84 and 90 by prime factors.Unit I A clerk's salary starts at Rs. 60,000 a month with a Rs. 2,500 yearly increment. Find the year-10 salary, the 10-year total, and the first year above Rs. 85,000.Unit II Sales of Rs. 400,000 grow 10% a year. Find year-5 sales and the 5-year total, and compare with a fixed Rs. 40,000 yearly rise.Unit II A committee of 5 is chosen from 6 men and 5 women. Find the number of committees with exactly 2 women and with at least 1 woman.Unit II A Rs. 331,000 loan at 10% is repaid in 3 equal year-end instalments. Find the instalment, prepare the schedule and find the total interest.Unit III A Rs. 2,000,000 renovation returns Rs. 800,000, Rs. 900,000 and Rs. 1,000,000 over 3 years. Find the NPV at 12% and advise.Unit III Goods listed at Rs. 150,000 carry trade discounts of 20% and 10% and terms 2/10, n/30. Find the net price, the day-8 payment and whether borrowing at 12% to take the discount pays.Unit III A bakery: price Rs. 1,500, variable cost Rs. 900, fixed cost Rs. 360,000. Find the break-even point, profit at 800 cakes, the units for a Rs. 150,000 profit and the margin of safety; draw the chart.Unit IV Demand p = 600 − 2q, cost C = 100q + 20,000. Without calculus, find the maximum profit, its price and the break-even outputs.Unit IV Demand p = 200 − 3q, supply p = 40 + 5q. Find the equilibrium, then the effect of a Rs. 16 per-unit tax on sellers.Unit IV R(x) = 150x − 0.2x², C(x) = 2,000 + 40x + 0.05x². Find the profit-maximising output, price and profit, and show that MR = MC.Unit V For C(x) = 2,000 + 40x + 0.05x² and R(x) = 150x − 0.2x², find MC and MR at 200 units, interpret, and find the profit there.Unit V MC = 30 + 0.6x and fixed cost Rs. 8,000. Find the total cost function, the cost of 100 units and the extra cost of increasing output from 100 to 200 units.Unit V Solve x + y + z = 6, 2x − y + z = 3, x + 2y − z = 2 by Gauss-Jordan elimination.Unit VI Find the inverse of [1 2 3; 0 1 4; 5 6 0] by the cofactor method and use it to solve AX = [14; 14; 17].Unit VI Two branches sell three goods. Use a quantity matrix and a price matrix to find each branch's revenue and the total.Unit VI

Answer frames

How to lay out a long answer, with a write-up check. 26 frames so far.