Mathematics – Page 3 – NBC Institute

QTB – May 2017 – L1 – SB – Q3a – Mathematics

Determine the annual savings required to accumulate a future sum under annuity terms.

Question

A lawyer plans to save a certain amount of money per annum for 5 years on the first day of the year. If the interest rate is 8%, for him to receive N696,910.50, determine x. (10 Marks)

Answer

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Tags: Annuity, Interest Rate, Present Value, Savings
Level: Level 1

Topic: Mathematics
Series: MAY 2017

QTB – May 2017 – L1 – SB – Q1a – Mathematics

Machine replacement time and net earnings calculation considering repair costs.

Question

a. A manufacturing company has purchased a machine generating earnings (₦’000) at time t of , where t is in years. The repair and maintenance cost at time t is
You are required to:

i. Determine when the machine should be replaced, assuming it has a zero salvage value. (4 Marks)

ii. Determine the total net earnings, including the cost of repairs and maintenance within the period of 11 years. (6 Marks)

Answer

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Tags: Depreciation, Machine Replacement, Net Earnings
Level: Level 1

Topic: Mathematics
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q7 – Mathematics

This question assesses understanding of histograms and their characteristics.

Question

Which of the following is NOT TRUE about a histogram?
A. A vertical rectangle is drawn to represent each class of the frequency distribution
B. A histogram is a graph of a grouped frequency distribution
C. The frequency of a class is represented by the height of its rectangle.
D. Histogram and bar charts look similar but they are constructed very differently.
E. The frequency of a class is represented by the area of the bar corresponding to the class.

Answer

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Tags: Business Mathematics, Data Representation, Graphs, Histogram
Level: Level 1

Topic: Mathematics
Series: MAY 2017

QTB – May 2017 – L1 – SA – Q6 – Mathematics

This question asks to calculate the marginal revenue at a given sales volume.

Question

If the sales function of a company is given as what is the marginal revenue when

A. 122
B. 120
C. 125
D. 130
E. 135

Answer

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Tags: Business Mathematics, Calculus, Derivatives, Marginal Revenue
Level: Level 1

Topic: Mathematics
Series: MAY 2017

QTB – MAY 2017 – L1 – SA – Q5 – Mathematics

A multiple-choice question asking for the point where the slope of a given function is zero.

Question

If , then the point at which the slope is zero is:

A. (-3,7)
B. (3,7)
C. (-3,-7)
D. (3,-7)
E. (3,-11)

Answer

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Tags: Calculus, Differentiation, Functions, Mathematical Modelling, Slope
Level: Level 1

Topic: Mathematics
Series: MAY 2017

QTB – MAY 2017 – L1 – SA – Q4 – Mathematics

A multiple-choice question calculating the income left after tax deductions from the taxable income.

Question

A man earns N150,000 per annum. He is allowed a tax-free pay of N40,000. If he pays 25 kobo in the Naira as tax on his taxable income, how much has he left?

A. N102,500
B. N112,500
C. N122,500
D. N132,500
E. N142,500

Answer

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Tags: Deductions, Income Tax, Personal Income, Taxable Income, Taxation
Level: Level 1

Topic: Mathematics
Series: MAY 2017

QTB – MAY 2017 – L1 – SA – Q3 – Mathematics.

A multiple-choice question assessing knowledge of simultaneous equations and variable relations.

Question

Which of the following is NOT TRUE about simultaneous equations?

A. The number of variables must be equal to the number of equations.
B. Where two lines intersect, the values of the variables at that point must satisfy the equations.
C. The simultaneous equations must be satisfied by values of the variables as well as their reciprocals.
D. Their solution involves finding the values of the variables which are true to all the simultaneous equations.
E. The result of adding the equations or subtracting one equation from the other will be satisfied by the values of the variables.

Answer

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Tags: Algebra, Linear Equations, Mathematical Methods, Simultaneous Equations, Variables
Level: Level 1

Topic: Mathematics
Series: MAY 2017

QTB – MAY 2017 – L1 – SA – Q2 – Mathematics.

A multiple-choice question calculating the variable cost per unit given total and fixed costs.

Question

A company produces 16,000 units of a product. The total cost of producing these units is N60,000. If the fixed cost is N12,000, the variable cost per unit of the output is:

A. N7.00
B. N6.00
C. N5.00
D. N4.00
E. N3.00

Answer

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Tags: Break-even Analysis, Costing, Fixed Costs, Production Efficiency, Variable Cost
Level: Level 1

Topic: Mathematics
Series: MAY 2017

QTB – MAY 2017 – L1 – SA – Q1 – Mathematics.

A multiple-choice question calculating future value based on compound interest over 15 years at 8% annually.

Question

How much will N22,500 amount to at 8% interest over 15 years compounded annually?

A. N71,337.81
B. N71,373.81
C. N71,378.81
D. N71,387.81
E. N71,733.81

Answer

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Tags: Compound Interest, Financial Mathematics, Future Value, Investment Growth, Time value of money
Level: Level 1

Topic: Mathematics
Series: MAY 2017

QTB – May 2016 – L1 – SB – Q5a – Mathematics

This question involves finding the total cost function and the cost of producing 50 items using marginal cost and integration.

Question

The marginal cost of producing a particular item is given by

Required:
i. Find the total cost function , if the cost of producing 2 items is N1,660.
(7 marks)

ii. Find the cost of producing 50 items.

Answer

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Tags: Business Finance, Integration, Marginal Cost, Total Cost
Level: Level 1

Topic: Mathematics
Series: MAY 2016

QTB – May 2016 – L1 – SA – Q1 – Mathematics

Calculates the number of units a company expects to sell in year 5 given initial and growth rate.

Question

A company expects to produce and sell 150,000 units of its product during the first year with this figure growing by 3% per annum. Then the number of units to be sold in year 5 is
A. 153,798
B. 163,798
C. 173,798
D. 183,798
E. 193,798

Answer

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Tags: Forecasting, Percentages, Sales Growth
Level: Level 1

Topic: Mathematics
Series: MAY 2016

QTB – Nov 2015 – L1 – SA – Q20 – Mathematics

This question identifies the condition at the stationary point of a function.

Question

A stationary point for the function $f (x)$ is a point at which:

A. $< 0$
B. $= 0$
C. $> 0$
D. $= 0$
E. $0$

Answer

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Tags: Calculus, Functions, Stationary Points
Level: Level 1

Topic: Mathematics
Series: NOV 2015

QTB – Nov 2015 – L1 – SA – Q16 – Mathematics

This question calculates the number of donations made in an arithmetic progression.

Question

A woman made weekly donations according to an Arithmetic Progression (AP). How many donations did she make if her first donation was N5,000, her second donation was N6,000, and her last donation was N49,000?

A. 44
B. 45
C. 46
D. 47
E. 48

Answer

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Tags: Arithmetic Progression, Donations, Series
Level: Level 1

Topic: Mathematics
Series: NOV 2015

QTB – Nov 2015 – L1 – SA – Q15 – Mathematics

This question calculates the accumulated amount from monthly deposits made in an account with no interest.

Question

An Accountant plans to give his wife a precious gift on her 50th birthday in 1½ years’ time. He intends to start with a deposit of N5 and doubles the amount every month throughout this period. Assuming no interest is paid on this account, determine the accumulated amount in this account at the end of this period:

A. N1,510,715
B. N1,410,715
C. N1,310,715
D. N1,210,715
E. N1,110,715

Answer

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Tags: Arithmetic Progression, Compound Amount, Sequence

Topic: Mathematics
Series: NOV 2015

QTB – May 2015 – L1 – SB – Q3b – Mathematics

This question involves expressing the interest rate in terms of future value and principal investment for a 3-year investment.

Question

Mr. Taiwo invested a certain amount of money P, at an annual interest rate r, for a period
of 3 years. The future value of this investment is given by

Express r in terms of S and P

Answer

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Tags: Future Value, Interest Rate, Investment
Level: Level 1

Topic: Mathematics
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q3 – Mathematics

Determining the production level at which average production cost is zero.

Question

The total cost function for SUNNY Enterprises is $c(x)=x^3−13x^2+40^x$ , where $x$ is the number of units produced (in hundreds). At what production level does the average production cost equal to zero?

A. 0, 500, 800
B. 500, 800
C. 0, 400, 900
D. 400
E. 400, 900

Answer

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Tags: Average Cost, Cost Function, Production Level
Level: Level 1

Topic: Mathematics
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q2 – Mathematics

Deriving the equation of a straight line for cost relation with given production and cost data.

Question

A firm produced 300 units of a commodity at a total cost of N680 and 700 units of the same commodity at a total cost of N1,060. If it is known that the cost relation is a straight line, derive the equation of this line.

A. y = – 0.95x + 395
B. y = 1.05x – 415.79
C. y = 0.95x + 395
D. y = 9.5x + 395
E. y = 1.05x + 419.75

Answer

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Tags: Cost Relation, Fixed Costs, Linear Equation
Level: Level 1

Topic: Mathematics
Series: MAY 2015

QTB – May 2015 – L1 – SA – Q1 – Mathematics

Calculating how long it takes for N500 to appreciate to N10,000 at 5% continuous interest.

Question

The present value of NA to be paid in t years in the future (assuming 5% continuous interest rate) is P (A, t) = Ae^0.05t. How long will it take N500 to appreciate to N10,000?

A. 5.99 years
B. 26.00 years
C. 52.00 years
D. 59.91 years
E. 599.10 years

Answer

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Tags: Continuous Interest, Present Value, Time value of money
Level: Level 1

Topic: Mathematics
Series: MAY 2015

Topic: Mathematics

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QTB – May 2017 – L1 – SB – Q3a – Mathematics

Determine the annual savings required to accumulate a future sum under annuity terms.

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QTB – May 2017 – L1 – SB – Q1a – Mathematics

Machine replacement time and net earnings calculation considering repair costs.

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QTB – May 2017 – L1 – SA – Q7 – Mathematics

This question assesses understanding of histograms and their characteristics.

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QTB – May 2017 – L1 – SA – Q6 – Mathematics

This question asks to calculate the marginal revenue at a given sales volume.

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QTB – MAY 2017 – L1 – SA – Q5 – Mathematics

A multiple-choice question asking for the point where the slope of a given function is zero.

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QTB – MAY 2017 – L1 – SA – Q4 – Mathematics

A multiple-choice question calculating the income left after tax deductions from the taxable income.

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QTB – MAY 2017 – L1 – SA – Q3 – Mathematics.

A multiple-choice question assessing knowledge of simultaneous equations and variable relations.

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QTB – MAY 2017 – L1 – SA – Q2 – Mathematics.

A multiple-choice question calculating the variable cost per unit given total and fixed costs.

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QTB – MAY 2017 – L1 – SA – Q1 – Mathematics.

A multiple-choice question calculating future value based on compound interest over 15 years at 8% annually.

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QTB – May 2016 – L1 – SB – Q5a – Mathematics

This question involves finding the total cost function and the cost of producing 50 items using marginal cost and integration.

You're reporting an error for "QTB – May 2016 – L1 – SB – Q5a – Mathematics"

QTB – May 2016 – L1 – SA – Q1 – Mathematics

Calculates the number of units a company expects to sell in year 5 given initial and growth rate.

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QTB – Nov 2015 – L1 – SA – Q20 – Mathematics

This question identifies the condition at the stationary point of a function.

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QTB – Nov 2015 – L1 – SA – Q16 – Mathematics

This question calculates the number of donations made in an arithmetic progression.

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QTB – Nov 2015 – L1 – SA – Q15 – Mathematics

This question calculates the accumulated amount from monthly deposits made in an account with no interest.

You're reporting an error for "QTB – Nov 2015 – L1 – SA – Q15 – Mathematics"

QTB – May 2015 – L1 – SB – Q3b – Mathematics

This question involves expressing the interest rate in terms of future value and principal investment for a 3-year investment.

You're reporting an error for "QTB – May 2015 – L1 – SB – Q3b – Mathematics"

QTB – May 2015 – L1 – SA – Q3 – Mathematics

Determining the production level at which average production cost is zero.

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QTB – May 2015 – L1 – SA – Q2 – Mathematics

Deriving the equation of a straight line for cost relation with given production and cost data.

You're reporting an error for "QTB – May 2015 – L1 – SA – Q2 – Mathematics"

QTB – May 2015 – L1 – SA – Q1 – Mathematics

Calculating how long it takes for N500 to appreciate to N10,000 at 5% continuous interest.

You're reporting an error for "QTB – May 2015 – L1 – SA – Q1 – Mathematics"

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