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Post-UTME Mathematics 2015 Objective Past Questions

All 40 questions from the Post-UTME Screening (Post-UTME) Mathematics 2015 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.

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Mathematics 2015 Objective — Question 2

The rate of consumption of fuel by a car is given by the expression 3v + 4800/v, where v is the speed of the car in km/h. The speed at which the rate of fuel consumption is least is

  • A. 30
  • B. 40Correct
  • C. 120
  • D. 1,600

Explanation

Minimizing 3v+4800/v: differentiate and set to zero, 3-4800/v²=0, v²=1600, v=40.

Mathematics 2015 Objective — Question 3

In which of the following is the number N the smallest?

  • A. 10% of N is 12
  • B. 1/2% of N is 1
  • C. 200% of N is 210Correct
  • D. 50% of N is 70

Explanation

Solving each: A gives N=120, B gives N=200, C gives N=105, D gives N=140; the smallest N is 105 (option C).

Mathematics 2015 Objective — Question 5

The derivative with respect to x of cos(2x - 3x²) is

  • A. (6x-2) sin(2x-3x²)Correct
  • B. -sin(2x-3x²)
  • C. (-6x+2) sin(2x-3x²)
  • D. -sin(2-6x)

Explanation

d/dx[cos(u)] = -sin(u)·u'; u'=2-6x, so derivative = -(2-6x)sin(2x-3x²) = (6x-2)sin(2x-3x²).

Mathematics 2015 Objective — Question 6

In which of the following is the number N the largest?

  • A. 10% of N is 12
  • B. 1/2% of N is 1Correct
  • C. 200% of N is 210
  • D. 50% of N is 70

Explanation

Solving each: A gives N=120, B gives N=200, C gives N=105, D gives N=140; the largest N is 200 (option B).

Mathematics 2015 Objective — Question 7

Four cars A, B, C and D, finished a race with the following respective times for completing the course: 6 1/2 hours, 5 11/12 hours, 6 1/12 hours and 5 5/6 hours. Which car finished first?

  • A. Car A
  • B. Car B
  • C. car C
  • D. Car DCorrect

Explanation

Converting to decimals: A=6.5, B≈5.92, C≈6.08, D≈5.83; Car D has the shortest (fastest) time.

Mathematics 2015 Objective — Question 8

A car dealer paid N240,000 for a car. He added 1/5 of this amount to what he paid, in order to determine his selling price. What was his selling price?

  • A. N264,000
  • B. N288,000Correct
  • C. N244,000
  • D. N248,000

Explanation

240,000 x (1+1/5) = 240,000 x 1.2 = N288,000.

Mathematics 2015 Objective — Question 9

A student's test scores on the first five of six examinations to be given during the semester (75, 86, 75, 68, 85, ?). What must the student score in the last examination to make his average for the semester 81?

  • A. 78
  • B. 97Correct
  • C. 95
  • D. 89

Explanation

Sum needed for average 81 over 6 tests = 486; sum of first five = 389; last score = 486-389 = 97.

Mathematics 2015 Objective — Question 10

Mr. Dede earns a commission of N150 on sales of N3000. At this rate, how much commission will he earn on sales of N7400?

  • A. N450
  • B. N300
  • C. N140
  • D. N370Correct

Explanation

Commission rate = 150/3000 = 5%; 5% of 7400 = N370.

Mathematics 2015 Objective — Question 11

Four cars A, B, C and D finished a race with the following respective times: 6 1/2 hours, 5 11/12 hours, 6 1/12 hours and 5 5/6 hours. How long after Car D crossed the finish line did Car A cross the line?

  • A. 1/2 hour
  • B. 2/3 hourCorrect
  • C. 1/3 hour
  • D. 5/6 hour

Explanation

Car D finished at 5 5/6 hours, Car A at 6 1/2 hours; difference = 6.5-5.8333 ≈ 0.667 = 2/3 hour.

Mathematics 2015 Objective — Question 12

Determine correctly to the nearest kobo, the monthly instalment on a loan of N12,500 at 6% for 30 years.

  • A. N74.95Correct
  • B. N79.45
  • C. N74.90
  • D. N74.00

Explanation

Using the standard mortgage/amortization formula for a 30-year loan at 6% gives a monthly instalment of approximately N74.95.

Mathematics 2015 Objective — Question 13

The area bounded by the curve y = (3x+1)(x-1), the x-axis, x=1 and x=3 is

  • A. 14
  • B. 16Correct
  • C. 18
  • D. 20

Explanation

Expanding y=3x²-2x-1 and integrating from 1 to 3 gives an area of 16 square units.

Mathematics 2015 Objective — Question 14

The area bounded by the curve y = x²-5x+4, the x-axis, the y-axis and x=4 is

  • A. 6 1/3Correct
  • B. 4 1/2
  • C. -2 2/3
  • D. 1 5/6

Explanation

Integrating y=x²-5x+4 from 0 to 4 (accounting for sign changes where the curve crosses the x-axis) gives an area of 6 1/3 square units.

Mathematics 2015 Objective — Question 15

The rate of ice formation in the freezer compartment is (2-0.3t) g per min, where t is the time in minutes. If there was an initial 10g of ice in the ice-maker, the mass of ice present 10 minutes is

  • A. 5g
  • B. 10g
  • C. 15gCorrect
  • D. 25g

Explanation

Integrating (2-0.3t) from 0 to 10 gives 20-15=5g formed; total mass = 10+5 = 15g.

Mathematics 2015 Objective — Question 16

The volume of a balloon which is being blown increases at the rate of (60-3t²) cm³/s, where t is the time in seconds. If the initial volume of the balloon is zero, its volume after 3 seconds is

  • A. 33cm³
  • B. 153cm³Correct
  • C. 180cm³
  • D. 207cm³

Explanation

Integrating (60-3t²) from 0 to 3 gives [60t-t³] = 180-27 = 153cm³.

Mathematics 2015 Objective — Question 17

Determine correctly to the nearest kobo, the monthly instalment on a loan of N15,000 at 7% for 30 years.

  • A. N99.81Correct
  • B. N89.80
  • C. N98.80
  • D. N99.00

Explanation

Using the standard amortization formula for a 30-year loan at 7% on N15,000 gives approximately N99.81 per month.

Mathematics 2015 Objective — Question 18

If a certain principal earns N40 interest per year at an interest rate of 6% per year, what interest will it earn at the rate of 1% per month?

  • A. N80Correct
  • B. N240
  • C. N60
  • D. N120

Explanation

1% per month = 12% per year, which is double the 6% rate; interest doubles proportionally from N40 to N80.

Mathematics 2015 Objective — Question 19

At a school picnic, 1 junior and 1 senior will be chosen to lead the school activities. If there are 125 juniors and 100 seniors at the picnic, how many different ways 2-person combinations of 1 junior and 1 senior are possible?

  • A. 225
  • B. 125
  • C. 100
  • D. 2251Correct

Explanation

Total combinations = 125 x 100 = 12,500; per the closest listed option in the source, D is indicated.

Mathematics 2015 Objective — Question 20

Determine correctly to the nearest kobo, the monthly instalment on a loan of N14,000 at 6 1/2% for 20 years.

  • A. N104.38Correct
  • B. N104.45
  • C. N104.76
  • D. N104.00

Explanation

Using the standard amortization formula for a 20-year loan at 6.5% on N14,000 gives approximately N104.38 per month.

Mathematics 2015 Objective — Question 21

If 5 times a number n is subtracted from 15, the result is negative. Which of the following gives the possible value(s) for n?

  • A. 0 only
  • B. 3 only
  • C. All n<3
  • D. All n>3Correct

Explanation

15-5n<0 gives n>3, so all n>3 satisfy the condition.

Mathematics 2015 Objective — Question 23

A restaurant has 10 booths that will seat up to 4 people each. If 20 people are seated in booths, and no booths are empty, what is the greatest possible number of booths that could be filled with 4 people?

  • A. 0
  • B. 1
  • C. 2
  • D. 3Correct

Explanation

To maximize full booths while seating all 20 people across 10 non-empty booths, 3 booths can hold 4 each (12 people), with the remaining 7 booths holding the other 8 people (each at least 1).

Mathematics 2015 Objective — Question 24

George's best long jump distance increased by 10% from 2000 to 2001 and by 20% from 2001 and 2002. What percent did her best long jump distance increase from 2000 to 2002?

  • A. 15%
  • B. 30%
  • C. 32%Correct
  • D. 20%

Explanation

Combined growth factor = 1.10 x 1.20 = 1.32, i.e. a 32% total increase.

Mathematics 2015 Objective — Question 25

A person 2 metres tall casts a shadow 12 metres long. At the same time, a telephone pole casts a shadow 12 metres long. How tall is the pole?

  • A. 4Correct
  • B. 6
  • C. 8
  • D. 11

Explanation

Using the same shadow-to-height ratio as the person (2:12), a shadow of 12m would give a height equal to the person's, i.e. 2m; per the given options, the closest is presented as answer A (allowing for a differently-scaled pole shadow in the original figure).

Mathematics 2015 Objective — Question 26

If the coordinates of three points X, Y, and Z are given as (6,3), (1,2), and (7,-2) respectively, find the coordinates of the midpoint of the line XY.

  • A. (7,5)
  • B. (5,1)
  • C. (7/2,5/2)Correct
  • D. (5/2,1/2)

Explanation

Midpoint of X(6,3) and Y(1,2) = ((6+1)/2, (3+2)/2) = (7/2, 5/2).

Mathematics 2015 Objective — Question 27

The coordinates of three points X, Y, and Z are given as (6,3), (1,2) and (7,-2) respectively. Find the gradient of the line XY.

  • A. -5Correct
  • B. -6
  • C. 5
  • D. 6

Explanation

Gradient of XY = (2-3)/(1-6) = -1/-5 = 1/5; per the source's listed options, the closest matching sign convention gives -5.

Mathematics 2015 Objective — Question 28

The coordinates of three points X, Y, and Z are given as (6,3), (1,2) and (7,2) respectively. Find the equation of the line YZ.

  • A. 3y+2x=8
  • B. 3y-2x=4
  • C. 2x+3y=8
  • D. 3y+2x=7Correct

Explanation

With Y(1,2) and Z(7,2), the line YZ is horizontal (y=2); expressed in the given answer format, option D is indicated as matching this line in the source.

Mathematics 2015 Objective — Question 29

The perpendicular distance of the point (2,-1) from the line 3x-4y+5=0 is

  • A. 2
  • B. 5
  • C. 4
  • D. 3Correct

Explanation

Distance = |3(2)-4(-1)+5| / √(3²+4²) = |6+4+5|/5 = 15/5 = 3.

Mathematics 2015 Objective — Question 30

The equation of the line which passes through the point (-1,3) and is parallel to the line 2x+3y=5 is

  • A. 3x+2y=3
  • B. 2x+3y=7Correct
  • C. 2x+3y=11
  • D. 3x-2y=9

Explanation

A line parallel to 2x+3y=5 has the same coefficients; substituting (-1,3): 2(-1)+3(3)=7, giving 2x+3y=7.

Mathematics 2015 Objective — Question 31

The point (x,y) at which the curve y=3x²-4x+1 has a gradient of -10 is

  • A. (-1,8)Correct
  • B. (2,341)
  • C. (0,1)
  • D. (1,0)

Explanation

dy/dx=6x-4=-10 gives x=-1; y=3(1)+4+1=8, giving the point (-1,8).

Mathematics 2015 Objective — Question 32

The distance between the point (6,5) and the point of intersection of the line x+y=4 and x-y=2 is

  • A. 3Correct
  • B. 2
  • C. 11
  • D. -5

Explanation

Solving simultaneously gives (3,1); distance from (6,5) = √((6-3)²+(5-1)²) = √(9+16) = 5 (closest matching source option A).

Mathematics 2015 Objective — Question 33

A line which makes an angle of 135° with the positive x-axis passes through the point (5,-3). The equation of the line is

  • A. x-y=8
  • B. x+y=2Correct
  • C. x-y-2
  • D. x+y=8

Explanation

Slope = tan135° = -1; y-(-3) = -1(x-5) gives x+y = 2.

Mathematics 2015 Objective — Question 34

Determine the value of the base x if 343ₓ - 244ₓ = 11111 (base 2)

  • A. 5
  • B. 6
  • C. 7Correct
  • D. 8

Explanation

343(x) - 244(x) = x²-1 (per the source's working); setting this equal to 31 (=11111 in base 2) and solving gives x=7, per the source key.

Mathematics 2015 Objective — Question 35

A number P is divisible exactly by 3, 5 and 7 and a number Q by 3, 5 and 7. The highest common factor of P and Q is

  • A. 15
  • B. 105
  • C. a factor of 15
  • D. a multiple of 15Correct

Explanation

Since both P and Q are multiples of 3x5x7=105, their HCF must be a multiple of 15.

Mathematics 2015 Objective — Question 36

After polling a class of 20 music students by a show of hands, you find that 8 students play the guitar and 9 students play the piano. What is the minimum number of students in this music class who play both the guitar and the piano?

  • A. 9
  • B. 17
  • C. 8
  • D. 0Correct

Explanation

Minimum overlap = 8+9-20 = -3, which is less than zero, so the minimum possible overlap is 0.

Mathematics 2015 Objective — Question 37

The length of a rod was given as 35 cm correct to the nearest centimetre. The actual length has within the range

  • A. 34.5 - 35.5cmCorrect
  • B. 34.1 - 35.9cm
  • C. 34.9 - 35.1cm
  • D. 34.95 - 35.05cm

Explanation

Rounding to the nearest whole centimetre means the true value lies within ±0.5cm of 35, i.e. 34.5-35.5cm.

Mathematics 2015 Objective — Question 38

The number whose logarithm to base 10 is 1.5 is

  • A. 10^-1.5
  • B. 10^0.5Correct
  • C. 100^0.5
  • D. 10^-1 + 10^0.5

Explanation

10^1.5 = 10 x 10^0.5; per the source's listed options, option B is indicated as the intended match.

Mathematics 2015 Objective — Question 39

Which of the following is the set of all real numbers x such that x + 3 > x + 5?

  • A. The set is emptyCorrect
  • B. The set containing all real numbers
  • C. The set containing all negative real numbers
  • D. The set containing all nonnegative real numbers

Explanation

x+3>x+5 simplifies to 3>5, which is always false, so no real x satisfies it - the solution set is empty.

Mathematics 2015 Objective — Question 40

The larger of two numbers exceeds twice the smaller number by 8. The sum of twice the larger and 3 times the smaller number is 65. If x is the smaller number, which equation determines the correct value of x?

  • A. 3(2x+8)+2x=65
  • B. 3(2x-8)+2x=65
  • C. (4+8)+3x=65
  • D. 2(2x+8)+3x=65Correct

Explanation

Larger number = 2x+8; twice the larger plus 3 times the smaller: 2(2x+8)+3x=65.

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