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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 1

The turning point of the curve y = 6 - 4x - x^2 occurs at

  • A. (-2, 10)Correct
  • B. (0, 6)
  • C. (2, -6)
  • D. (4, -26)

Explanation

dy/dx = -4-2x = 0, so x=-2. y = 6-4(-2)-(-2)^2 = 6+8-4 = 10. Turning point (-2, 10).

Mathematics 2015 Objective — Question 2

The radius of a circle is increasing at the rate of 0.4 cm/s. Find the rate of increase in cm^2/s of the area, when the radius is 5cm.

  • A. 40*pi
  • B. 10*pi
  • C. 5*pi
  • D. 4*piCorrect

Explanation

A = pi*r^2, dA/dt = 2*pi*r*(dr/dt) = 2*pi*5*0.4 = 4*pi.

Mathematics 2015 Objective — Question 4

In a test, the scores of 20 students are 9,10,9,5,13,6,4,7,11,8,11,5,6,4,11,10,2,11,15 and 9. Find the modal score.

  • A. 15
  • B. 11Correct
  • C. 9
  • D. 8

Explanation

Counting occurrences: 11 appears 4 times (more than any other value: 9 appears 3 times, 10, 5, 6, 4 each appear 2 times). Mode = 11.

Mathematics 2015 Objective — Question 5

Table: Marks 2,5,8,11; No. of students 3,6,x,y. The total mark scored by 3 and x students is 30, and that by 6 and y students is 74. How many students were in the class?

  • A. 15
  • B. 16Correct
  • C. 68
  • D. 77

Explanation

For marks=2 (3 students) and marks=8 (x students): 2(3)+8x=30, so 8x=24, x=3. For marks=5 (6 students) and marks=11 (y students): 5(6)+11y=74, so 11y=44, y=4. Total students = 3+6+3+4 = 16.

Mathematics 2015 Objective — Question 6

The weekly earnings of each of five brothers were 100 naira, 120 naira, 125 naira, 150 naira and 110 naira. Find the variance of the weekly earning.

  • A. 200
  • B. 250
  • C. 282
  • D. 284Correct

Explanation

Mean = 605/5 = 121. Deviations: -21,-1,4,29,-11. Squared: 441,1,16,841,121, sum=1420. Variance = 1420/5 = 284.

Mathematics 2015 Objective — Question 7

Frequency distribution graph shown (values rising to a peak of 12 around x=6, then falling to about 8 at x=8). Find the cumulative frequency for 5<=x<=8 from the frequency distribution graph.

  • A. 22
  • B. 30
  • C. 32
  • D. 40Correct

Explanation

Reading approximate values from the graph at x=5,6,7,8 and summing them gives a total of approximately 40.

Mathematics 2015 Objective — Question 8

Table: Marks 2,3,4,5,6,7,8,9; No. of students 3,4,4,1,0,5,1,2. The table shows the marks distribution of students in a test. Find the probability of the students that passed the test if the cut-off mark is 6.

  • A. 4/5
  • B. 9/20
  • C. 2/5Correct
  • D. 7/20

Explanation

Total students = 3+4+4+1+0+5+1+2 = 20. Students with marks >=6 (pass) = 0+5+1+2 = 8. P(pass) = 8/20 = 2/5.

Mathematics 2015 Objective — Question 9

How many distinct arrangements can be made using all the letters of the word MALARIA?

  • A. 3
  • B. 7
  • C. 210
  • D. 840Correct

Explanation

MALARIA has 7 letters with A repeated 3 times. Arrangements = 7!/3! = 5040/6 = 840.

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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