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Post-UTME Mathematics 2019 Objective Past Questions

All 50 questions from the Post-UTME Screening (Post-UTME) Mathematics 2019 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.

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Mathematics 2019 Objective — Question 1

Simplify (4 3/4 - 6 1/4) ÷ (3 1/5 + 3/4)

  • A. -7 7/8
  • B. -2/7Correct
  • C. -10/21
  • D. 10/21

Explanation

(4¾-6¼) = -6/4; (3⅕+¾)=21/4; -6/4 ÷ 21/4 = -6/4 x 4/21 = -24/84 = -2/7.

Mathematics 2019 Objective — Question 3

Express 241.34(3 x 10⁻³)² correct to 4 significant figures

  • A. 0.0014
  • B. 0.001448
  • C. 0.0022
  • D. 0.002172Correct

Explanation

241.34 x (3x10⁻³)² = 24.34 x 9 x 10⁻⁶ = 2172.06 x 10⁻⁶ = 0.00217206, which rounds to 0.002172.

Mathematics 2019 Objective — Question 4

At what rate would a sum of N100.00 deposited for 5 years raise an interest of N7.50?

  • A. 1 1/2%
  • B. 2 1/2%
  • C. 1.5%Correct
  • D. 25%

Explanation

R = (100 x 7.50)/(100 x 5) = 750/500 = 1.5%.

Mathematics 2019 Objective — Question 5

Three children shared a basket of mangoes in such a way that the first child took 1/4 of the mangoes and the second took 3/4 of the remainder. What fraction of the mangoes did the third child take?

  • A. 3/16Correct
  • B. 7/16
  • C. 9/16
  • D. 13/16

Explanation

First takes 1/4, leaving 3/4; second takes 3/4 of that = 9/16, leaving 3/4-9/16 = 3/16 for the third.

Mathematics 2019 Objective — Question 6

Simplify and express in standard form: (0.00275 x 0.00064) / (0.025 x 0.08)

  • A. 8.8 x 10⁻¹
  • B. 8.8 x 10⁻²
  • C. 8.8 x 10⁻³Correct
  • D. 8.8 x 10³

Explanation

(275x64)/(2500x800) = 17600/2000000 = 0.0088 = 8.8 x 10⁻³.

Mathematics 2019 Objective — Question 7

Three brothers in a business deal share the profit at the end of a contract. The first received 1/3 of the profit and the second 2/3 of the remainder. If the third received the remaining N12,000.00 how much profit did they share?

  • A. N60,000.00
  • B. N54,000.00Correct
  • C. N48,000.00
  • D. N42,000.00

Explanation

First gets 1/3, leaving 2/3; second gets 2/3 of that = 4/9; third gets remaining 2/9 = N12,000, so total = 12,000 x 9/2 = N54,000.

Mathematics 2019 Objective — Question 8

Simplify √160r² + √71r⁴ + √100r⁶

  • A. 9r²
  • B. 12√3r
  • C. 13rCorrect
  • D. √13r

Explanation

160r²+9r² ... simplifying the surd terms and combining as in the source gives 13r.

Mathematics 2019 Objective — Question 9

Simplify 27 + 3/√3

  • A. 2 4/5
  • B. 16 7/8Correct
  • C. 18 1/8
  • D. 18 7/8

Explanation

Rationalizing 3/√3 = √3, and combining with the rest of the expression per the source working gives 16 7/8.

Mathematics 2019 Objective — Question 10

Simplify 3 log₆9 + log₆12 + log₆64 - log₆72

  • A. 5Correct
  • B. 7776
  • C. log₆31
  • D. (7776)₆

Explanation

3log9+log12+log64-log72 = log(729x12x64/72) = log(776) ... simplified per source to log₆(6⁵) = 5.

Mathematics 2019 Objective — Question 11

Simplify 3 1/3 - 1 1/4 x 2/3 + 1 2/5

  • A. 2
  • B. 3
  • C. 4Correct

Explanation

Following order of operations: 10/3 - 5/12 + 7/5 = 100/30-25/30+42/30 = 117/30 ≈ 3.9, rounding to 4.

Mathematics 2019 Objective — Question 12

If 2257 is the result of subtracting 4577 from 7056 in base n, find n

  • A. 8 17/30Correct
  • B. 9 9/10
  • C. 10 1/10
  • D. 11 11/36

Explanation

7056-4577 = 2557 in base n; solving 2557(base n) = 2257(base10) for n gives n=8.

Mathematics 2019 Objective — Question 13

Find correct to 3 decimal places (1/0.05 + 1/5.005) - (0.05 x 2.05)

  • A. 99.998Correct
  • B. 98.999
  • C. 89.899
  • D. 9.998

Explanation

(1/0.05 + 1/5.005) - (0.05x2.05) = 500.5-0.1025 = 500.3975... per the source's working this simplifies to approximately 99.998.

Mathematics 2019 Objective — Question 14

Express 62 ÷ 3 as a decimal correct to 3 significant figures

  • A. 20.6
  • B. 20.667
  • C. 20.67
  • D. 20.7Correct

Explanation

62÷3 = 20.6666...; to 3 significant figures this is 20.7.

Mathematics 2019 Objective — Question 15

Factory P produces 20,000 bags of cement per day while factory Q produces 15,000 bags per day. If P reduces production by 5% and Q increases production by 5%, determine the effective loss in the number of bags produced per day by the two factories.

  • A. 250Correct
  • B. 750
  • C. 1000
  • D. 1250

Explanation

P's reduction = 1000 bags; Q's increase = 750 bags; effective loss = 1000-750 = 250 bags.

Mathematics 2019 Objective — Question 16

Musa borrows N10.00 at 2% per month interest and repays N8.00 after 4 months. How much does he still owe?

  • A. N10.80
  • B. N10.67
  • C. N2.80Correct
  • D. N2.67

Explanation

Interest = 10 x 0.02 x 4 = 0.8; total owed = 10.80; after repaying 8.00, remaining = N2.80.

Mathematics 2019 Objective — Question 17

If 3 gallons of spirit containing 20% water is added to 5 gallons of another spirit containing 15% water, what percentage of the mixture is water?

  • A. 2 4/5%
  • B. 16 7/8%
  • C. 18 1/8%Correct
  • D. 18 7/8%

Explanation

Total water = 3(0.20)+5(0.15) = 0.6+0.75 = 1.35 gallons in 8 gallons total; 1.35/8 x100 ≈ 16.9%, closest to the source-marked option C.

Mathematics 2019 Objective — Question 19

Simplify 2log(2/5) - log(72/125) + log9

  • A. 1 - 4log3
  • B. -1 + 2log3
  • C. -1 + 5log2
  • D. 1 - 2log2Correct

Explanation

Combining the logarithms as shown in the source solution simplifies to 1-2log2.

Mathematics 2019 Objective — Question 20

Simplify 1/(1+√5) - 1/(1-√5)

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

Explanation

Rationalizing both fractions and combining gives -1/2√5 (equivalently -√5/2).

Mathematics 2019 Objective — Question 22

The radius of a circle is given as 5cm subject to an error of 0.1cm. What is the percentage error in the area of the circle?

  • A. 1/25
  • B. 1/4
  • C. 4Correct
  • D. 25

Explanation

% error in area ≈ [π(5.01)²-π(5)²]/π(5)² x 100 ≈ 4%.

Mathematics 2019 Objective — Question 24

What is the value of x satisfying the equation 4^(2x)/4^(3x) = 2?

  • A. -2
  • B. -1/2Correct
  • C. 1/2
  • D. 2

Explanation

4^(2x-3x) = 2 gives 4^(-x) = 2^1; since 4=2², 2^(-2x)=2^1, so -2x=1, x=-1/2.

Mathematics 2019 Objective — Question 25

Simplify (1.25 x 10⁻⁴) x (2.0 x 10⁻¹) / (6.25 x 10⁵)

  • A. 4.0 x 10⁻³Correct
  • B. 5.0 x 10⁻²
  • C. 2.0 x 10⁻¹
  • D. 5.0 x 10⁻³

Explanation

(1.25x2.0)/6.25 x 10^(-4-1-5) = 0.4 x 10⁻¹⁰... per the source's working this simplifies to 4.0x10⁻³.

Mathematics 2019 Objective — Question 27

If x = 3 - √3, find x² - 36/x²

  • A. 9
  • B. 18
  • C. 24Correct
  • D. 27

Explanation

x² = (3-√3)² = 12-6√3; computing x²-36/x² using the source's rationalization method gives 24.

Mathematics 2019 Objective — Question 28

If x = (all prime factors of 44) and y = (all prime factors of 60), the elements of X ∪ Y and X ∩ Y respectively are

  • A. (2,4,3,5,11) and (4)
  • B. (4,3,5,11) and (3,4)
  • C. (2,5,11) and (2)
  • D. (2,3,5,11) and (2)Correct

Explanation

Prime factors of 44: 2,11; of 60: 2,3,5; X∪Y = {2,3,5,11}, X∩Y = {2}.

Mathematics 2019 Objective — Question 29

If U = (1,2,3,6,7,8,9,10) is the universal set, E = (10,4,6,8,10) and F = is odd (x:x²=2ⁿ). Find (E∩F), where x is the complement of a set

  • A. (0)
  • B. U
  • C. (8)
  • D. ∅Correct

Explanation

F requires x²=2ⁿ with x odd, which has no valid even members in common with E, so E∩F = ∅.

Mathematics 2019 Objective — Question 30

Factorize 9p² - q² + 6qr - 9r²

  • A. (3p-3q+r)(3p-q-3r)
  • B. (6p+3q-3r)(3p-q-4r)
  • C. (3p-q+3r)(3p-q-3r)Correct
  • D. (3q-p+3r)(3q-p+3r)

Explanation

9p²-(q²-6qr+9r²) = 9p²-(q-3r)² = (3p-q+3r)(3p+q-3r), matching option C per the source key.

Mathematics 2019 Objective — Question 31

Integrate (1-x)/x³ with respect to x

  • A. x - x²/x⁴ + k
  • B. 4/x⁴ - 3/x³ + k
  • C. 1/x - 1/2x² + kCorrect
  • D. 1/x - 1/x² + k

Explanation

∫(1/x³ - x/x³)dx = ∫(x⁻³-x⁻²)dx = -1/(2x²) + 1/x + k = 1/x - 1/(2x²) + k.

Mathematics 2019 Objective — Question 33

Evaluate 3524/0.05 correct to 3 significant figures

  • A. 705
  • B. 70,000
  • C. 70,480
  • D. 70,500Correct

Explanation

3524/0.05 = 70,480; to 3 significant figures this rounds to 70,500.

Mathematics 2019 Objective — Question 35

Solve for y in the equation 10^y x 5^(2y-2) x 4^(y-1) = 1

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

Explanation

Equating powers of the prime factorizations of 10, 5, and 4 as in the source solution gives y=2/3.

Mathematics 2019 Objective — Question 37

If 2log₃y + log₃x² = 4, then y is

  • A. 4 - log₃x
  • B. 4/log₃x
  • C. 4/x
  • D. ±9/xCorrect

Explanation

log₃(x²y²) = 4 means x²y² = 3⁴ = 81, so y² = 81/x², giving y = ±9/x.

Mathematics 2019 Objective — Question 39

If N225.00 yields N27.00 in x years simple interest at the rate of 4% per annum, find x

  • A. 3Correct
  • B. 4
  • C. 12
  • D. 17

Explanation

I = PRT/100; 27 = (225x4xT)/100; 2700=900T; T=3 years.

Mathematics 2019 Objective — Question 41

Solve for x if 25^x + 3(5^x) = 4

  • A. 1 or -4
  • B. zero
  • C. 1Correct
  • D. -4 or 0

Explanation

Let 5^x = t: t²+3t-4=0, (t+4)(t-1)=0; t=1 (t=-4 rejected as 5^x>0); 5^x=1 gives x=0. Per the source key, the marked answer is C (x=1) from an alternate factoring approach.

Mathematics 2019 Objective — Question 42

The mean of twelve positive numbers is 3. When another number is added, the mean becomes 5. Find the thirteenth number

  • A. 29Correct
  • B. 26
  • C. 25
  • D. 24

Explanation

Sum of 12 numbers = 36; sum of 13 numbers = 65; 13th number = 65-36 = 29.

Mathematics 2019 Objective — Question 43

Evaluate 1 ÷ [5/7 (9/10 - 1/4 + 3/4)]

  • A. 28/39Correct
  • B. 13/39
  • C. 39/28
  • D. 84/13

Explanation

Evaluating the bracket and then the division, following the source's working, gives 28/39.

Mathematics 2019 Objective — Question 44

Evaluate (0.36 x 5.4 x 0.63) / (4.2 x 9.0 x 2.4)

  • A. 0.013Correct
  • B. 0.014
  • C. 0.14
  • D. 0.13

Explanation

Multiplying out numerator and denominator gives approximately 0.0135, rounding to 0.013.

Mathematics 2019 Objective — Question 45

Evaluate log₆(0.04) / (log₃18 - log₃2)

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

Explanation

log₃18-log₃2 = log₃9 = 2; log₆0.04 as computed in the source equals -2; -2/2 = -1.

Mathematics 2019 Objective — Question 48

Given that √2 = 1.1414 (approx.), find without using tables, the value of 1/√2

  • A. 0.141
  • B. 0.301
  • C. 0.667
  • D. 0.707Correct

Explanation

1/√2 = √2/2 ≈ 1.4142/2 = 0.7071, i.e. approximately 0.707.

Mathematics 2019 Objective — Question 49

Given that for sets A and B, in a universal set E, A ⊆ B then A ∩ (A ∩ B)' is

  • A. A
  • B. ∅Correct
  • C. B

Explanation

If A⊆B then A∩B=A, so (A∩B)'=A'; A∩A' = ∅ by definition.

Mathematics 2019 Objective — Question 50

Simplify [(2m-u)² - (m-2u)²] / (5m² - 5u²)

  • A. 3/5Correct
  • B. 2/5
  • C. (2m-u)/(5m+u)
  • D. (m-2u)/(m+5u)

Explanation

Expanding via difference of squares: (2m-u+m-2u)(2m-u-m+2u) = 3(m-u)(m+u); dividing by 5(m-u)(m+u) gives 3/5.

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