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This is the official Post-UTME Past Questions and Answers of the Michael Okpara University of Agriculture (MOUAU). Which consists of 101 pages for Candidates intending to write Post-UTME into Faculties/Colleges of Arts and Sciences.

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## Sample of MOUAU Post UTME Past Questions and Answers

- The probability of an event A given by P(A) is a number between (a) -1 and 1 (b) 0 and ½ (c) 0 and 1 (d) -1 and 0.
- Noting that, sin2θ + cos2θ = 1, simplify 1−???????2? (a) 11+???? (b) 11−???? (c) 11+???? (d) 11−????
- A circle has an eccentricity (a) < 1 (b) 1 (c) > 1 (d) 0.
- It two elements A and B are independent then P(A and B) is (a) P(A ∩ B) (b) (A B) (c) P(A) (d) P(B).
- Simplify 3?+3− 3?+23?+1 −3? (a) -9 (b) 9 (c) 10 (d) -10.
- Noting that cos∝ =(90−∝),find y in terms of x in the equation cos?1+12?? = sin ?32?? (a) y = 178+?3 (b) y = ?−1783 (c) 178−?3 (d) −(178+?)3.
- For what values of x is x–1< – 1? (a) 0 < x < 1 (b) x < -1, x > 0 (c) x > 1, x < 0 (d) -1 < x < 0.
- In how many ways can the letters of the word NWAFOR be permuted? (a) 7200 (b) 72 (c) 720 (d) 72000.
- If ∝,? are the roots of equation 18 + 15x – 3×2 = 0, find ∝? – ∝− ? (a) 11 (b) -11 (c) 10 (d) -10.
- Resolve 1(1−?2) into partial fractions (a) 12(1+?)− 12(1−?) (b) 12(1+?)+ 12(?−1) (c) 12(?+1)+ 12(1−?) (d) 12(1−?2)
- Given that the sum of infinity ?∞ = a + ar + ar2 + ….. = ?1−? , to what sum does the infinite series 1 – 23+ 49− 827+⋯ coverage (a) – 35 (b) 53 (c) − 53 (d) 35
- What is the value of x for which x2 – 5x + 6 is minimum? (a) 52(b) −52 (c) 3 (d) -3.
- Integrate 5×4 + e-x with respect to x (a) −?−?+5?+? (b) ?−?+?5+? (c) −?−?−?−5+? (d) −?−?+?4+?.
- If X = {2, 3, 6, 7, 8} and Y = {6, 7, 10, 3, 17}, find Y – {X Y). (a) { } (b) {10, 17} (c) {2, 3, 6, 7, 8, 10, 17} (d) {3, 6, 7}.
- Find the angle in the line 1√3?−?=0 makes with positive y-axis (a) 300 (b) 600 (c) 00 (d) 450.
- Find the value of p which satisfies the equation √?− 6? = 1 (a) 4 (b) -4 (c) 9 (d) -9.
- Find the area of circle 4×2 + 4y2 – 400 = 0 (a) 10? ??.????? (b) 40? ??.????? (c) 400? ??.????? (d) 100? ??.?????.
- Let the mean of x, y-1, z5 be 6 find the mean of 10, y-1, 12, x z5. (a) 7 (b) 8 (c) 9 (d) 10.
- What is the addition of y and x- intercepts of the line 23+ 32?+9=0? (a) -19.5 (b) 19.5 (c) 20.5 (d) -20.5
- Given that h(x) = 3 + 2x and f(x) = 1 – x, find h(– f (x)). (a) 1 – 2x (b) 1 + 2x (c) 2x – 1 (d) -1 – 2x.
- Find the value of k in the equation 55√2−√8=?√2 (a) 4/3 (b) ¾ (c) -3/4 (d) -4/3.
- Evaluate ∫3????3??10 (a) 3 (b) 4 (c) 1 (d) 2.

## ANSWERS TO THESE POST-UTME SCREENING EXERCISE QUESTIONS

- C
- 1−cos????2?

Recall that: sin2θ + cos2 θ = 1

sin2θ = 1 – cos2 θ

1−cos?1− ???2?

But 1 – cos2 θ = (1 – cos θ)(1 + cos θ) 1 1−cos?1− ???2?

= 1−cos?(1−cos?)(1+??? ?)

= 11+??? ?Ans:A - D
- A
- 3?+3− 3?+23?+1 −3? = 3? ? 33−3?? 323? ? 31− 3? = 3?+3− 3?+23? (3−1)

= 3?? 32? 23? ? 2 = 32 = 9 Ans:B - cos?1+12?? = sin ?32??

But cos = sin (90 – )

= cos?1+12?? = sin [90−?1+ 12??]

Cos ?1+12?? = sin ?32??

= sin ?90−?1+ 12???=sin(32?)

= 90−?1+ 12??=32?

= 90−?2+?2??=32?

Multiply through by 2

180 – (2 + x) = 3y

180 – 2 – x = 3y

178 – x = 3y

y = 1/3 (178 – x)

y = 178−?3 Ans: C - ?−1=<−1

1?<−1

Multiply through by ?2

1?? ??2<−1 ? ?2

?<−?2

?+?2<0

? (1+?)<0

?=0 ?? 1+?= 0 then ?=0 ??−1

Factor

x < – 1 – 1 < x < 0 x > 0

x

1 + x

-ve

-ve

-ve

+ve

+ve

+ve

x(1 + x)

+ve

-ve

+ve

Since ?(1 + ?) < 0 (?.?.????????) ?ℎ? ???????? ?? ?ℎ? ?????????? ?? – 1 < ? < 0 Ans: D

- The word NWAFOR has six (6) distinct letters. n = 6

The number of ways of arranging n distinct object is n!

No of ways = n! = 6! = 720 Ans: C - 18 + 15? – 3?2 = 0

a = – 3, b = 15, c = 18

?+ ?= −??= −15−3=5

??= ??= 18−3= −6

??− ?−?=??−(?+?)

= –6 – (5) = – 11 Ans:B - 11−?2

??? 1 – ?2 = (1 – ?)(1 + ?)

11−?2= 1(1−?)(1+?) .

A linear factor of the form ax + b always gives a partial fraction of ???_?

1(1−?)(1+?)= ?1−?+ ?1+?

1 (1−?)(1+?)

= ?(1+?)+?(1−?)(1−?)(1+?)

1 = A(1 + x) + B(1 – x)

Let x = 1

1 = A(1 + 1) + B(1 – 1)

1 = 2A + B(0)

1 = 2A

A = ½

??? ? = –1

1 = A(-1 + 1) + B[1 – (-1)]

1 = A(0) + B(1 + 1)

B = ½

1(1−?)(1+?)= ?1−?+ ?1+?

= 121−?+ 121+?

12(1−?)+12(1+?)

= 1(1−?)(1+?)= 11−?2= 12(1−?)+12(1+?) Ans: C - 1−23+49−827+⋯

T1 = 1, T2 = −23,?3= 49

For a given series to be an A.P

?2−?1=?3−?2

For a given series to be a G.P

?2?1=?32

The series is a G.P

r = ?2?1= −231

r = −23

?∞=?1−?

a = T1 = 1

?∞=11−?−23?=111+23

= 13+23=153= 35 Ans: D - ??? ? = ?2 – 5? + 6

Minimum and maximum are turning point. At turning ????=0

???? = 2?−5=0

2? – 5 = 0

x = 52 Ans: A - ∫(5?4 +?−?)??

= 5?4+14+1+(−?−?)+?

5?55−?−?+?

= ?5−??+?

∫(5?4+??+?5+????: ? - X = {2, 3, 6, 7, 8} Y = {6, 7, 10, 3, 17}

The intersect of two sets X and Y is a set that contain elements that are common to both sets. ?∩?={3,6,7}

The difference of two sets A and B (i.e. A – B) is a set, which contain only elements that are formed in set A but not in set B.

Y – (?∩?) = {6, 7, 10, 3, 17} – {3, 6, 7} = {10, 17}

Y – (?∩?) = {10, 17} Ans: B - 1√3?−?=0

?√3−?=0

Multiply through with √3

y – x√3=0

y = x√3

Divide through by ?

??= √31

but tan θ = ??= √31

θ = tan-1 (√3) = 600

The angle 600 is the angle the line makes with the positive x-axis

0yxB

Θ + ? = 90

60 + ?=90

?=90−60

? = 300

Note that the angle the line 1√3?−?=0 makes with the positive y-axis is given by tan ?=??Ans: A - √?− 6√?=1

Multiply through by √?

P – 6 = √?

Square both side (P – 6)2 = (√?)2

P2 – 12P + 36 = P

P2 – 12P – P + 36 = 0

P = 9 or 4

Check to see if 9 or 4 satisfied the equation

√?−6√?=1

When P = 9

√9−6√?=1

3−63=1

3 – 2 = 1

1 = 1

Hence the value p = 9 satisfied the equation when p = 4

√4−6√4=1

2−62=1

2 – 3 = 1

-1 1

Hence the value p = 4 does not satisfy the equation ∴?=9Ans: C

- 4×2 + 4y2 – 400 = 0

Divide through by 4

x2 + y2 – 100 = 0

x2 + y2 = 100

x2 + y2 + 102……………(i)

The general equation of a circle is given by x2 + y2 = r2 ………………………….(ii)

From equation i and ii

?2= 102

r = 10

Area of a circle (A) = ?r2

A = ?(10)2

A = 100? Ans:D - ?=Σ??

For the numbers: x, y-1& z5

?= ?+?−1+?53=6

x + y-1 + z5 = 3 x 6 = 18

x + y-1 + z5 = 18……………………(i)

?=Σ??

For the numbers: 10, y-1, 12, x, z5

?=10+?−1+12+?+?55

?=10+12+?+?−1+?55

But x + y-1 + z5 = 18

?=10+12+185

?=405=8 Ans: B - 23+ 32?+9=0?

2?3+ 3?2=−9

4?+9?6=−9

4x + 9x = -9 x 6

Divide through by 36

4?36+ 9?36=−9?636

?9+?4=−32

Multiply through by 23

23??9+23??4=−32?23

2?27+?6=−1

Multiply through by -1

−2?27+?6=−1

The above equation can be written as shown below

−?276−?6=1………….(?)

The double intercept form of the equation of a straight line is

??+??=1……………(??)

a = −272,?=−6

a + b = −272−61

= −27−122

= −392 = -19.5 Ans: A - h(x) = 3 + 2x

f(x) = 1 – x = – (x – 1)

-f(x) = -[(x – 1)]

= x – 1

h[- f(x)] = h(x – 1)

= 3 + 2(x – 1)

= 3 + 2x – 2

h[-f(x)] = 2x + 1 Ans: B - 55√2−√8=?√2

= 55√2−2√2=?√2

Multiply through by 2√2

5 – 2√2?2√2?=2√2(?√2)

5 – 4 (2) = 2k(2)

5 – 8 = 4k

-3 = 4k

k = -3/4Ans: C - ∫3????3??10

∫3????3??10

∫3???? 3? ??10

= ∫3? ?? 3 ??10

= ∫???? ? ??=0??

∫3??? 3 ??=[3?]0110

= 31−30

= 3 – 1 = 2 Ans: D

### Recommended:

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- MOUAU Post UTME Form 2024/2025 – www.mouau.edu.ng
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On the other hand, you can download more post UTME past questions and answers for all the Universities in Nigeria. Which is in PDF format **HERE**.