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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

1. 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.
2. Noting that, sin2θ + cos2θ = 1, simplify 1−???????2? (a) 11+???? (b) 11−???? (c) 11+???? (d) 11−????
3. A circle has an eccentricity (a) < 1 (b) 1 (c) > 1 (d) 0.
4. 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).
5. Simplify 3?+3− 3?+23?+1 −3? (a) -9 (b) 9 (c) 10 (d) -10.
6. 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.
7. 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.
8. In how many ways can the letters of the word NWAFOR be permuted? (a) 7200 (b) 72 (c) 720 (d) 72000.
9. If ∝,? are the roots of equation 18 + 15x – 3×2 = 0, find ∝? – ∝− ? (a) 11 (b) -11 (c) 10 (d) -10.
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)
11. 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
12. What is the value of x for which x2 – 5x + 6 is minimum? (a) 52(b) −52 (c) 3 (d) -3.
13. Integrate 5×4 + e-x with respect to x (a) −?−?+5?+? (b) ?−?+?5+? (c) −?−?−?−5+? (d) −?−?+?4+?.
14. 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}.
15. Find the angle in the line 1√3?−?=0 makes with positive y-axis (a) 300 (b) 600 (c) 00 (d) 450.
16. Find the value of p which satisfies the equation √?− 6? = 1 (a) 4 (b) -4 (c) 9 (d) -9.
17. Find the area of circle 4×2 + 4y2 – 400 = 0 (a) 10? ??.????? (b) 40? ??.????? (c) 400? ??.????? (d) 100? ??.?????.
18. 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.
19. 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
20. 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.
21. Find the value of k in the equation 55√2−√8=?√2 (a) 4/3 (b) ¾ (c) -3/4 (d) -4/3.
22. Evaluate ∫3????3??10 (a) 3 (b) 4 (c) 1 (d) 2.

## ANSWERS TO THESE POST-UTME SCREENING EXERCISE QUESTIONS

1. C
2. 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
3. D
4. A
5. 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
6. 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
7. ?−1=<−1
1?<−1
Multiply through by ?2
1?? ??2<−1 ? ?2
?<−?2
?+?2<0
? (1+?)<0
?=0 ?? 1+?= 0 then ?=0 ??−1
Recommended:  MOUAU Admission List 2023/2024 for UTME and Direct Entry (DE)
Recommended:  MOUAU Admission List 2023/2024 for UTME and Direct Entry (DE)

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

1. 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
2. 18 + 15? – 3?2 = 0
a = – 3, b = 15, c = 18
?+ ?= −??= −15−3=5
??= ??= 18−3= −6
??− ?−?=??−(?+?)
= –6 – (5) = – 11 Ans:B
3. 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
4. 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
5. ??? ? = ?2 – 5? + 6
Minimum and maximum are turning point. At turning ????=0
???? = 2?−5=0
2? – 5 = 0
x = 52 Ans: A
6. ∫(5?4 +?−?)??
= 5?4+14+1+(−?−?)+?
5?55−?−?+?
= ?5−??+?
∫(5?4+??+?5+????: ?
7. 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
8. 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
9. √?− 6√?=1
Multiply through by √?
Recommended:  MOUAU Post UTME Form 2023/2024 - www.mouau.edu.ng

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

1. 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
2. ?=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
3. 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
4. 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
5. 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
6. ∫3????3??10
∫3????3??10
∫3???? 3? ??10
= ∫3? ?? 3 ??10
= ∫???? ? ??=0??
∫3??? 3 ??=[3?]0110
= 31−30
= 3 – 1 = 2 Ans: D

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