Download MOUAU Post UTME Past Questions and Answers – PDF

Download MOUAU Post UTME Past Questions and Answers – PDF

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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.

This booklet contains the updated MOUAU Post-UTME Questions and Answers from 2010 to date and some essentials about MOUAU and its admission processes.

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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−𝑐𝑜𝑠𝜃𝑠𝑖𝑛2𝜃 (a) 11+𝑐𝑜𝑠𝜃 (b) 11−𝑐𝑜𝑠𝜃 (c) 11+𝑠𝑖𝑛𝜃 (d) 11−𝑠𝑖𝑛𝜃
  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 3𝑛+3− 3𝑛+23𝑛+1 −3𝑛 (a) -9 (b) 9 (c) 10 (d) -10.
  6. Noting that cos∝ =(90−∝),find y in terms of x in the equation cos􁉀1+12𝑥􁉁 = sin 􁉀32𝑦􁉁 (a) y = 178+𝑥3 (b) y = 𝑥−1783 (c) 178−𝑥3 (d) −(178+𝑥)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 ∝,𝛽 are the roots of equation 18 + 15x – 3×2 = 0, find ∝𝛽 – ∝− 𝛽 (a) 11 (b) -11 (c) 10 (d) -10.
  10. Resolve 1(1−𝑥2) into partial fractions (a) 12(1+𝑥)− 12(1−𝑥) (b) 12(1+𝑥)+ 12(𝑥−1) (c) 12(𝑥+1)+ 12(1−𝑥) (d) 12(1−𝑥2)
  11. Given that the sum of infinity 𝑆∞ = a + ar + ar2 + ….. = 𝑎1−𝑟 , 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) −𝑒−𝑥+5𝑥+𝑘 (b) 𝑒−𝑥+𝑥5+𝐾 (c) −𝑒−𝑥−𝑥−5+𝐾 (d) −𝑒−𝑥+𝑥4+𝐾.
  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√3𝑦−𝑥=0 makes with positive y-axis (a) 300 (b) 600 (c) 00 (d) 450.
  16. Find the value of p which satisfies the equation √𝑃− 6𝑝 = 1 (a) 4 (b) -4 (c) 9 (d) -9.
  17. Find the area of circle 4×2 + 4y2 – 400 = 0 (a) 10𝜋 𝑠𝑞.𝑢𝑛𝑖𝑡𝑠 (b) 40𝜋 𝑠𝑞.𝑢𝑛𝑖𝑡𝑠 (c) 400𝜋 𝑠𝑞.𝑢𝑛𝑖𝑡𝑠 (d) 100𝜋 𝑠𝑞.𝑢𝑛𝑖𝑡𝑠.
  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+ 32𝑦+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=𝑘√2 (a) 4/3 (b) ¾ (c) -3/4 (d) -4/3.
  22. Evaluate ∫3𝑥𝑙𝑜𝑔3𝑑𝑥10 (a) 3 (b) 4 (c) 1 (d) 2.

ANSWERS TO THESE POST-UTME SCREENING EXERCISE QUESTIONS

  1. C
  2. 1−cos𝜃𝑠𝑖𝑛2𝜃
    Recall that: sin2θ + cos2 θ = 1
    sin2θ = 1 – cos2 θ
    1−cos𝜃1− 𝑐𝑜𝑠2𝜃
    But 1 – cos2 θ = (1 – cos θ)(1 + cos θ) 1 1−cos𝜃1− 𝑐𝑜𝑠2𝜃
    = 1−cos𝜃(1−cos𝜃)(1+𝑐𝑜𝑠 𝜃)
    = 11+𝑐𝑜𝑠 𝜃Ans:A
  3. D
  4. A
  5. 3𝑛+3− 3𝑛+23𝑛+1 −3𝑛 = 3𝑛 𝑋 33−3𝑛𝑋 323𝑛 𝑋 31− 3𝑛 = 3𝑛+3− 3𝑛+23𝑛 (3−1)
    = 3𝑛𝑋 32𝑋 23𝑛 𝑋 2 = 32 = 9 Ans:B
  6. cos􁉀1+12𝑥􁉁 = sin 􁉀32𝑦􁉁
    But cos = sin (90 – )
    = cos􁉀1+12𝑥􁉁 = sin [90−􁉀1+ 12𝑥􁉁]
    Cos 􁉀1+12𝑥􁉁 = sin 􁉀32𝑦􁉁
    = sin 􁉂90−􁉀1+ 12𝑥􁉁􁉃=sin(32𝑦)
    = 90−􁉀1+ 12𝑥􁉁=32𝑦
    = 90−􁉀2+𝑥2𝑥􁉁=32𝑦
    Multiply through by 2
    180 – (2 + x) = 3y
    180 – 2 – x = 3y
    178 – x = 3y
    y = 1/3 (178 – x)
    y = 178−𝑥3 Ans: C
  7. 𝑥−1=<−1
    1𝑥<−1
    Multiply through by 𝑥2
    1𝑥𝑋 𝑧𝑥2<−1 𝑋 𝑥2
    𝑥<−𝑥2
    𝑥+𝑥2<0
    𝑥 (1+𝑥)<0
    𝑥=0 𝑜𝑟 1+𝑥= 0 then 𝑥=0 𝑜𝑟−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 𝑥(1 + 𝑥) < 0 (𝑖.𝑒.𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒) 𝑡ℎ𝑒 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑖𝑛𝑒𝑞𝑢𝑎𝑙𝑖𝑡𝑦 𝑖𝑠 – 1 < 𝑥 < 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 + 15𝑥 – 3𝑥2 = 0
    a = – 3, b = 15, c = 18
    𝛼+ 𝛽= −𝑏𝑎= −15−3=5
    𝛼𝛽= 𝑐𝑎= 18−3= −6
    𝛼𝛽− 𝛼−𝛽=𝛼𝛽−(𝛼+𝛽)
    = –6 – (5) = – 11 Ans:B
  3. 11−𝑥2
    𝐵𝑢𝑡 1 – 𝑥2 = (1 – 𝑥)(1 + 𝑥)
    11−𝑥2= 1(1−𝑥)(1+𝑥) .
    A linear factor of the form ax + b always gives a partial fraction of 𝐴𝑎𝑥_𝑏
    1(1−𝑥)(1+𝑥)= 𝐴1−𝑥+ 𝐵1+𝑥
    1 (1−𝑥)(1+𝑥)
    = 𝐴(1+𝑥)+𝐵(1−𝑥)(1−𝑥)(1+𝑥)
    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
    𝐿𝑒𝑡 𝑥 = –1
    1 = A(-1 + 1) + B[1 – (-1)]
    1 = A(0) + B(1 + 1)
    B = ½
    1(1−𝑥)(1+𝑥)= 𝐴1−𝑥+ 𝐵1+𝑥
    = 121−𝑥+ 121+𝑥
    12(1−𝑥)+12(1+𝑥)
    = 1(1−𝑥)(1+𝑥)= 11−𝑥2= 12(1−𝑥)+12(1+𝑥) Ans: C
  4. 1−23+49−827+⋯
    T1 = 1, T2 = −23,𝑇3= 49
    For a given series to be an A.P
    𝑇2−𝑇1=𝑇3−𝑇2
    For a given series to be a G.P
    𝑇2𝑇1=𝑇32
    The series is a G.P
    r = 𝑇2𝑇1= −231
    r = −23
    𝑆∞=𝑎1−𝑟
    a = T1 = 1
    𝑆∞=11−􀵫−23􀵯=111+23
    = 13+23=153= 35 Ans: D
  5. 𝐿𝑒𝑡 𝑦 = 𝑥2 – 5𝑥 + 6
    Minimum and maximum are turning point. At turning 𝑑𝑦𝑑𝑥=0
    𝑑𝑦𝑑𝑥 = 2𝑥−5=0
    2𝑥 – 5 = 0
    x = 52 Ans: A
  6. ∫(5𝑥4 +𝑒−𝑥)𝑑𝑥
    = 5𝑥4+14+1+(−𝑒−𝑥)+𝑐
    5𝑥55−𝑒−𝑥+𝑐
    = 𝑥5−𝑒𝑥+𝑐
    ∫(5𝑥4+𝑒𝑥+𝑥5+𝑐𝐀𝐧𝐬: 𝑨
  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. 𝑋∩𝑌={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 – (𝑋∩𝑌) = {6, 7, 10, 3, 17} – {3, 6, 7} = {10, 17}
    Y – (𝑋∩𝑌) = {10, 17} Ans: B
  8. 1√3𝑦−𝑥=0
    𝑦√3−𝑥=0
    Multiply through with √3
    y – x√3=0
    y = x√3
    Divide through by 𝑥
    𝑦𝑥= √31
    but tan θ = 𝑦𝑥= √31
    θ = tan-1 (√3) = 600
    The angle 600 is the angle the line makes with the positive x-axis
    0yxB
    Θ + 𝛽 = 90
    60 + 𝛽=90
    𝛽=90−60
    𝛽 = 300
    Note that the angle the line 1√3𝑦−𝑥=0 makes with the positive y-axis is given by tan 𝛽=𝑥𝑦Ans: A
  9. √𝑃− 6√𝑝=1
    Multiply through by √𝑃

P – 6 = √𝑃
Square both side (P – 6)2 = (√𝑃)2
P2 – 12P + 36 = P
P2 – 12P – P + 36 = 0
P = 9 or 4
Check to see if 9 or 4 satisfied the equation
√𝑃−6√𝑃=1
When P = 9
√9−6√𝑃=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 ∴𝑝=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
    𝑟2= 102
    r = 10
    Area of a circle (A) = 𝜋r2
    A = 𝜋(10)2
    A = 100𝜋 Ans:D
  2. 𝑥=Σ𝑥𝑛
    For the numbers: x, y-1& z5
    𝑥= 𝑥+𝑦−1+𝑧53=6
    x + y-1 + z5 = 3 x 6 = 18
    x + y-1 + z5 = 18……………………(i)
    𝑥=Σ𝑥𝑛
    For the numbers: 10, y-1, 12, x, z5
    𝑥=10+𝑦−1+12+𝑥+𝑦55
    𝑥=10+12+𝑥+𝑦−1+𝑦55
    But x + y-1 + z5 = 18
    𝑥=10+12+185
    𝑥=405=8 Ans: B
  3. 23+ 32𝑦+9=0?
    2𝑥3+ 3𝑦2=−9
    4𝑥+9𝑦6=−9
    4x + 9x = -9 x 6
    Divide through by 36
    4𝑥36+ 9𝑦36=−9𝑋636
    𝑥9+𝑦4=−32
    Multiply through by 23
    23𝑥𝑥9+23𝑥𝑦4=−32𝑥23
    2𝑥27+𝑦6=−1
    Multiply through by -1
    −2𝑥27+𝑦6=−1
    The above equation can be written as shown below
    −𝑥276−𝑦6=1………….(𝑖)
    The double intercept form of the equation of a straight line is
    𝑥𝑎+𝑦𝑏=1……………(𝑖𝑖)
    a = −272,𝑏=−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=𝑘√2
    = 55√2−2√2=𝑘√2
    Multiply through by 2√2
    5 – 2√2􀵫2√2􀵯=2√2(𝑘√2)
    5 – 4 (2) = 2k(2)
    5 – 8 = 4k
    -3 = 4k
    k = -3/4Ans: C
  6. ∫3𝑥𝑙𝑜𝑔3𝑑𝑥10
    ∫3𝑥𝑙𝑜𝑔3𝑑𝑥10
    ∫3𝑥𝑙𝑜𝑔 3𝑒 𝑑𝑥10
    = ∫3𝑥 𝐼𝑛 3 𝑑𝑥10
    = ∫𝑎𝑥𝐼𝑛 𝑎 𝑑𝑥=0𝑎𝑥
    ∫3𝑥𝐼𝑛 3 𝑑𝑥=[3𝑥]0110
    = 31−30
    = 3 – 1 = 2 Ans: D
  1. MOUAU Admission List 2022/2023 for UTME and Direct Entry (DE)
  2. MOUAU Post UTME Form 2022/2023 – www.mouau.edu.ng
  3. How to Succeed in the University or Polytechnic Environment
  4. How to Pass Post UTME | What to Read for Post UTME 2022/2023

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.

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