# Unibadan Post UTME Past Questions/Answers In Maths

University of Ibadan 2018 past questions and answers in Post UTME Mathematics will not only be useful to candidates writing Mathematics in UI post UTME exams, but will be of practical help to other candidates preparing for post UTME exams in Mathematics in other Universities in Nigeria as a whole.  Good luck.

1. (1.28 x 104) ÷ ((6.4 x 102) equals (a) 2 x 10-5 (b) 2 x 10-1 (c) 2 x 100 (d) 2 x 101

(e) 2 x 105      Ans. D

1. A man and wife went to buy an article costing N400. The woman had 10% of the cost and the man 40% of the reminder. How much did they have altogether? (a) N216 (b) 200     (c) 184 (d) 144 (e) 100           Ans. C
2. Add the same number to the numerator and denominator of 3/18. If the resulting fraction is ½, then the number added is (a) 13 (b) 14 (c) 15 (d) 12 (e) 11 Ans. D
3. After getting a rise of 15% , a man’s new monthly salary is N345. How much per month did he earn before the increase? (a) 330 (b) 396.75 (c) N300 (d) 293.25 (e) 360 Ans. C
4. Assuming loge 4.4 = 1.4816 and loge 7.7 = 2.0142, then the value of loge ¼ is (a) 0.5326 (b) 3.4958 (c)0.4816 (d) 0.0142 (e) 1.3594 Ans. A
5. Evaluate (2 + 4-1/2)2   (a) ¼ (b) 5/4 (c) 9/4 (d) 4 (e) 9             Ans. C
6. Evaluate correct to 4 decimal places 827.51 x 0.015, (a) 8.8415 (b) 12.4127 (c) 124.1265 (d) 12.4120 (e( 114.1265                Ans. B
7. Express 130 kilometres per second in meters per hour (a) 7.8 x 105 (b) 468 x 106 (c) 7,800,000 (d) 4.68 x 106 (e) 780 x 10-6                       Ans. B
8. Find the square root of 170-20┘30 (a) 2 ┘10-5 ┘3 (b) 3┘5-8┘6 (c) 2┘5-5┘6 (d)5┘10-2┘3 (e) 5┘10-2┘3
9. If (25) x -1 = 64(5/2)6, then x has the value (a) 7 (b) 4 (c) 32 (d) 64 (e) 5 Ans. C
10. If a circular paper disc is trimmed in such a way that its circumference is reduced in the ratio 2.5, in what ratio is the surface are reduced? (a) 8:125 (b) 2:5 (c) 8:25 (d) 4:25 (e) 4:10            Ans. D

1. In base ten, the number 101101 (base 2) equals (a) 15 (b) 4 (c) 45 (d) 32 (e) 90 Ans. C

Ans. D

1. Simplify 5x x 25x -1

125x + 1                    = (a) 52x-1 (b) 5x+ (c) 5 – 5 (d) 5x+1 (e)53    Ans. C

1. Simplify (a-1/a) (a4/3+/a2/7)

(a2-1/a2)  = (a) a2/3 (b) a-1/3 (c) a2+1 (d) a (e) a1/3           Ans. E

1. Simplify f1/2 g2h1/3 ÷ f5/2gh7/3 (a) (g/fh)2 (b) f5/2h7 (c)f5/4gh7/9 (d) g2      (e) Ans. A

F5h7       f2h2

1. Simplify 2 5 – 1 7 x 6

12     8      5    (a) 1/6 (b) 13/20 (c) 11/30 (d) 9/4 (e) 5/3     Ans. A

1. Solve the system of equation: 2x +y = 32, 33y- x = 27 (a) (3,2) (b) -3,2) (c)( -3,-2) (d) (-3,-2) (e) 2,2) Ans. A
2. The annual profits of a transport business were divided between the two partners A and B in the ratio 3:5. If B receives N3,000 more than A, the total profit was: (a) N5,000  (b) N1,800 (c)N12,000 (d) N24,000 (e)N8,000
3. The diameter of a metal rod is measured as 23.40cm to four significant figures. What is the maximum error in the measurement? (a) 0.05cm (b) 0.5cm (c) 0.04cam (d) 0.005cm (e)0.004cm Ans. D
4. The ratio of the price of a loaf of bread to the price of a packet of sugar in 1975 was r:t, in 1980 the price of a loaf went up by 25% and that of a packet of sugar by 10%. Their new ratio is now (a)40r:50t (b) 44r:50t (c)50r:44t (d) 55r:44t (e) 44r:55t Ans. C
5. The sum of 37/8 and 1 1/3 is less than the difference between 3/8 and 12/3 by (a) 32/3 (b) 51/4 (c) 61/2 (d) 0 (e) 81/8 Ans. C
6. Two distinct sectors in the same circle subtend 1000 and 300 respectively at the centre of the circle. Their corresponding arcs are in the ratio (a)1:100 (b) 3:1 (c) 5:2 (d) 10:3 (e) 13:30 Ans. D
7. What is log7(49a) – log10(0.01)? (a) 49a/100 (b) a/2+2 (c) 72a + 2 (d) 2a + 2 (e) 2a/2         Ans. D

1. What is the number whose logarithm to base 10 is .3482? (a) 223.6 (b) 0.2228 (c) 2.235 (d) 22.37 (e) 0.02229 Ans. E
2. When a dealer sells a bicycle for N81, he makes a profit of 8%. What did he pay for the bicycle? (a) N73 (b) 74:52 (c) N75 (d) 7:52 (e) 87.48 Ans. C
3. Write the decimal number 39 to base 2. (a) 10011 (b) 110111 (c) 111001 (d) 100101 (e) 19.5         Ans. A
4. A father is now three times as old as his son. Twelve years ago, he was six times as old as his son. How old are the son and the father? (a) 20 and 45 (b) 100 and 150 (c) 45 and 65 (d) 35 and 75 (e) 20 and 60        Ans. E
5. A steel ball of radius 1 cm is dropped into a cylinder of radius 2cm and height 4cam. If the cylinder is now filled with water, what is the volume of water in the cylinder?

(a) 44/3cm3 (b) 12πcm3 (c)38/3πcm3 (d) 40/3 πcm3(e) 32/33πcm3   Ans. A

1. Find a two-digit number such that three times the tens digit is 2 less than twice the units digit, and twice the number is 20 is 20 greater than the number obtained by reversing the digits. (a) 24 (b) 42 (c) 74 (d) 47 (e) 72
2. Find the roots of the equation 10x2 – 13x-3 = 0 (a) x = 3/5 or -1/2 (b) x=3/10 or -1 (c) x = 3/10 or 1 (d) x = 1/5 pr -3/2 (e) x = 1/5 or 3/3 Ans. E
3. If a function is defined by f(x+1) = 3×2 – x+4, find f(0). (a) 4 (b) 6 (c) 0 (d) 8 (e) 2 Ans. D
4. If sin x equals cosine x, what is x in radians? (a) π/2 (b) π/3 (c) π/4 (d) π?6 (e) π/12 Ans. C
5. If x2 + 4 = 0, then x = (a) 4 (b) -4 (c) 2 (d) +2 (e) none of the these.
6. In a geometric progression, the first term is 153 and the sixth term is 17/27, the sum of the first four terms is (a) 860/3 (b) 680/3 (c) 608/3 (d) 806/3 (e) 680/27 Ans. B
7. List all integer values of x satisfying the inequality -1 < 2x – 5 ≤ 5 (a)2,3,4,5 (b) 2,5 (c0 3,4,5 (d) 2,3,4 (e) 3,4 Ans. C
8. Make C the subject of the equation a(b+c) + 5/d – 2= 0 (a)c= 2d-5-b/ad (b) c=5-2d-b/ad (c) c=5-2d-abd/ad (d) c=2d-5-abd/ad (e) c=2d-ab-5/ad
9. Multiply (3x+5y+4z) by (2x-3y+z) (a) 6x2 + xy- 15y2+ 4z2 +11xz-7yz (b) 6x2 + 3xy- 15y2+ 4z2 +11xz-7yz (c) 6x2 + 3xy- 15y2+ 4z2 +13xz-8yz (d) 6x2 + 5xy- 15y2+ 4z2 +13xz-7yz                  (e) 6x2 + xy- 15y2+ 4z2 +13xy-7yz
10. Multiply (x + 3y + 5) by (2x2 + 5y + 2) Ans.     B
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(A)       2x3 + 3yx2 + 10xy + 15y2 + 13y + 10x2 + 2x + 10

(B)       2x3 + 6yx2 + 5xy+15y2 + 31y + 10x2 + 2x + 10

(C)       2x3 + 3yx2 + 5xy + 10y2 + 13y + 5x2 + 2x + 10

(D)       2x3 + 6yx2 + 5xy + 15y2 + 13y + 10x2 + 2x + 10

(E)        2x3 + 2yx2 + 10xy + 10y2 + 31y + 5x2 + 2x + 10

1. Multiplyx2 +x+ 1 by x2– x+ 1 Ans.   B            (A)       x4+3x2+x+1      (B)             x4+x2+1            (C)       x4 + 4x2 – 6x+1   (D) X4 -6x2 – 4x+1         (E)        x4– x3 – x2+x +1
2. The factors of 6x – 5 – x2 are

(A)       -(x+ 3)(x+ 2)                (B) (x – 5)(x – 1)                                Ans.   D                           (C)       -(x +5)(x +1)                   (D) (x – 5)(1 – x)           (E)        (x +5)(1 – x)

1. The quantity (x + y) is a factor of A. Ans.   D

(A)       x2+y2   (B)       x3 – y3   (C) 2x2—3xy+y2 – x+1

(D)       2x3 + 2x2y – xy + 3x – y2 + 3y    (E)        x5– y5

1. The set of values of x and y which satisﬁes the equations <i>x<sup>2</sup>

– y – l = 0</i> and <i>y – 2x + 2 = O</> I                                                           Ans.   A

(A)       l, 0       (B) 1, 1 (C) 2, 2 (D) 0, 2 (E) l, 2

1. The solution of the equation x2 – 2x = 8 is

(A) x=0or2       (B) x=-2or4      (C) x=2             (D) x=-4           (E) x=2or4    Ans.   B

1. The solution of the quadratic equation bx2 + cx + a = 0 is given by

(A)    b (B) b       (C) b

(D) b      (E) b

1. The sum of the root of a quadratic equation is 5/2 and the product of its roots is 4. The quadratic equation is                                                                      Ans.   B

(A) 2x2+5x+8= 0           (B) 2x2– 5x+8=0           (C) 2x2 – 8x+5= 0

(D) 2x2+8x – 5=0         (E) 2x2+5x – 8=0

1. Three numbers x, y and z are connected by the relationships y = 4/9x + 1 and z = 4/9y + 1 (C) Ifx = 99, ﬁnd z                                                            Ans.    C

(A) 61/3   (B) 20   (C) 21 (D) 1764/9 (E) None ofthe above

1. What factor is common to all the expressions: x2– x, 2x2 + x – 1 and x2– 1?

(A) x (B) x – 1 (C) x + 1 (D) No common factor (E) (2x – 1)               Ans.    D

1. A canal has rectangular cross section of width 10cm and breadth 1m. If water of uniform density l gm cm-3 ﬂows through it at a constant speed of l000mm per minute, the adjacent sea is

(A) 100,000    (B) 1,000,000 (C) 120,000    (D) 30,000 (E) 350,000     Ans.  A

1. A cuboid has a diagonal oflength 9cm and a square base of side 4cm. What is its height? B (A) 9cm (B) √65cm             (c) 4√2cm        (D) 7cm           (E) 6.5cm  Ans.  B

1. A cylinder of height h and radius r is open at one end. Its surface area is

(A)  (B)  (C)  (D) (E) Ans.  E

1. A pyramid is constructed on a cuboid. The ﬁgure has Ans. E

(A) 12 faces (B) 13 vertices (C) 14 edges (D) 15 edges (E) 16 edges

1. A quadrant of a circle of radius 6cm is cut away from each corner of a rectangle 25cm long and 18cm wide. Find the perimeter of the remaining ﬁgure.1/2 (A) 38cm (B) (38 + 12)cm     (C) (86  – 12)cm (D) (86 – 6 )cm                      (E) (86 +12)cm  Ans. B

1. A rectangular picture 6cm by 8cm is enclosed by a frame ½ cm wide. Calculate the area of the frame.

(A) l5sq.cm (B) 20sq.cm (C) 13sq.cm (D) 16sq.cm(E) l7sq cm  Ans. A

1. A regular hexagon is constructed inside a circle of diameter 12cm. The area of the hexagonis                                                                                     Ans. C

(A) 36cm2 (B) 36/cm2 (c) 54√3cm2(D) 54/√3cm2 (E) 54√xcm2

1. A regular hexagon is constructed inside a circle of diameter 12cm. The area of the hexagon is                                                                                     Ans. C
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(A) 36cm2 (B) 36/cm2 (C) 54√3cm2 (D) 54/√3cm2 (B) 54/√3xcm2

1. A solid cylinder of radius 3cm has a total surface area of 36cm2. Find its height. (A) 2cm (B) 3cm (C) 4cm (D) 5cm (E) 6cm  Ans. B

1. A square of cardboard is taped at the perimeter by a piece of ribbon 20cm long. What is the area of the board?

(A) 20sq.cm (B) 25sq.cm (C) 36sq.cm (D) l00sq.cm (E) l6sq.cm  Ans. B

1. A triangle has angles 30, 15 and 135°, the side opposite to the angle 30 is length 6cm. The side opposite to the angle 135° is equal to Ans.  C

(A) 12cm (B) 6m (C) 6√2cm (D) l2√2cm (E) 6√3cm

1. An isosceles triangle of sides 13cm, 13cm, 10cm is inscribed in a circle. What is the radius of the circle?

(A) 71/24cm (B) 12cm (C) 8cm (D) 7cm (E)√69cm    Ans.  A

1. Differentiate (x21/x )2 with respect to x.                                                      Ans.  E

(A) 4x3– 2 – 2/x3(B)4x3– 2+2/x3 (C) 4x3– 3x – 2/x (D) 4x3– 4x – 2/x

(E) 4x3– +6 + 2/x3

1. Find the area of the curved surface of a cone whose base radius is 6cm and whose A, height is 8cm (Take = 22/7).

(A) 188.57cm2 (B) 1320cm2 (C) 188cm2 (D) 188.08cm2 (E) 100cm2   Ans.  A

1. Find the total surface area of a solid cone of radius 2√3cm and slanting side 4√3cm. (A) 8√cm3 (B) 24cm3 (C)15cm3 (D) 36cm3 (E) 30cm3 Ans. D

1. If the four interior angles of a quadrilateral are (p+l0), (p-30), (2p-45) 0 and (p+15)°, then p is (a) 125° (b) 82° (c) 135° (d) 105° (e) 60°    Ans.  B

1. If the hypotenuse of a right angled isosceles triangle is 2, what is the length of each of the other sides?

(A) 2     (B) 12    (C) 22   (D) 1     (E) 2 – 1    Ans.  A

1. lf the value ofis taken to be: 22/7, the area ofa semicircle ofdiameter 42m is(A) 5544m2 (B) 1386m2 (c) 132m2 (D) 264m2 (E) 693mAns. E

1. ln a circle of radius 10cm, a cord oflength 10cm is xcm from its centre where x is (A) 102 (B) 53 (c) 103 (u) 52 (E) 10                Ans. B

1. PQRS is a cyclic quadrilateral with PQ as diameter of the circle. lf PQS = 150°, find QRS.            (A) 75° (B) 37½° (C) 127½° (D) 105° (E) None of the above Ans. D

1. The difference between the length and width of a rectangle is 6cm and the area is 135cm2. What is the length? Ans. C

1. At what value ofx does the function y= -3 – 2x +x2 attain a minimum value? (A)   4 (B) 2       (C) -1 (D) -4 (E)  1                      Ans. E

1. Differentiate (x22

(A) 4x3 – 2 – 2/x3       (B) 4x3 – 2 + 2/x3 (C) 4x3 – 2 – 2/x (D) 4x3 – 4x – 2/x               (E) 4x3 – +6 + 2/x3 Ans. E

1. Evaluate x2 – 2x)dx

(4) 4      (B) 2  (C) ¾  (D)(E)     Ans.  C

1. Find the derivative ofy = sin (2x2 + 3x – 4).

(A)   – cos(2x3+ 3x – 4)    (B)   -(6x2 + 3)cos(2x3 + 3x – 4)       (C) cos(2x3 +

3x – 4) (D) (6x2 + 3x)cos(2x3 + 3x – 4)      (E) cos(2x3 + 3x – 4)    Ans.  D

1. lf= x + cos x,ﬁnd y.

(A) x2/2– sinx + c (B) x2– sinx + c (C) x2/2 + sinx + c  (D) x2+sinx+c                  (E) x2/4+sinx+c     Ans. C

1. lfthe maximum value of y = l+ hx – 3x2 is 13, ﬁnd h. Ans. B

(A) 13 (B) l2 (C)  11    (D) 10  (E) l4.

1. Ifs = (2+3t)(5t – 4),ﬁnd.when t = 4/5 sec

(A) 0 unit per sec. (B) I5 units per sec. (C) 22 units per sec. (D) 26 units per

sec. (E) 24 units per sec.   Ans. C

1. lfy = (1 – 2x)3, ﬁnd the value ofa x=-1

(A) -6   (B) 57 (C) -54             (D) 27 (E) -27  Ans. C

1. lfy = 3 cos 4x,equals

(A) 6sin8x(B) -24sin4x (C) l2sin4x (D) -12sin4x      (E) 24sin4x         Ans. D

1. Integrate with respect tox

(A) + k       (B)  + k     (C) (D) 27 (E) -2 Ans. E

1. Integrate with respect to X

X3

(A) X-X2   + K   (B) 4 – 3 + K                (C) 1 + 1 + K    (D) 1 – 1 + K    (E) 1 – 1 + K

X4                                       X4     X3                                   X      2X2                          3X2   2X                              X     2X2

Ans. E

1. The derivative of cosec x is B (a) tan x cosec x (b) –cot x cosec x (c) tan x sec (d) –cot x sec x (e) cot x cosec x Ans. B

1. The minimum value of in equation =x2 – 6x + 8

(A)    8            (B)       3 (C)                0          (D)       -1         (E)        5  Ans. D

1. The slope of the tangent to the curve = 22 – 2x + 5 at the point (1, 6) is

(A)       4          (B)       1         (C)       6         (D)       5         (E)       3   Ans. C

1. Two variables x andare such that = 4x – 3 an = 5 when x = 2. Find  terms of.

(A) 2x2 –3 x+5(B) 2x2 –  x+3(C)2x –3  x (D)     4    (E)               6 Ans. B

1. 7 pupils of average age 12 years leave a class of 25 pupils of average 11 years join the class, what is the average of the pupils now in the class?
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(A) 13 years (B) 12years 7½months (C)3 years 5 months (D) 13 years 10 months      (E) 11 years  Ans. A

1. A bag contains 4 white balls and 6 red balls. Two balls are taken from the bag without replacement. What is the probability that they are both red?

(A) 1/3       (B) 2/9   (C) 2/15  (D) 1/5     (E)3/5   Ans. E

1. Bola chooses at random a number between 1 and 300. What is the probability that the number is divisible by 4?

(A) 1/3      (B) 1/4   (C) 1/5     (D) 1/5     (E)1/300  Ans. B

1. Determine the mean monthly salary of 50 employees of a company from the following frequency distribution:
 Monthly salary Frequency N20,000.00 10 N32,500.00 5 N10,000.00 20 N12,000.00 2 N6,000.00 10 N8,000.00 3
• N21, 500.30 (B)       N13, 400.10 (C) N4, 300.10 (D) N8, 000.00 (E)

N 5,000.30.  Ans. B

1. Find the mean deviation of 1, 2, 3 and 4.

(A)   2.5      (B)       2.0       (C)      1.0       (D)       1.5       (E)        1.2 Ans. C

1. If M represents the median and D the mode of the measurements, 5,9,3,5,7,5,8, the (M, D) is

(A)   (6,5)        (B)       (5,8)     (C)      (5,7)     (D)       (5,5)     (E)        (7,5)   Ans. D

1. In a basket of fruits, there are 6 grapes, 11 bananas and 13 oranges. If one fruit is chosen at random, what is the probability that the fruit is either a grape or a banana? (A) 17/30 (B)     11/30           (C)       6/30       (D)       5/30            (E) 7/Ans. A

1. In a school, 220 students offer Biology or mathematics or both, 125 offer biology and 110 Mathematics. How many offer biology but not mathematics?

(A) 95         (B)       80        (C)      125      (D)       110      (E)        120  Ans. D

1. In a school, there are 35 students in Class 2A and 40 in class 2. The mean score for class 2 A in an English literature examination in 60.0 and tat for 2B in the same paper is 52.5. Find to one place of decimals, the mean for the combined classes

(A) 1.5 (B)       56.0     (C)      56.2     (D)       56.3     (E)        56.5  Ans. B

1. In a soccer competition in one season, a club had scored the following goals: 2, 0, 3, 3, 2, 1, 4, 0, 0, 5, 1, 0, 2, 2, 1, 3, 1, 4and 1. The mean, median and mode are respectively (A) 1, 1.8 and 1.5          (B)       1.8, 1.5 and 1  (C)            1.8,1 and 1.5 (D) 1.5, 1and 1.8   (E)    1.5, 1.8 and 1  Ans. B

1. In how many ways can 2 students be selection form a group of 5 students in a debating competition? (A) 25ways (B)   10ways  (C)          15ways            (D) 20ways      (E)       16ways  Ans. D

1. The arithmetic mean of the ages 30 pupils in a class is 15.3 years. One boy leaves the class and one girl is enrolled, and the new average age of 30 pupils I the class becomes 15.2years. How much older is the boy than the girl?

(A) 30 years            (B)   6 years     (C)   9 years   (D)   3 years   (E)   1 year  Ans. D

1. The letters of the word “MATRICULATION” are cut and put into a box. One letter is drawn at random form the box. Find the probability of drawing a vowel.

(A) 7/13(B)5/13(C) 6/13(D)8/13(E)4/13  Ans. C

1. The mean of the numbers 3, 6, 4, x and 7 is 5. Find the standard deviation.

(A) (B)(C)   2  (D)   3   (E)  5    Ans. A

1. The weights of 30 new-bon babies are given as follows: 6, 9, 5, 7, 6, 7, 5, 8, 9, 5, 7, 5, 8, 7, 8, 7,8, 6, 5, 7, 6, 9, 9, 7, 8, 8, 7, 8, 9, 8, the mode is.

(A)    6      (B)    5   (C)   8    (D)   7    (E)   10  Ans. D

1. Thirty boys and x girls sat for test. The mean of the boys were respectively 6 and 8. Find x if the total score was 468.

(A)    38     (B)    24   (C)   36    (D)   22    (E)   41  Ans. C

1. Two fair dice are rolled what is the probability that both show up the same number of points? (A) 1/36(B)7/36(C)1/2 (D)1/3(E)1/6 Ans. E

In summary, the above questions in Mathematics are what candidates should expect to prepare them adequately to build their confidence in the University of Ibandan (Post UTME Exams) and other post UTME exams in other universities as well as JAMB questions in Nigeria. You are enjoined to study them with all amounts of seriousness and determination to pass the exams since most questions are most often repeated yearly.