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Mathematics past questions: JAMB UTME 2021

40 objective questions, with answers. Free to read and practise.

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40 questions, one at a time, marked as you go or at the end. No account needed.

  1. 1.
    4, 16, 30, 20, 10, 14 and 26 are represented on a pie chart. Find the sum of the angles of the bisectors representing all numbers equals to or greater than 16
    1. A.48 °
    2. B.84 °
    3. C.92 °
    4. D.276 °
    Show answer

    Answer: D 276 °

  2. 2.
    A car travels from calabar to Enugu, a distance of P km with an average speed of U km per hour and continues to benin, a distance of Q km, with an average speed of Wkm per hour. Find its average speed from Calabar to Benin
    1. A.\(\frac{(p + q)}{pw + qu}\)
    2. B.\(\frac{uw(p + q)}{pw + qu}\)
    3. C.\(\frac{uw(p + q)}{pw}\)
    4. D.\(\frac{uw}{pw + qu}\)
    Show answer

    Answer: B \(\frac{uw(p + q)}{pw + qu}\)

  3. 3.
    A cylinder pipe, made of metal is 3cm thick.If the internal radius of the pipe is 10cm.Find the volume of metal used in making 3m of the pipe.
    1. A.153 \(\pi\) cm ^{3}
    2. B.207 \(\pi\) cm ^{3}
    3. C.15 300 \(\pi\) cm ^{3}
    4. D.20 700 \(\pi\) cm ^{3}
    Show answer

    Answer: D 20 700 \(\pi\) cm ^{3}

  4. 4.
    A group of market women sell at least one of yam, plantain and maize. 12 of them sell maize, 10 sell yam and 14 sell plantain. 5 sell plantain and maize, 4 sell yam and maize, 2 sell yam and plantain only while 3 sell all the three items. How many women are in the group?
    1. A.25
    2. B.19
    3. C.18
    4. D.17
    Show answer

    Answer: A 25

  5. 5.
    A trapezium has two parallel sides of lengths 5cm and 9cm. If the area is 91cm \(^2\) , find the distance between the parallel sides
    Diagram for this question
    1. A.13 cm
    2. B.4 cm
    3. C.6 cm
    4. D.7 cm
    Show answer

    Answer: A 13 cm

  6. 6.
    At what rate would a sum of N100.00 deposited for 5 years raise an interest of N7.50?
    1. A.\(\frac{1}{2}\) %
    2. B.2 \(\frac{1}{2}\) %
    3. C.1.5%
    4. D.25%
    Show answer

    Answer: C 1.5%

  7. 7.
    Correct 241.34(3 x 10 \(^{-3}\) ) \(^2\) to 4 significant figures
    1. A.0.0014
    2. B.0.001448
    3. C.0.0022
    4. D.0.002172
    Show answer

    Answer: D 0.002172

  8. 8.
    determine the maximum value of y=3x \(^2\) + 5x - 3
    1. A.6
    2. B.0
    3. C.2
    4. D.No correct option
    Show answer

    Answer: D No correct option

  9. 9.
    Each of the interior angles of a regular polygon is 140°. How many sides has the polygon?
    1. A.9
    2. B.8
    3. C.7
    4. D.5
    Show answer

    Answer: A 9

  10. 10.
    Factorize completely 81a \(^4\) - 16b \(^4\)
    1. A.(3a + 2b)(2a - 3b\()(9a ^{2} + 4b ^{2} )\)
    2. B.(3a - 2b)(2a - 3b\()(4a ^{2} - 9b ^{2} )\)
    3. C.(3a - 2b)(3a + 2b\()(9a ^{2} + 4b ^{2} )\)
    4. D.(6a - 2b)(8a - 3b\()(4a ^{3} - 9b ^{2} )\)
    Show answer

    Answer: C (3a - 2b)(3a + 2b\()(9a ^{2} + 4b ^{2} )\)

  11. 11.
    factorize m \(^3\) - m \(^2\) + 2m - 2
    1. A.\((m ^{2} + 1)(m - 2)\)
    2. B.(m - 1)(m + 1)(m + 2)
    3. C.(m - 2)(m + 1)(m - 1)
    4. D.\((m ^{2} + 2)(m - 1)\)
    Show answer

    Answer: D \((m ^{2} + 2)(m - 1)\)

  12. 12.
    Find the derivative of the function y = 2x \(^2\) (2x - 1) at the point x = -1?
    1. A.18
    2. B.16
    3. C.-4
    4. D.-6
    Show answer

    Answer: B 16

  13. 13.
    Find the length of a side of a rhombus whose diagonals are 6cm and 8cm
    1. A.8cm
    2. B.5cm
    3. C.4cm
    4. D.3cm
    Show answer

    Answer: B 5cm

  14. 14.
    Find the mean deviation of 1, 2, 3 and 4
    1. A.1.0
    2. B.1.5
    3. C.2.0
    4. D.2.5
    Show answer

    Answer: A 1.0

  15. 15.
    Find the probability that a number selected at random from 41 to 56 is a multiple of 9
    1. A.\(\frac{1}{8}\)
    2. B.\(\frac{2}{15}\)
    3. C.\(\frac{3}{16}\)
    4. D.\(\frac{7}{8}\)
    Show answer

    Answer: A \(\frac{1}{8}\)

  16. 16.
    find the value of p if the line which passes through (-1, -p) and (-2,2) is parallel to the line 2y+8x-17=0?
    1. A.\(\frac{-2}{7}\)
    2. B.\(\frac{7}{6}\)
    3. C.\(\frac{-6}{7}\)
    4. D.2
    Show answer

    Answer: D 2

  17. 17.
    Find x if log \(_9\) x = 1.5
    1. A.27
    2. B.15
    3. C.3.5
    4. D.32
    Show answer

    Answer: A 27

  18. 18.
    If (x + 2) and (x - 1) are factors of the expression \(Lx + 2kx^{2} + 24\) , find the values of L and k.
    1. A.l = -12, k = -6
    2. B.l = -2 , k = 1
    3. C.l = -2 , k = -1
    4. D.l = 0, k = 1
    Show answer

    Answer: B l = -2 , k = 1

  19. 19.
    If g(x) = x \(^2\) + 3x find g(x + 1) - g(x)
    1. A.(x + 2)
    2. B.2(x + 2)
    3. C.(2x + 1)
    4. D.\((x ^{2} + 4)\)
    Show answer

    Answer: B 2(x + 2)

  20. 20.
    If the binary operation \(\ast\) is defined by m \(\ast\) n = mn + m + n for any real number m and n, find the identity of the elements under this operation
    1. A.e = 1
    2. B.e = -1
    3. C.e = -2
    4. D.e = 0
    Show answer

    Answer: D e = 0

  21. 21.
    If w varies inversely as \(\frac{uv}{u + v}\) and w = 8 when u = 2 and v = 6, find a relationship between u, v, w.
    1. A.uvw = 16(u + v)
    2. B.16uv = 3w(u + v)
    3. C.uvw = 12(u + v)
    4. D.12uvw = u + v
    Show answer

    Answer: C uvw = 12(u + v)

  22. 22.
    In how many ways can 2 students be selected from a group of 5 students in a debating competition?
    1. A.25 ways
    2. B.10 ways
    3. C.15 ways
    4. D.20 ways
    Show answer

    Answer: B 10 ways

  23. 23.
    List all integers satisfying the inequality in -2 < 2x-6 < 4
    1. A.2,3,4 and 5
    2. B.2,3
    3. C.2,5
    4. D.3,4
    Show answer

    Answer: D 3,4

  24. 24.
    Musa borrows N10.00 at 2% per month simple interest and repays N8.00 after 4 months. How much does he still owe?
    1. A.N10.80
    2. B.N10.67
    3. C.N2.80
    4. D.N2.67
    Show answer

    Answer: C N2.80

  25. 25.
    P(-6, 1) and Q(6, 6) are the two ends of the diameter of a given circle. Calculate the radius.
    1. A.6.5 units
    2. B.13.0 units
    3. C.3.5 units
    4. D.7.0 units
    Show answer

    Answer: A 6.5 units

  26. 26.
    Simplify \(\sqrt{27}\) + \(\frac{3}{\sqrt{3}}\)
    1. A.4 \(\sqrt{3}\)
    2. B.\(\frac{4}{\sqrt{3}}\)
    3. C.3 \(\sqrt{3}\)
    4. D.\(\frac{\sqrt{3}}{4}\)
    Show answer

    Answer: A 4 \(\sqrt{3}\)

  27. 27.
    Simplify 2log \(\frac{2}{5}\) - log \(\frac{72}{125}\) + log 9
    1. A.1 - 4 log3
    2. B.-1 + 2 log 3
    3. C.-1 + 5 log2
    4. D.1 - 2log 2
    Show answer

    Answer: D 1 - 2log 2

  28. 28.
    Simplify and express in standard form \(\frac{0.00275 \times 0.00640}{0.025 \times 0.08}\)
    1. A.\(8.8 x 10 ^{-1}\)
    2. B.\(8.8 x 10 ^{-2}\)
    3. C.\(8.8 x 10 ^{-3}\)
    4. D.\(8.8 x 10 ^{3}\)
    Show answer

    Answer: A \(8.8 x 10 ^{-1}\)

  29. 29.
    Solve the following equation: \(\frac{2}{(2r - 1)}\) - \(\frac{5}{3}\) = \(\frac{1}{(r + 2)}\)
    1. A.( -1, \(\frac{5}{2}\) )
    2. B.( 1, - \(\frac{5}{2}\) )
    3. C.( \(\frac{5}{2}\) , 1 )
    4. D.(2,1)
    Show answer

    Answer: B ( 1, - \(\frac{5}{2}\) )

  30. 30.
    The angle of a sector of a circle, radius 10.5cm, is 48°, Calculate the perimeter of the sector
    1. A.8.8cm
    2. B.25.4cm
    3. C.25.6cm
    4. D.29.8cm
    Show answer

    Answer: D 29.8cm

  31. 31.
    The angles of a quadrilateral are 5x-30, 4x+60, 60-x and 3x+61.find the smallest of these angles
    1. A.5x - 30
    2. B.4x + 60
    3. C.60 - x
    4. D.3x + 61
    Show answer

    Answer: C 60 - x

  32. 32.
    The locus of a point which moves so that it is equidistant from two intersecting straight lines is the?
    1. A.perpendicular bisector of the two lines
    2. B.angle bisector of the two lines
    3. C.bisector of the two lines
    4. D.line parallel to the two lines
    Show answer

    Answer: C bisector of the two lines

  33. 33.
    The mean of ten positive numbers is 16. When another number is added, the mean becomes 18. Find the eleventh number
    1. A.3
    2. B.16
    3. C.38
    4. D.30
    Show answer

    Answer: C 38

  34. 34.
    The ratio of the length of two similar rectangular blocks is 2 : 3. If the volume of the larger block is 351cm \(^3\) , then the volume of the other block is?
    1. A.234.00 c\(m ^{3}\)
    2. B.526.50 c\(m ^{3}\)
    3. C.166.00 c\(m ^{3}\)
    4. D.687c\(m ^{3}\)
    Show answer

    Answer: A 234.00 c\(m ^{3}\)

  35. 35.
    Three brothers in a business deal share the profit at the end of a contract. The first received \(\frac{1}{3}\) of the profit and the second \(\frac{2}{3}\) of the remainder. If the third received the remaining N12000.00 how much profit did they share?
    1. A.N60 000.00
    2. B.N54 000.00
    3. C.N48 000.00
    4. D.N42 000.00
    Show answer

    Answer: B N54 000.00

  36. 36.
    Three children shared a basket of mangoes in such a way that the first child took \(\frac{1}{4}\) of the mangoes and the second \(\frac{3}{4}\) of the remainder. What fraction of the mangoes did the third child take?
    1. A.\(\frac{3}{16}\)
    2. B.\(\frac{7}{16}\)
    3. C.\(\frac{9}{16}\)
    4. D.\(\frac{13}{16}\)
    Show answer

    Answer: A \(\frac{3}{16}\)

  37. 37.
    Two numbers are removed at random from the numbers 1, 2, 3 and 4. What is the probability that the sum of the numbers removed is even?
    1. A.\(\frac{2}{3}\)
    2. B.\(\frac{1}{2}\)
    3. C.\(\frac{1}{3}\)
    4. D.\(\frac{1}{4}\)
    Show answer

    Answer: D \(\frac{1}{4}\)

  38. 38.
    What is the n-th term of the sequence 2, 6, 12, 20...?
    1. A.4n - 2
    2. B.\(2(3 ^{n - 1} )\)
    3. C.\(n ^{2} + n\)
    4. D.\(n ^{2} + 3\)n + 2
    Show answer

    Answer: C \(n ^{2} + n\)

  39. 39.
    What is the rate of change of the volume V of a hemisphere with respect to its radius r when r = 2?
    1. A.8π
    2. B.16π
    3. C.2π
    4. D.4π
    Show answer

    Answer: A 8π

  40. 40.
    X is due east point of y on a coast. Z is another point on the coast but 6.0km due south of Y. If the distance ZX is 12km, calculate the bearing of Z from X
    1. A.240°
    2. B.150°
    3. C.60°
    4. D.270°
    Show answer

    Answer: A 240°

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