Mathematics 2018 JAMB Past Questions




Mathematics 2018 JAMB Past Questions

1.In a class of 40 students, 32 offer Mathematics, 24 offer Physics and 4 offer neither Mathematics nor Physics. How many offer both Mathematics and Physics?
  • A. 4
  • B. 8
  • C. 16
  • D. 20 
 Correct Answer: Option D

2.Find the values of x for which

- < 4
  • A. x < 8
  • B. x > -6
  • C. x < 4
  • D. x > -3 
 Correct Answer: Option B
3
Find \N\
  • A. 65
  • B. 23
  • C. 17
  • D. 91 
 Correct Answer: Option C

4. If X, Y can take values from the set (1, 2, 3 ,4), find the probability that the product of X and Y is not greater than 6
  • A.

  • B.
  • C.
  • D.

  • Correct Answer: Option C
    Explanation
    Each multiplication of elements gives 16 results out of which the ones that are not greater than 6 are asterisked (*) and they are 8 in numbers
      Pr(product of x and y NOT > 6 ) =
    =


    5
    The pie chart shows the monthly expenditure of a public servant. The monthly expenditure on housing is twice that of school fees. How much does the worker spend on housing if his monthly income is N7200?
    • A. 1000
    • B. 2000
    • C. 3000
    • D. 4000 

      6. Evaluate 5log x 2
      • A. 8
      • A.
    • B. 1
    • C.
    •  Correct Answer: Option B

       7. A trader realises 10x - x
       Naira profit from the sale of x bags of corn. How many bags will give him the maximum profit?
      • A. 7
      • B. 6
      • C. 5
      • D. 4
       Correct Answer: Option C
      Explanation
       Profit (P) = 102

        Maximum profit can be achieved when the differential of profit with respect to number of bags(x) is 0
        i.e.
      = 0
       
      = 10 - 2x = 0
        10 = 2x
        Then x =
      = 5
        Answer is C
      8. If y = 23
       101
       , find y, leaving your answer in base two
      • A. 1110
      • B. 10111
      • C. 11101
      • D. 111100
       Correct Answer: Option B
      9
      Find the value of x in the diagram
      • A. 10°
      • B. 28°
      • C. 36°
      • D. 40°
      Correct Answer: Option D
      Explanation
      The diagram shows angles at a point, the total angle at a point is 360
        x - 10 + 4x - 50 + 2x + 3x + 20 = 360
        10x - 40 = 360
        10x = 360 + 40
        10x = 400
        x =
        x = 40
      10. Solve for t in the equation t + (21 - t) = 11
      • A.
    • B.
    • C. 5
    • D. 9
     Correct Answer: Option D
    Explanation
    t + (21 - t) = 11
      Multiply through by the LCM of 4 and 3 which is 12
      12 x(t) + 12 x (
    (21 - t)) = (11 x 12)
      9t + 4(21 - t) = 132
      9t + 84 - 4t = 132
      5t + 84 = 132
      5t = 132 - 84 = 48
      t =
      t = 9
      Answer is D
      11. A school girl spends of her pocket money on books and
       on dress. What fraction remains?
      • A.
    • B.
    • C.
    • D.
    •  Correct Answer: Option C
      12. If + = 1. Make y the subject of the relation.
      • A.
    • B.
    • C.
    • D.
    • Correct Answer: Option A
      13. Calculate the total surface area of a cupboard which measures 12cm by 10cm by 8cm
      • A. 1920cm
    • B. 592cm
    • C. 296cm
    • D. 148cm
    •  Correct Answer: Option B
      Explanation
      Total surface area of a cupboard is given by the equation A = 2(lb + bh + lh) L = 12, b = 10, h = 8
        A = 2((12 x 10) + (10 x 8) + (12 x 8))
        A = 2(120 + 80 + 96)
        A = 2 x 296
        A = 592cm
        Answer is B
      14. Convert 0.04945 to two significant figures
      • A. 0.040
      • B. 0.049
      • C. 0.050
      • D. 0.49
      Correct Answer: Option C
      15. The probabilities that John and James pass an examination are 
      and
      respectively. Find the probability of both boys failing the examination.
       A.
    • B.
    • C.
    • D.
     Correct Answer: Option D
    Explanation
    Pr(both John and James passed)
      =
    x   =
      Pr(john and james failed)= 1- Pr(john and james passed)
      = 1 –
      =
      Answer is D
    16. An arc of a circle of radius 14cm subtends angle 300° at the centre. Find the perimeter of the sector formed by the arc (take π = )
    • A. 14.67cm
    • B. 42.67cm
    • C. 101.33cm
    • D. 513.33cm 
     Correct Answer: Option C
    17. Simplify
    • A. 25
    • A.


  • B. 1
  • C.

  • Correct Answer: Option B
    18
    Make T the subject of the relation.
    • A. T =


  • B. T =
  • C. T =R -
  • D. T =

  •  Correct Answer: Option C
    19.What is the place value of 9 in the number 3.0492?
    • A.


  • B.
  • C.
  • D.

  • Correct Answer: Option B
    20. If the simple interest on a sum of money invested at 3% per annum for 2
      years is N123, find the principal.
    • A. N676.50
    • B. N820
    • C. N1,640
    • D. N4,920 
     Correct Answer: Option C

     21. A machine valued at N20,000 depreciates by 10% every year. What will be the value of the machine at the end of two years?
    • A. N16,200
    • B. N14,200
    • C. N12,000
    • D. N8,000 
     Correct Answer: Option A
    Explanation
    Since it depreciates by 10% At the end of first year, its value = 90% of 20000
      = x 20000 =18000
      At the end of second year, its value = 90% of 18000
      = x 18000 = ₦16,200
      Answer is A
    22. The table shown gives the marks scored by a group of student in a test. Use the table to answer the question given.
    Mark 0 1 2 3 4 5
    Frequency 1 2 7 5 4 3

    What is the median mark?
    • A. 1
    • B. 2
    • C. 3
    • D.

    Correct Answer: Option C
    Explanation
    Total frequency = 1 + 2 + 7 + 5 + 4 + 3 = 22
      Median is the middle number
     = Nth2
      term = 22th2 = 11th term
      Going in ascending order, 11th term is 3, going in descending order 11th term is 3
      Median = 3 + 32 = 62 = 3
      Answer is C
    23. The table shown gives the marks scored by a group of student in a test. Use the table to answer the question given.
    Mark 0 1 2 3 4 5
    Frequency 1 2 7 5 4 3
    What is the probability of selecting a student from the group that scored 2 or 3
    • A.


  • B.
  • C.
  • D.

  •  Correct Answer: Option D
    24 A boy walks 800m in 20 minutes. Calculate his average speed in Km/H
    • A. 2.4
    • B. 4
    • C. 24 
    Correct Answer: Option A
    25.A car uses one litre of petrol for every 14km. If one litre of petrol cost N63.00, how far can the car go with N900.00 worth of petrol?
    • A. 420Km
    • B. 405Km
    • C. 210Km
    • D. 200Km 
     Correct Answer: Option D
    Explanation
    since 1litre cost ₦63
      So ₦900 is the cost of
    litres
      = 14.2857litres of petrol
    nbsp; The car uses 1 litre for 14km
      So 14.2857 litres will be used for (14.2857 x 14)
      = 200km
      Answer is D


    26
      In the diagram, GI is a tangent to the circle at H. If EF||GI, calculate the size of ∠EHF
      • A. 126°
      • B. 72°
      • C. 54°
      • D. 28°  
         Correct Answer: Option B
        27. How many times, correct to the nearest whole number, will a man run round a circular track of diameter 100m to cover a distance of 1000m?
      • A. 3
      • B. 4
      • C. 5
      • D. 6
      Correct Answer: Option B
      Explanation
      In terms of distance, a circle has a total distance or perimeter of 2π or π
        Where r is radius and D is the diameter
        So perimeter =
      x 100
        = 314.2857m
        To cover a distance of 1000m, he is going to round the circular track for
      = 3.18
        It means it is on the number 4 round after the third round he is going to cover up to 1000m
      28
      Use the cummulative frequency curve to answer the question. Estimate the median of the date represented on the graph
      • A. 35.5
      • B. 36.5
      • C. 37.5
      • D. 38.5
       Correct Answer: Option A
      29
      Use the cummulative frequency curve to answer the question. What is the 80th percentile?
      • A. 45.5
      • B. 46.5
      • C. 47.5
      • D. 48.5
      Correct Answer: Option C
      30.  
      • A. 8.8 x 10
    • B. 8.8 x 10
    • C. 8.8 x 10
    • D. 8.8 x 10
    31. Two sisters, Taiwo and Kehinde, own a store. The ratio of Taiwo's share to Kehinde's is 11:9. Later Kehinde sells
     of her share to Taiwo for N720.00. Find the value of the store
    • A. N1,080.00
    • B. N2,400.00
    • C. N3,000.00
    • D. N3,600.00 
     Correct Answer: Option B
    32. A room is 12m long, 9m wide and 8m high. Find the cosine of the angle which a diagonal of the room makes with the floor of the room 
    • A.


  • B.
  • C.
  • D.

  •  Correct Answer: Option A
    33. Divide the L.C.M of 48, 64 and 80 by their H.C.F
    • A. 20
    • B. 30
    • C. 48
    • D. 60 
     Correct Answer: Option D
    34. Find the equation of the line through (5,7) parallel to the line 7x + 5y = 12 
    • A. 5x + 7y = 20
    • B. 7x + 5y = 70
    • C. xy = 7
    • D. 15x + 17y = 90 
     Correct Answer: Option B
    35. A man's initial salary is N540.00 a month and increases after each period of six months by N36.00 a month. Find his salary in the eight month of the third year.
    • A. N828.00
    • B. N756.00
    • C. N720.00
    • D. N684.00 
     Correct Answer: Option C
    Explanation
    Since the salary increases by 36 after every 6 months
      Every 6 months that can be counted on the eight month of the third year is 5
      (i.e. 2 times in the first year, 2 times in the second year and once in the third year)
      His salary then = initial salary + increment
      = 540 + 5(36)
      = 540 + 180
      = ₦720.00
      It can also be solves using a sequence in form of an AP
      Answer is C

     36. A man stands on a tree 150cm high and sees a boat at an angle of depression of 74°. Find the distance of the boat from the base of the tree.
      • A. 52cm
      • B. 43cm
      • C. 40cm
      • D. 15cm 

      Correct Answer: Option B
      Explanation
      Tan 74 = 150/x
        x = 150/tan 74
        = 43.01cm
      37. Integrate the expression 6x- 2x + 1
    • A. 3x - 2x + x + c 
    • B. 2x- x+ x + c
    • C. 2x– 3x+ c
    • D. x+ x– x + c 
     Correct Answer: Option B
      38. In how many ways can the letters LEADER be arranged?
      • A. 72
      • B. 144
      • C. 360
      • D. 720 

      Correct Answer: Option C
      Explanation
      The word LEADER has 1L 2E 1A 1D and 1R making total of 6! =
        =
        = 360
      39.
      In the figure below, /MX/ = 8cm, /XN/ = 12cm, /NZ/ = 4cm and ∠ XMN = ∠ XZY. Calculate /YM/
      • A. 32cm
      • B. 24 cm
      • C. 16 cm
      • D. 12 cm 

      Correct Answer: Option C
      Explanation
      From the figure,
        ∠ XMN = ∠ XZY
        Angle X is common
        So, ∠ XNM = ∠ XYZ
        Then from the angle relationship
       
      = =   XM = 8, XZ = 12 + 4 = 16,
        XN = 12, XY = 8 + YM
       
      =   Cross multiply
        8(8 + YM) = 192
        64 + 8YM = 192
        8YM = 128
        YM =
        = 16cm
      40.  Express 495g as a percentage of 16.5kg
    • A. 3%
    • B. 3
    • C. 15%
    • D. 30% 

    Correct Answer: Option A
    Explanation
    The two numbers must be expressed in the same unit. To convert 495g to kg, it will be divided by 1000
      495g =
      = 0.495kg
      To express in percentage, 0.495 will be divided by 16.5 and then multiplied by 100
      % will be added to the answer
    x 100
      = 3%

    41. Evaluate (2√3 - 4) (2√3 + 4) 
    • A. -4
    • B. -2
    • C. 2
    • D.

    Correct Answer: Option A
    Explanation
    2√3 - 4) ( 2√3 + 4)
      = 12 + 8√3 - 8√3 – 16
      = 12 – 16
      = -4
      The two expressions in the bracket are conjugate of each other
    42. Find the equation of the tangent at the point (2, 0) to the curve y = x- 2x
    • A. y = 2x - 4
    • B. y = 2x + 4
    • C. y = 2x - 2
    • D. y = 2x + 2 

    Correct Answer: Option A
    Explanation
    The gradient to the curve is found by differentiating the curve equation with respect to x
      So 2x - 2
      The gradient of the curve is the same with that of the tangent.
      At point (2, 0) = 2(2) - 2
      = 4 – 2 = 2
      The equation of the tangent is given by (y - y1) (x – x1)
      At point (x1, y1) = (2, 0)
      y - 0 = 2(x - 2)
      y = 2x - 4
    43
    Use the quadratic equation curve to answer this questions
    What is the 80th percentile?
    • A. -5.3
    • B. 0.5
    • C. 3
    • D.
     Correct Answer: Option A
    44. Evaluate log 8 – log
    • A. -1 1
    • B. -1
    • C. 1
    • D.
     Correct Answer: Option D
    Explanation
    log2 8 – log3 19
      = log 2 23 – log3 91
      = log2 23 – log3 32
      Based on law of logarithm
      = 3 log2 2 – (-2 log3 3)
      But log2 2 = 1,
      log3 3 = 1
      So, = 3 + 2
      = 5

    45. Tanθ is positive and Sinθ is negative. In which quadrant does θ lies
    • A. Second only
    • B. Third only
    • C. Fourth only
    • D. First and third only
    Correct Answer: Option B
    Explanation
      First quadrant: Sin, Cos and Tan are all positive
      Second quadrant: Sin is positive, Cos is negative and Tan is negative
      Third quadrant: Tan is positive, Sin is negative and Cos is negative
      Fourth quadrant: Cos is positive, Sin is negative and Tan is negative
      The correct option is the third quadrant only where Tanθ is positive and Sinθ is negative


    Correct Answer: Option B
    Explanation
    The total number of students is ∑ f = 3 + 4 + 5 + 6 + 7 + 6 + 5 + 4
      = 40


    47
    The figure below is a Venn diagram showing the elements arranged within sets A,B,C,ε.
    Use the figure to answer this question
    What is n(A U B)1 ?
    • A. 2
    • B. 3
    • C. 4
    • D. 7
    Correct Answer: Option C
    Explanation
    A = (p, q, r, t, u, v)
      B = (r, s, t, u)
      A U B = Elements in both A and B = (p, q, r, s, t, u, v)
      (A U B)1 = elements in the universal set E but not in (A U B)= (w, x, y, z)
      n(A U B) 1 = number of the elements in (A U B)1 = 4







     48. What is the loci of a distance 4cm from a given point P?
    • A. A straight line of length 4cm
    • B. a circle of radius 4cm
    • C. perpendicular to point P at 4cm
    • D. a circle of diameter 4cm 
     Correct Answer: Option B
    49. Given that Sin (5
    − 28) = Cos(3 − 50), O < 90

    Find the value of x
    • A. 14


  • B. 21
  • C. 32
  • D. 39
  •  Correct Answer: Option B
    Explanation
    Sin(5x - 28) = Cos(3x - 50)………..i
      But Sinα = Cos(90 - α)
      So Sin(5x - 28) = Cos(90 - [5x - 28])
      Sin(5x - 28) = Cos(90 - 5x + 28)
      Sin(5x - 28) = Cos(118 - 5x)………ii
      Combining i and ii
      Cos(3x - 50) = Cos(118 - 5x)
      3x - 50 = 118 - 5x
      Collecting the like terms
      3x + 5x = 118 + 50
      8x = 168
      x =
      x = 21
      Answer is B

    50. Find the average of the first four prime numbers greater than 10
    • A. 20
    • B. 19
    • C. 17
    • D. 15 
    Correct Answer: Option D
    Explanation
    Prime numbers are numbers that has only two factors (i.e 1 and itself). They are numbers that are only divisible by 1 and their selves. First four Prime numbers greater than 10 are 11, 13, 17 and 19
      Average = sum of numbers / number
      =
      =
      = 15

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