JAMB - Mathematics (1987)

• 1

  Convert 241 in base 5 to base 8,

  Хариулт

  (B)

  107₈
• 2

  Find the least length of a rod which can be cut into exactly equal strips, each of either 40cm or 48cm in length

  Хариулт

  (B)

  240cm
• 3

  A rectangular lawn has an area of 1815 square yards. if its length is 50 meters, find its width in meters given that 1 metre equals 1.1 yards

  Хариулт

  (D)

  30.00
• 4

  Reduce each number to two significant figures and then evaluate \(\frac{0.021741 \times 1.2047}{0.023789}\)

  Хариулт

  (C)

  1.1
• 5

  A train moves from P to Q at an average speed of 90km/h and immediately returns from Q to P through the same route at an average speed of 45km/h. Find the average speed for the entire journey

  Хариулт

  (C)

  67.50km\h
• 6

  If the length of a square is increased by 20% while while its width is decreased by 20% to form a rectangle, what is the ratio of the area of the rectangle to the area of the square?

  Хариулт

  (D)

  24 : 25
• 7

  Two brothers invested a total of N5,000.00 on a farm project, the farm yield was sold for N 15,000.00 at the end of the season. If the profit was shared in the ratio 2 : 3, what is the difference in the amount to profit received by the brothers?

  Хариулт

  (A)

  N2,000.00
• 8

  A man invests a sum of money at 4% per annum simple invest. After 3 years, the principal amounts to N7,000.00. Find the sum invested

  Хариулт

  (B)

  N6,250.00
• 9

  By selling 20 oranges for N1.35 a trader makes a profit of 8%. What is his percentage gain or loss if he sells the same 20 oranges for N1.10?

  Хариулт

  (C)

  12%
• 10

  Four boys and ten girls can cut a field in 5 hours if the boys work at \(\frac{5}{4}\) the rate at which the girls work. How many boys will be needed to cut the field in 3 hours?

  Хариулт

  (D)

  20
• 11

  Evaluate without using tables (0.008) -\(\frac{1}{3}\) x (0.16) - \(\frac{3}{2}\)

  Хариулт

  (A)

  \(\frac{625}{8}\)
• 12

  Simplify without using tables \(\frac{Log_26 - Log_23}{Log_28 - 2Log_2\frac{1}{2}}\)

  Хариулт

  (A)

  \(\frac{1}{5}\)
• 13

  Simplify without using tables \(\frac{2\sqrt{14} \times 3\sqrt{21}}{7\sqrt{24} \times 2\sqrt{98}}\)

  Хариулт

  (D)

  \(\frac{3\sqrt{2}}{28}\)
• 14

  If P = \(\frac{\frac{2}{3}({1 - r^2})}{n^2}\), find n when r = \(\sqrt{\frac{1}{3}}\) and p = 1

  Хариулт

  (D)

  \(\frac{2}{3}\)
• 15

  If a = u\(^2\) - 3v\(^2\) and b = 2uv + v\(^2\) evaluate (2a - b)(a - b\(^2\)), when u = 1 and v = -1

  Хариулт

  (A)

  9
• 16

  The formula Q = 1.5 + 0.5n gives the cost Q(in Naira)of feeding n people for a week. Find (in kobo) the extra cost of feeding one additional person

  Хариулт

  (D)

  50k
• 17

  If P varies inversely as V and V varies directly as R², find the relationship between P and R given that R = 7 when P = 2

  Хариулт

  (B)

  PR² = 98
• 18

  Make y the subject of the formula Z = x\(^2\) + \(\frac{1}{y^3}\)

  Хариулт

  (C)

  y = \(\frac{1}{(Z - x^2)^{\frac{1}{3}}}\)
• 19

  Find the values of m which make the following quadratic function a perfect square. x² + 2(m + 1)x + m + 3

  Хариулт

  (C)

  1, -2
• 20

  Factorize 6^{2x + 1} + 7(6^x) - 5

  Хариулт

  (B)

  [3(6^x) + 5][2(6^x) - 1]
• 21

  Find the values of y which satisfy the simultaneous equations x + y = 5, x2 - 2y2 = 1

  Хариулт

  (C)

  -12, +2
• 22

  An (n - 2)² sided figure has n diagonals. Find the number n diagonals for 25-sided figure

  Хариулт

  (A)

  7
• 23

  Solve the inequality x - 1 > 4(x + 2)

  Хариулт

  (B)

  x < -3
• 24

  Simplify \(\frac{x^2 - y^2}{2x^2 + xy - y^2}\)

  Хариулт

  (C)

  \(\frac{x - y}{2x - y}\)
• 25

  The minimum value of y in the equation y = x\(^2\) - 6x + 8 is

  Хариулт

  (D)

  -1
• 26

  Find the eleventh term of the progression 4, 8, 16.....

  Хариулт

  (B)

  2¹²
• 27

  Three angles of a nonagon are equal and the sum of six other angles is 1110o. Calculate the size of one of the equal angles

  Хариулт

  (D)

  50^o
• 28

  Two chords QR and NP of a circle intersect inside the circle at x. If RQP = 37o, RQN = 49o and QPN = 35o, find PRQ

  Хариулт

  (D)

  59^o
• 29

  The sine, cosine and tangent of 210o are respectively

  Хариулт

  (D)

  \(\frac{-1}{2}\), \(\frac{\sqrt{-3}}{2}\), \(\frac{\sqrt{3}}{3}\)
• 30

  If tan \(\theta\) = \(\frac{m^2 - n^2}{2mn}\) find sec\(\theta\)

  Хариулт

  (B)

  \(\frac{m^2 + n^2}{2mn}\)
• 31

  From two points x and y, 8m apart, and in line with a pole, the angles of elevation of the top of the pole are 30ºand 60º respectively. Find the height of the pole assuming that x, y, and the foot of the pole are on the same horizontal plane and x and y are on the same side of the pole.

  Хариулт

  (B)

  4\(\sqrt{3}\)
• 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

  Хариулт

  (A)

  \(\frac{5}{17}\)
• 33

  What is the circumference of latitude 0°S if R is the radius of the earth?

  Хариулт

  (B)

  2\(\pi\) R cos \(\theta\)
• 34

  The base of a pyramid is a square of side 8cm. If its vertex is directly above the centre, find the height, given that the edge is 4\(\sqrt3\)cm

  Хариулт

  (C)

  4cm
• 35

  What is the locus of the mid-points of all chords of length 6cm within a circle of radius 5cm and with centre 0

  Хариулт

  (B)

  The perpendicular bisector of the chords
• 36

  Taking the period of day light on a certain day to be from 5.30a.m to 7.00p.m. Calculate the angle of a pie chart designed to show the periods of the day light and of darkness on that day

  Хариулт

  (D)

  202^o30' 157^o 30'
• 37

  The goals scored by 40 football teams from three league divisions are recorded below
  \(\begin{array}{c|c} \text{Number of goals} & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline frequency & 4 & 3 & 15 & 16 & 1 & 0 & 1\end{array}\)
  What is the total number of goals scored by all the terms?

  Хариулт

  (C)

  91
• 38

  The numbers 3, 2, 8, 5, 7, 12, 9 and 14 are the marks scored by a group of students in a class test. If P is scored by an group of students in a class test. If P is the mean and Q the median, the P + Q is

  Хариулт

  (D)

  15
• 39

  Below are the scores of group of students in a music test
  \(\begin{array}{c|c}scores & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline \text{No, of students} & 3 & 6 & 10 & 8 & 6 & 5 & 2 & 4 & 12\end{array}\)
  If CF(x) is the number of students with scores less than or equal to x, find CF(6)

  Хариулт

  (B)

  38
• 40

  Find the probability of selecting a figure which is a parallelogram from a square, a rectangle, a rhombus, a kite and a trapezium

  Хариулт

  (A)

  \(\frac{3}{5}\)
• 41

  

  An (\(n - 2)^2\) sided figure has n diagonals. Find the number n diagonals for a 25-sided figure

  Хариулт

  (A)

  7
• 42

  

  In the diagram, POQ is a diameter, 0 is the centre of the circle and TP is a tangent. Find the value of x

  Хариулт

  (A)

  30^o
• 43

  

  In the diagram above, QR // TS, QR : TS = 2.3, Find the ratio of the area of triangle PQR to the area of the trapezium QRST.

  Хариулт

  (B)

  4:5
• 44

  

  Three angles of a nonagon are equal and the sum of six other angles is 1110^o. Calculate the size of one of the equal angles.

  Хариулт

  (D)

  50^o
• 45

  

  In the figure, find the value of x

  Хариулт

  (C)

  90^o