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Mathematics
1 9 83 - 2 0 0 4
JAMB
Questions And Answers
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Mathematics 1983
1. If M represents the median and D the mode of the 10. If x + 2 and x – 1 are factors of the expressions lx +
measurements 5, 9, 3, 5, 8 then (M,D) is 2kx2 + 24, find the values of l and k
A. (6,5) B. (5,8) C. (5,7) A. l = -6, k = -9 B. l = -2, k = 1 C. l = -2, k = -1
D. (5,5) E. (7,5) D. l = 0, k = 1 E. l = 6, k = 0
2. A construction company is owned by two partners X 11. Make T the subject of the equation
and Y and it is agreed that their profit will be divided in av = 3 2V + T
the ratio 4:5. at the end of the year. Y received #5,000 1- V a 2T
more than x. what is the total profit of the company for
the year? A. 3av/(1-v) B. 2v(1-v)2 - a2v2/2a2v2 - (1-V)2
A. #20,000.00 B. P’0#25,000.00 C. #30,000.00 C. 2v(1 - v) + a v / 2a2v2 + (1 - v)2
2 3 2
D. #15,000.003 E.#45,000.00 D. 2v(1 - v)2 - a4v3/2a3v3 - (1 - v)3
E. 2v(1-v)3 - a4v3/2a3v3 + (1-v)3
3. Given a regular hexagon, calculate each interior angle
of the hexagon. 12.
A. 600 B. 300 C. 1200 Additional
Mathematics
0 0
D. 45 E. 135 (2x-24)O Biology
(3 x-18)O
O
x
Geography
4. Solve the following equations (2 x+12)O
4x – 3 = 3x + y = 2y + 5x – 12 (x+12)O
French
History
A. 4x = 5, y = 2 B. x = 2, y = 5 C. x = -2, y = -5
D. x = 5, y = -2 E. x = -5, y = -2
In a class of 60 pupils, the statistical distribution of the
5. If x = 1 is root of the equation number of pupils offering Biology, History, French,
x3 – 2x2 – 5x + 6, find the other roots Geography and Additional Mathematics is as shown in
A. -3 and 2 B. –2 and 2 C. 3 and –2 the pie chart above. How many pupils offer Additional
D. 1 and 3 E. –3 and 1 Mathematics?
A. 15 B. 10 C. 18
6. If x is jointly proportional to the cube of y and the D. 12 E. 28
fourth power of z. In what ratio is x increased or
decreased when y is halved and z is doubled? 13 The value of (0.303)3 – (0.02)3 is
A. 4:1 increase B. 2:1 increase C. 1:4 decrease A. 0.019 B. 0.0019 C. 0.00019
D. 1: 1 no change E. 3: 4 decrease D. 0.000019 E. 0.000035
7. P Q 14. y varies partly as the square of x and y partly as the
O
O
60 inverse of the square root of x. write down the
45 expression for y if y = 2 when x = 1 and y = 6 when x =
8 cm 4
A. y = 10x2 + 52 B. y = x2 + 1
S R 31 31√x √x
C. y = x2 + 1 D. y = x2 + 1 E. y = 10 (x2 + 1 )
In the above figure PQR = 600, QPR = 900, PRS = 900, x 31 31√ x 31( √x)
RPS = 450, QR= 8cm. Determine PS 15. Simplify (x – 7) / (x2 – 9) ( x2 – 3x)/( x2 - 49)
A. 2√3cm B. 4√6cm C. 2√6cm A. x/ (x - 3)(x + 7) B. (x + 3) (x + 7)/x C. x/(x - 3) (x -
D. 8√6cm E. 8cm 7)
D. x/(x + 3) (x + 7) E. x/(x + 4) (x + 7)
8. Given that cos z = L, where z is an acute angle find an
expression for Co +Z - cosecz 16. The lengths of the sides of a right-angled triangle at (3x
sec Z + tan z + 1)cm, (3x - 1)cm and x cm.
A. l - L B. L2-√1−L2 C. -L-√1−L A. 2 B. 6 C. 18
1+L L2+L-1 (C1+L) +√1−L2 D. 12 E. 0
D. √L−1. E. L-(L2-1) 17. The scores of a set of a final year students in the first
(L1+L2) +√1−L2 1+ √1 - L2+ √1 - L2 semester examination in a paper are
41,29,55,21,47,70,70,40,43,56,73,23,50,50. find the median
9. If 0.0000152 x 0.00042 = A x 108, where of the scores.
1 £ A < 10, find A and B. A. 47 B. 481/2 C. 50
A. A = 9, B = 6`.38 B. A = 6.38, B = -9 C. A = 6.38, B = 9 D. 48 E. 49
D. A = 6.38, B = -1 E. A = 6.38, B = 1
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y
18. 12 A. –28, 7 B. 6, -28 C. 6, -1
9 D. –1, 7 E. 3, 2
6
3 25. Find the missing value in the following table.
-3 -2 -1 3 2 1
-3
-6
x -2 -1 0 1 2 3
O
3
-9 y=x -x+3 3 3 3 9 27
-12
-15
A. -3 B. 3 C. –9
D. 13 E. 9
x
Which of the following equations represents the above 26.
graph?
A. y = 1 + 2x + 3x2 B. y = 1 – 2x + 3x2 C. y = 1 + 2x 3x2
D. y = 1 – 2x – 3x2 E. y = 3x2 + 2x - 1 O
O
x
H
G
19. x
130O
If O is the centre of the circle in the figure above. Find
the value of x
O
A. 50 B. 260 C. 100
30 D. 65 E. 130
K F
27. Find the angle of the sectors representing each item in
The above figure FGHK is a rhombus. What is the value a pie chart of the following data. 6,10,14,16,26
of the angle x? A. 150, 250,350,400,650, B. 600, 1000,1400,1600,2600
A. 900 B. 300 C. 1500 0 0, 0, 0,
C. 6 , 10 14 16 26 0,
D. 300, 500,700,800,1300
0 0
D. 120S E. 60 E. None of the above
0-8 m
20. P 28. The scores of 16 students in a Mathematics test are
0
65,65,55,60,60,65,60,70,75,70,65,70,60,65,65,70
R What is the sum of the median and modal scores?
2m
A. 125 B. 130 C. 140
Q D. 150 E. 137.5
30O
29. The letters of the word MATRICULATION are cut and
PQRS is a desk of dimensions 2m x 0.8m which is inclined put into a box. One of the letter is drawn at random from
at 300 to the horizontal. Find the inclination of the the box. Find the probability of drawing a vowel.
diagonal PR to the horizontal.
A. 23035’ B. 300 C. 15036’ A. 2/13 B. 5/13 C. 6/13
0 0
D. 10 E. 10 42’ D. 8/13 E. 4/13
21. Find x if (x base 4)2 = 100 1000base 2 30. Correct each of the number 59.81789 and 0.0746829 to
A. 6 B. 12 C. 100 three significant figures and multiply them, giving your
D. 210 E. 110 answer to three significant figures.
A. 4.46 B. 4.48 C. 4.47
22. Simplify log10a1/2 + 1/4log10a – 1/12log10a7 D. 4.49 E. 4.50
A. 1 B. 7/6log10a C. 0
D. 10 E. a 31. If a rod of length 250cm is measured as 255cm longer in
error, what is the percentage error in measurement?
23. If w varies inversely as V and u varies directly as w3, A. 55 B. 10 C. 5
find the relationship between u and V given that u = 1, D. 4 E. 2
when V = 2
A. u = 8V3 B. u = 2 V C. V = 8/u2 32. If (2/3)m (3/4)n = 256/729, find thevalues of m and n
2 3
D. V = 8u E. U = 8/v A. m = 4, n = 2 B. m = -4, n = -2 C. m = -4, n = 2
D. m = 4, n = -2 E. m = -2, n = 4
24. Solve the simultaneous equations for x
x2 + y – 8 = 0 33. Without using tables find the numerical value of log749
y + 5x – 2 = 0 + log7(1/7)
A. 1 B. 2 C. 3
D. 7 E. 0
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34. Factorize completely 81a – 16b4
4
A. (3a + 2b) (2a – 3b) (9a2 + 4b2) 41. In the figure below find PRQ
B. (3a - 2b) (2a – 3b) (4a2 - 9b2)
C. (3a - 2b) (3a – 2b) (9a2 + 4b2)
D. (3a - 2b) (2a – 3b) (9a2 + 4b2)
E. (3a - 2b) (2a – 3b) (9a2 - 4b2) 235
o
R
35. One interior angle of a convex hexagon is 1700 and
each of the remaining interior angles is equal to x0. find
x Q
P
A. 1200 B. 1100 C. 1050
0 0
D. 102 E. 100 A. 661/20 B. 621/20 C. 1250
D. 1050 E. 650
36. PQRS is a cyclic quadrilateral in which PQ = PS. PT is a
tangent to the circle and PQ makes and angle 500 with
the tangent as shown in the figure below. What is the 42. Simplify 27a9/8
size of QRS? A. 9a2/2 B. 9a3/2 C. 2/3a2
R
D. 2/3a2 E. 3a3/2
43. Okro
14.5
Beans kg
S Q 14.5 kg Rice
45.4
O Yams kg
50
T 184.5 kg
P
0 0
A. 50 B. 40 C. 1100
D. 800 E. 1000
The farm yields of four crops on a piece of land in
37. A ship H leaves a port P and sails 30km due South. Ondo are represented on the pie chart above. What is
Then it sails 60km due west. What is the bearing of H the angle of the sector occupied by Okro in the chart?
from P? A. 911/20 B. 191/30 C. 331/30
A. 26034’ B. 243026’ C. 116034’ D. 110
E. 910
0 0
D. 63 26’ E. 240
O
44. (x+3y)
38. In a sample survey of a university community the O
following table shows the percentage distribution of P 45
Q O R
the number of members per household. y
No of members (3x+y)O
per household 1 2 3 4 5 6 7 8 Total
Number of
households 3 12 15 28 21 10 7 4 100
In the figure above, PQR is a straight line. Find the
A. 4 B. 3 C. 5 values of x and y
D. 4.5 E. None A. x = 22.50 and y = 33.750
B. x = 150 and y = 52.50
39. On a square paper of length 2.524375cm is inscribed a C. x = 22.50 and y = 45.00
square diagram of length 0.524375. find the area of the D. x = 56.250 and y = 11.50
paper no covered by the diagram correct to 3 significant E. x = 18.0 and y = 56.50
figures.
45. PQR is the diameter of a semicircle RSP with centre at
A. 6.00cm2 B. 6.10cm2 C. 6.cm2
2 2 Q and radius of length 3.5cmc. if QPT = QRT = 600. Find
D. 6.09cm E. 4.00cm
the perimeter of the figure (PTRS p = 22/7)
S
40. If f(X) = 1 + x - 1 find f(1-x)
x-1 x2-1
P
A. 1/x + 1/(x+2) B. x +1/(2x -1) O R
60 O 60
O
C. -1/x - 1/(x-2) D. -1/x + 1/(x2-1)
T
A. 25cm B. 18ccm C. 36cm
D. 29cm E. 25 5 cm
Mathematics
1 9 83 - 2 0 0 4
JAMB
Questions And Answers
, Uploaded on www.myschoolgist.com.ng
Mathematics 1983
1. If M represents the median and D the mode of the 10. If x + 2 and x – 1 are factors of the expressions lx +
measurements 5, 9, 3, 5, 8 then (M,D) is 2kx2 + 24, find the values of l and k
A. (6,5) B. (5,8) C. (5,7) A. l = -6, k = -9 B. l = -2, k = 1 C. l = -2, k = -1
D. (5,5) E. (7,5) D. l = 0, k = 1 E. l = 6, k = 0
2. A construction company is owned by two partners X 11. Make T the subject of the equation
and Y and it is agreed that their profit will be divided in av = 3 2V + T
the ratio 4:5. at the end of the year. Y received #5,000 1- V a 2T
more than x. what is the total profit of the company for
the year? A. 3av/(1-v) B. 2v(1-v)2 - a2v2/2a2v2 - (1-V)2
A. #20,000.00 B. P’0#25,000.00 C. #30,000.00 C. 2v(1 - v) + a v / 2a2v2 + (1 - v)2
2 3 2
D. #15,000.003 E.#45,000.00 D. 2v(1 - v)2 - a4v3/2a3v3 - (1 - v)3
E. 2v(1-v)3 - a4v3/2a3v3 + (1-v)3
3. Given a regular hexagon, calculate each interior angle
of the hexagon. 12.
A. 600 B. 300 C. 1200 Additional
Mathematics
0 0
D. 45 E. 135 (2x-24)O Biology
(3 x-18)O
O
x
Geography
4. Solve the following equations (2 x+12)O
4x – 3 = 3x + y = 2y + 5x – 12 (x+12)O
French
History
A. 4x = 5, y = 2 B. x = 2, y = 5 C. x = -2, y = -5
D. x = 5, y = -2 E. x = -5, y = -2
In a class of 60 pupils, the statistical distribution of the
5. If x = 1 is root of the equation number of pupils offering Biology, History, French,
x3 – 2x2 – 5x + 6, find the other roots Geography and Additional Mathematics is as shown in
A. -3 and 2 B. –2 and 2 C. 3 and –2 the pie chart above. How many pupils offer Additional
D. 1 and 3 E. –3 and 1 Mathematics?
A. 15 B. 10 C. 18
6. If x is jointly proportional to the cube of y and the D. 12 E. 28
fourth power of z. In what ratio is x increased or
decreased when y is halved and z is doubled? 13 The value of (0.303)3 – (0.02)3 is
A. 4:1 increase B. 2:1 increase C. 1:4 decrease A. 0.019 B. 0.0019 C. 0.00019
D. 1: 1 no change E. 3: 4 decrease D. 0.000019 E. 0.000035
7. P Q 14. y varies partly as the square of x and y partly as the
O
O
60 inverse of the square root of x. write down the
45 expression for y if y = 2 when x = 1 and y = 6 when x =
8 cm 4
A. y = 10x2 + 52 B. y = x2 + 1
S R 31 31√x √x
C. y = x2 + 1 D. y = x2 + 1 E. y = 10 (x2 + 1 )
In the above figure PQR = 600, QPR = 900, PRS = 900, x 31 31√ x 31( √x)
RPS = 450, QR= 8cm. Determine PS 15. Simplify (x – 7) / (x2 – 9) ( x2 – 3x)/( x2 - 49)
A. 2√3cm B. 4√6cm C. 2√6cm A. x/ (x - 3)(x + 7) B. (x + 3) (x + 7)/x C. x/(x - 3) (x -
D. 8√6cm E. 8cm 7)
D. x/(x + 3) (x + 7) E. x/(x + 4) (x + 7)
8. Given that cos z = L, where z is an acute angle find an
expression for Co +Z - cosecz 16. The lengths of the sides of a right-angled triangle at (3x
sec Z + tan z + 1)cm, (3x - 1)cm and x cm.
A. l - L B. L2-√1−L2 C. -L-√1−L A. 2 B. 6 C. 18
1+L L2+L-1 (C1+L) +√1−L2 D. 12 E. 0
D. √L−1. E. L-(L2-1) 17. The scores of a set of a final year students in the first
(L1+L2) +√1−L2 1+ √1 - L2+ √1 - L2 semester examination in a paper are
41,29,55,21,47,70,70,40,43,56,73,23,50,50. find the median
9. If 0.0000152 x 0.00042 = A x 108, where of the scores.
1 £ A < 10, find A and B. A. 47 B. 481/2 C. 50
A. A = 9, B = 6`.38 B. A = 6.38, B = -9 C. A = 6.38, B = 9 D. 48 E. 49
D. A = 6.38, B = -1 E. A = 6.38, B = 1
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y
18. 12 A. –28, 7 B. 6, -28 C. 6, -1
9 D. –1, 7 E. 3, 2
6
3 25. Find the missing value in the following table.
-3 -2 -1 3 2 1
-3
-6
x -2 -1 0 1 2 3
O
3
-9 y=x -x+3 3 3 3 9 27
-12
-15
A. -3 B. 3 C. –9
D. 13 E. 9
x
Which of the following equations represents the above 26.
graph?
A. y = 1 + 2x + 3x2 B. y = 1 – 2x + 3x2 C. y = 1 + 2x 3x2
D. y = 1 – 2x – 3x2 E. y = 3x2 + 2x - 1 O
O
x
H
G
19. x
130O
If O is the centre of the circle in the figure above. Find
the value of x
O
A. 50 B. 260 C. 100
30 D. 65 E. 130
K F
27. Find the angle of the sectors representing each item in
The above figure FGHK is a rhombus. What is the value a pie chart of the following data. 6,10,14,16,26
of the angle x? A. 150, 250,350,400,650, B. 600, 1000,1400,1600,2600
A. 900 B. 300 C. 1500 0 0, 0, 0,
C. 6 , 10 14 16 26 0,
D. 300, 500,700,800,1300
0 0
D. 120S E. 60 E. None of the above
0-8 m
20. P 28. The scores of 16 students in a Mathematics test are
0
65,65,55,60,60,65,60,70,75,70,65,70,60,65,65,70
R What is the sum of the median and modal scores?
2m
A. 125 B. 130 C. 140
Q D. 150 E. 137.5
30O
29. The letters of the word MATRICULATION are cut and
PQRS is a desk of dimensions 2m x 0.8m which is inclined put into a box. One of the letter is drawn at random from
at 300 to the horizontal. Find the inclination of the the box. Find the probability of drawing a vowel.
diagonal PR to the horizontal.
A. 23035’ B. 300 C. 15036’ A. 2/13 B. 5/13 C. 6/13
0 0
D. 10 E. 10 42’ D. 8/13 E. 4/13
21. Find x if (x base 4)2 = 100 1000base 2 30. Correct each of the number 59.81789 and 0.0746829 to
A. 6 B. 12 C. 100 three significant figures and multiply them, giving your
D. 210 E. 110 answer to three significant figures.
A. 4.46 B. 4.48 C. 4.47
22. Simplify log10a1/2 + 1/4log10a – 1/12log10a7 D. 4.49 E. 4.50
A. 1 B. 7/6log10a C. 0
D. 10 E. a 31. If a rod of length 250cm is measured as 255cm longer in
error, what is the percentage error in measurement?
23. If w varies inversely as V and u varies directly as w3, A. 55 B. 10 C. 5
find the relationship between u and V given that u = 1, D. 4 E. 2
when V = 2
A. u = 8V3 B. u = 2 V C. V = 8/u2 32. If (2/3)m (3/4)n = 256/729, find thevalues of m and n
2 3
D. V = 8u E. U = 8/v A. m = 4, n = 2 B. m = -4, n = -2 C. m = -4, n = 2
D. m = 4, n = -2 E. m = -2, n = 4
24. Solve the simultaneous equations for x
x2 + y – 8 = 0 33. Without using tables find the numerical value of log749
y + 5x – 2 = 0 + log7(1/7)
A. 1 B. 2 C. 3
D. 7 E. 0
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34. Factorize completely 81a – 16b4
4
A. (3a + 2b) (2a – 3b) (9a2 + 4b2) 41. In the figure below find PRQ
B. (3a - 2b) (2a – 3b) (4a2 - 9b2)
C. (3a - 2b) (3a – 2b) (9a2 + 4b2)
D. (3a - 2b) (2a – 3b) (9a2 + 4b2)
E. (3a - 2b) (2a – 3b) (9a2 - 4b2) 235
o
R
35. One interior angle of a convex hexagon is 1700 and
each of the remaining interior angles is equal to x0. find
x Q
P
A. 1200 B. 1100 C. 1050
0 0
D. 102 E. 100 A. 661/20 B. 621/20 C. 1250
D. 1050 E. 650
36. PQRS is a cyclic quadrilateral in which PQ = PS. PT is a
tangent to the circle and PQ makes and angle 500 with
the tangent as shown in the figure below. What is the 42. Simplify 27a9/8
size of QRS? A. 9a2/2 B. 9a3/2 C. 2/3a2
R
D. 2/3a2 E. 3a3/2
43. Okro
14.5
Beans kg
S Q 14.5 kg Rice
45.4
O Yams kg
50
T 184.5 kg
P
0 0
A. 50 B. 40 C. 1100
D. 800 E. 1000
The farm yields of four crops on a piece of land in
37. A ship H leaves a port P and sails 30km due South. Ondo are represented on the pie chart above. What is
Then it sails 60km due west. What is the bearing of H the angle of the sector occupied by Okro in the chart?
from P? A. 911/20 B. 191/30 C. 331/30
A. 26034’ B. 243026’ C. 116034’ D. 110
E. 910
0 0
D. 63 26’ E. 240
O
44. (x+3y)
38. In a sample survey of a university community the O
following table shows the percentage distribution of P 45
Q O R
the number of members per household. y
No of members (3x+y)O
per household 1 2 3 4 5 6 7 8 Total
Number of
households 3 12 15 28 21 10 7 4 100
In the figure above, PQR is a straight line. Find the
A. 4 B. 3 C. 5 values of x and y
D. 4.5 E. None A. x = 22.50 and y = 33.750
B. x = 150 and y = 52.50
39. On a square paper of length 2.524375cm is inscribed a C. x = 22.50 and y = 45.00
square diagram of length 0.524375. find the area of the D. x = 56.250 and y = 11.50
paper no covered by the diagram correct to 3 significant E. x = 18.0 and y = 56.50
figures.
45. PQR is the diameter of a semicircle RSP with centre at
A. 6.00cm2 B. 6.10cm2 C. 6.cm2
2 2 Q and radius of length 3.5cmc. if QPT = QRT = 600. Find
D. 6.09cm E. 4.00cm
the perimeter of the figure (PTRS p = 22/7)
S
40. If f(X) = 1 + x - 1 find f(1-x)
x-1 x2-1
P
A. 1/x + 1/(x+2) B. x +1/(2x -1) O R
60 O 60
O
C. -1/x - 1/(x-2) D. -1/x + 1/(x2-1)
T
A. 25cm B. 18ccm C. 36cm
D. 29cm E. 25 5 cm
