Mathematics 2017 JAMB Past Questions
- A. {2, 3}
- B. {2, 3, 4}
- C. {3, 4, 6}
- D. {2}
- A.
- B.
- C.
- D.
- A.
- B.
- C.
- D.
- A. 2.6cm
- B. 3.5cm
- C. 3.6cm
- D. 7.0cm
1. Given T = { even numbers from 1 to 12 }
N = {common factors of 6, 8 and 12}
Find T ∩ N
Find T ∩ N
Correct Answer: Option D
N = {common factors of 6,8 and 12}
Find T ∩ N
T = {2, 4, 6, 8, 10, 12}
N = {2}
T ∩ N = {2} i.e value common to T & N
Explanation
T = {evenn numbers from 1 to 12}N = {common factors of 6,8 and 12}
Find T ∩ N
T = {2, 4, 6, 8, 10, 12}
N = {2}
T ∩ N = {2} i.e value common to T & N
2.What is the next number in the series 2, 1, , ...
Correct Answer: Option D
Explanation
2, 1, , .....
There are 4 terms in the series
Therefore the next number will be the 5th term
Tn = ar (formular for geometric series)
a = first term = 2
r = common rate = =
n = number of terms
T5 = 5th term = ?
T5 = ar
= ar
= 2 × (ar)4
= 2 ×
=
3. If U = {x : x is an integer and 1 ≤ x ≤ 20 }
E1 = {x: x is a multiple of 3}
E2 = {x: x is a multiple of 4} and an integer is picked at random from U, find the probability that it is not in E2
E2 = {x: x is a multiple of 4} and an integer is picked at random from U, find the probability that it is not in E2
Correct Answer: Option A
Explanation
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}E1 = {3, 6, 9, 12, 15, 18}
E2 = {4, 8, 12, 16, 20}
Probability of E2 =
i.e
Probability of set E2 = 1 −
=
=
4.The curved surface area of a cylinder 5cm high is 110cm2. Find the radius of its base
π =
Explanation
Curved surface area of cylinder = 2πrh110 = 2 × × r × 5
r =
= 3.5cm
- A. q −
- B. 7 −
- C. 8 −
-
D.
7 +
Correct Answer: Option B
Explanation
Y = Px2 + q
Y = 2x2 - 1
Px2 + q = 2x2 - 1
Px2 = 2x2 - 1 - q
p =
at x = 2
P =
=
=
P =- A.
- B. √3 −
- C. √2
- D. 1 +
- A.
- B. -1
- C. 1
- D.
- A. 24oC
- B. 20oC
- C. 34oC
- D. 30oC
- A. 4
- B. 3
- C. 2
- D. 3
- A.
- B.
- C.
- D.
6Evaluate (3o ) in surd formCorrect Answer: Option D
Explanation
sin =
=
∴ (sin45 + sin30)
=
= +
=
=
7. If y = x Sin x, findCorrect Answer: Option C
Explanation
y = xsinx
=
=
At x =
= sin +
= 1 + × 10
= 1
8.If temperature t is directly proportional to heat h, and when t = 20oC, h = 50 J, find t when h = 60J
Correct Answer: Option A
Explanation
t ∝ h, t = 20, h
t = ? h = 60
t = kh where k is constant
20 = 50k
k =
k =
when h = 60, t = ?
t = × 60
t = 24oC
9. Evaluate 1 - (x ) + ( 5 + )Correct Answer: Option D
10. Given m = Nmake T the subject of the formulaCorrect Answer: Option B
Explanation
M = N
,
make T subject of formula square both sides
M =
TM = NSL
T =
11.Simplify 3 × - A. 3
5. If two graphs Y = px2 + q and y = 2x2 − 1 intersect at x =2, find the value of p in terms of q
Correct Answer: Option B
Explanation
3 ×= 3 ×
= 3
= 3
=
= 9
12.The locus of a point which is equidistant from the line PQ forms a
- A. circle centre P
- B. pair of parallel lines each opposite to PQ
- C. circle centre Q
- D. perpendicular line to PQ
Explanation
The locus of points at a fixed distance from the point P is a circle with the given P at its centre.The locus of points at a fixed distance from the point Q is a circle with the given point Q at its centre
The locus of points equidistant from two points P and Q i.e line PQ is the perpendicular bisector of the segment determined by the points
Hence, The locus of a point which is equidistant from the line PQ forms a perpendicular line to PQ
13.Given T = {even numbers from 1 to 12}
N = {common factors of 6, 8 and 12} Find T n N
- A. {2, 3}
- B. {2, 3, 4}
- C. {3, 4, 6}
- D. {2}
Correct Answer: Option D
= { 2, 4, 6, 8,10, 12}
N = {common factors of 6, 8 and 12}
= {2} Find T n N = {2}
Explanation
Given T = {even numbers from 1 to 12}= { 2, 4, 6, 8,10, 12}
N = {common factors of 6, 8 and 12}
= {2} Find T n N = {2}
14
![](https://myschool.ng/storage/classroom/21169946070_17_04.jpg)
Given the quadrilateral RSTO inscribed in the circle with O as centre. Find the size angle x and given RST = 60o
- A. 100o
- B. 140o
- C. 120o
-
D.
10oCorrect Answer: Option C
Explanation
If RST = 60o
RXT = 2 × RST
(angle at the centre twice angle at the circumference)
RXT = 2 × 60
= 120o
15. Find the sum of the range and the mode of the set of numbers 10, 9, 10, 9, 8, 7, 7, 10, 8, 10, 8, 4, 6, 9, 10, 9, 7, 10, 6, 5 - A. 16
- B. 14
- C. 12
- D. 10
Correct Answer: Option A
Explanation
Range = Highest Number - Lowest NumberMode is the number with highest occurrence
10, 9, 10, 9, 8, 7, 7, 10, 8, 4, 6,, 9, 10, 9, 7, 10, 6, 5
Range = 10 − 4 = 6
Mode = 10
Sum of range and mode = range + mode = 6 + 10
= 16
16. Find the sum to infinity of the series
, , ,..........
- A.
Correct Answer: Option A
∑ = arn − 1
=
− r
a =
r = ÷
r = ×
=
S = −
= ÷
= ×
=
Explanation
Sum to infinity∑ = arn − 1
=
a =
r = ÷
r = ×
=
S = −
= ÷
= ×
=
17
![](https://myschool.ng/storage/classroom/13609270755_17_24.jpg)
The base in which the operation was performed was
- A. 6
- B. 2
- C. 4
- D. 5
18.The value of x + x ( xx) when x = 2 is
- A. 16
- B. 10
- C. 18
- D. 24
Explanation
when x=2, we have19. In a regular polygon, each interior angle doubles its corresponding exterior angle. Find the number of sides of the polygon
- A. 8
- B. 6
- C. 4
- D. 3
Explanation
2x + x = 180o3x = 180o
x = 60o (exterior angle of the polygon)
angle =
60 =
n =
n = 6 sides
20. A cylindrical tank has a capacity of 3080m3. What is the depth of the tank if the diameter of its base is 14m? Take pi = 22/7.
- A. 23m
- B. 25m
- C. 20m
- D. 22m
Explanation
Capacity = Volume = 3080m3base diameter = 14m
radius =
= 7m
Volume of Cylidner = Capacity of cylinder
πr2h = 3080
× 7 × 7 × h = 3080
h =
h = 20m
21. Simplify 4+ 5 − 3
- A. 7
- B. − 7
- C. − 7
Correct Answer: Option D
= 4 × 9 + 5 × 4 − 3 × 25
= 4 × 3 + 5 × 2 − 3 × 5
= 12 + 10 − 15
= (12 + 10 − 15)
= 7
Explanation
4 + 5 − 3= 4 × 9 + 5 × 4 − 3 × 25
= 4 × 3 + 5 × 2 − 3 × 5
= 12 + 10 − 15
= (12 + 10 − 15)
= 7
22.A man covered a distance of 50 miles on his first trip, on a later trip he traveled 300 miles while going 3 times as fast. His new time compared with the old distance was?
- A. three times as much
- B. the same
- C. twice as much
- D. half as much
Explanation
Let the speed of the 1st trip be x miles/hrand the speed of the 2nd trip be 3x miles/hr
Speed = distance/time
∴ Time taken to cover a distance of 50 miles on the 1st trip
=
time taken to cover a distance of 300 miles on the next trip
=
=
∴the new time compared with the old time is twice as much
23
![](https://myschool.ng/storage/classroom/3024646250_17_20.jpg)
In the figure, find x
- A. 40o
- B. 55o
- C. 50o
- D. 60o
Correct Answer: Option A
Explanation
Sum of angle at a point = 360o2x + 3x + 4x = 360
9x = 360
x =
x = 40o
24. Divide 4x3 - 3x + 1 by 2x - 1
- A. 2x2 -x + 1
- B. 2x2 - x -1
- C. 2x2 + x + 1
- D. 2x2 + x -1
Correct Answer: Option D
Explanation
by method of long division, we get the answer.25. A car dealer bought a second-hand car for of 250,000 and spent N 70,000 refurbishing it. He then sold the car for N400,000. What is the percentage gain?
- A. 60%
- B. 32%
- C. 25%
- D. 20%
Explanation
Total Cost Price = N(250,000 + 70,000)= N 32,000
Selling Price = N 400,000(Given)
Gain = Selling Price - Cost Price
= 400,000 - 300,000
= 80,000
% gain = × 100
= × 100
Gain % = 25%
26. Find the number of ways that the letters of the word EXCELLENCE be arranged
- A.
Correct Answer: Option C
It is a ten letter word = 10!
Since we have repeating letters, we have to divide to remove the duplicates accordingly. There are 4 Es, 2 Cs, 2 Ls
∴ there are
ways to arrange
Explanation
EXCELLENCEIt is a ten letter word = 10!
Since we have repeating letters, we have to divide to remove the duplicates accordingly. There are 4 Es, 2 Cs, 2 Ls
∴ there are
ways to arrange
27. Evaluate
and leave the answer in standard form
- A. 3.3 x 10-4
- B. 3.3 x 10-3
- C. 3.3 x 10-5
- D. 3.3 x 10-8
Correct Answer: Option A
to standard form
=
= 33 × 10
= 33 × 10
= 33 × 10-5
= 3.3 x 10^-4
Explanation
to standard form
=
= 33 × 10
= 33 × 10
= 33 × 10-5
= 3.3 x 10^-4
28.If a rod 10cm in length was measured as 10.5cm, calculate the percentage error
- A. 5%
- B. 10%
- C. 8%
- D. 7%
Explanation
Actual measurement = 10cmapproximated value of measurement = 10.5cm
% error = × 100
= × 100
= × 100
ignore -sign i.e take absolute value
= × 100
= 5 %
29. Find the principal which amounts to ₦ 5,500 at a simple interest in 5 years at 2% per annum
- A. ₦ 4,900
- B. ₦ 5,000
- C. ₦ 4,700
- D. ₦ 4,000
Correct Answer: Option B
Amount = Principal + Simple Interest
I =
R = rate, T = time
I =
I =
I =
Amount A = P + I
5500 = P +
Multiply through by 100
5500 = 10P + P
5500 = 11P
p =
p = ₦5000
Explanation
Principal = P, Simple Interest = I, Amount = AAmount = Principal + Simple Interest
I =
R = rate, T = time
I =
I =
I =
Amount A = P + I
5500 = P +
Multiply through by 100
5500 = 10P + P
5500 = 11P
p =
p = ₦5000
30.
![](https://myschool.ng/storage/classroom/27221866290_17_31.jpg)
The pie chart shows the
allocation of money to each sector in a farm. The total amount allocated
to the farm is ₦ 80 000. Find the amount allocated to fertilizer
- A. ₦ 35, 000
- B. ₦ 40,000
- C. ₦ 25,000
- D. ₦ 20,000
Correct Answer: Option D
Explanation
![](https://myschool.ng/storage/classroom_answers/19660236765_sol_17_31.jpg)
∴ To get the angle occupied by fertilizer we have,
40 + 50 + 80 + 70 + 30 + fertilizer(x) = 360
270 + x = 360
x = 360 - 270
x = 90
Total amount allocated to the farm
= ₦ 80,000
∴Amount allocated to the fertilizer
=
= × 80,000
= ₦20,000
31. In how many ways can the word MATHEMATICS be arranged?
- A.
Correct Answer: Option C
There are 2Ms and 2As and 2Es
Divide the number of repeating letters
=
Explanation
MATHEMATICS is an eleven letter word = 11!There are 2Ms and 2As and 2Es
Divide the number of repeating letters
=
32. In how many ways can the word MACICITA be arranged?
- A.
- D. 8!
Correct Answer: Option C
Since we have repeating letters, we have to divide to remove duplicates accordingly. There are 2A, 2C, 2I
∴
Explanation
MACICITA is an eight letter word = 8!Since we have repeating letters, we have to divide to remove duplicates accordingly. There are 2A, 2C, 2I
∴
33. y is inversely proportional to x and y and 6 when x = 7. Find the constant of the variation
- A. 47
- B. 42
- C. 54
- D. 46
Explanation
Y ∝Y = 6, X = 7
Y = where k is constant
6 =
k = 42
34
![](https://myschool.ng/storage/classroom/13610949966_17_04.jpg)
In the diagram MN, PQ and RS are parallel lines. What is the value of the angle marked X?
- A. 123o
- B. 170o
- C. 117o
- D. 137o
Correct Answer: Option C
MN = PQ = RS (parallel lines)
Label the angle in the lines
a = i (corresponding angles are equal)
b = x (corresponding angles are equal)
If |MN| = |RS|
If a = i
and a = 63 = i
a + b = 180 (Adjacent interior angles are supplementary i.e add to 180)
∴ i + x = 180
63 + x = 180
x = 180 - 63
x = 1170
Explanation
MN || PQ || RSMN = PQ = RS (parallel lines)
Label the angle in the lines
a = i (corresponding angles are equal)
b = x (corresponding angles are equal)
If |MN| = |RS|
If a = i
and a = 63 = i
a + b = 180 (Adjacent interior angles are supplementary i.e add to 180)
∴ i + x = 180
63 + x = 180
x = 180 - 63
x = 1170
35.Find the equation of the locus of a point p (x, y) such that pv = pw, where v= (1, 1) and w = (3, 5)
- A. 2x + 2y = 9
- B. 2x + 3y = 8
- C. 2x + y = 9
- D. x + 2y = 8
Explanation
The locus of a point p(x, y) such that pv = pw where v = (1, 1)and w = (3, 5). This means that the point p moves so that its distance from v and w are equidistance
=
=
square both sides
(x - 1)2 + (y - 1)2 = (x - 3)2 + (y - 5)2
x2 - 2x + 1 + y2 - 2y + 1 = x2 - 6x + 9 + y2 - 10y + 25
x2 + y2 -2x -2y + 2 = x2 + y2 - 6x - 10y + 34
Collecting like terms
x2 - x2 + y2 - y2 - 2x + 6x -2y + 10y = 34 - 2
4x + 8y = 32
Divide through by 4
x + 2y = 8
36. Find ∫(x2 + 3x − 5)dx
A.
- - 5x + k
B.
- + 5x + k
C.
+ - 5x + k
D.
+ + 5x + k
37.In the diagram below MN is a chord of a circle KMN centre O and radius 10cm. If
- A. 10cm
- B. 18cm
- C. 17cm
- D. 12cm
Correct Answer: Option A
Explanation
Sin 70o
x = 10 Sin 70o
= 9.3969
Hence, length of chord MN = 2x
= 2 × 9.3969
= 18.79
= 19cm (nearest cm)
38. If m * n = [mn − nm] for m, n belong to R, evaluate − 3 * 4- A. 3
- B. 4
- C. 5
- D. 6
Correct Answer: Option C
Explanation
m * n = -
m = − 3
n = 4
∴ − 3 × 4 = -
=
=
=
39. Factorize completely x2 + 12xy + y2 + 3x + 3y - 18- A. (x + y + 6)(x + y -3)
- B. (x - y - 6)(x - y + 3)
- C. (x - y + 6)(x - y - 3)
- D. (x + y - 6)(x + y + 3)
Correct Answer: Option A
Explanation
x(x + y - 3) + y(x + y - 3) + 6(x + y - 3)
= (x + y - 3)(x + y + 6)
= (x + y + 6)(x + y -3)
40. Make S the subject of the relationp = s +- A. s =
- B. s = nr +
- C. s = + m2
- D. s = + m2 Correct Answer: Option A
-
Explanation
p = s +
p = s + ( 1 + )
p = s (1 + )
nr × p = s (nr + m2)
s =
- A. 9
- B. - 9
- C. 6
- D. - 6
- A. 3/2
- B. 2/1
- C. -1
- D. 3/2
- A. 4a
- B.
- C. 8a
- D.
- A. 1, − 2
- B. − 2, n = 1
- C. , 1
- D.
Correct Answer: Option B
Explanation
= m + n√6
x
=
=
=
= − 2 + √6
∴ m + n = − 2 + √6
m = − 2, n = 1 - A.
- B.
- C.
- D.
41. The operation * on the set R of real number is defined by x * y = 3x + 2y − 1, find 3*− 1
Correct Answer: Option C
Explanation
x * y is an operation on 3x + 2y − 1Find 3A − 1
x = 3, y = −1
3 * − 1 on 3x + 2y − 1
3(3) + 2(−1) −1
= 9 − 2 − 1
= 6
42. Find the gradient of the line joining the points (3, 2) and (1, 4)
Correct Answer: Option C
Gradient =
= \)
(X1, Y1) = (3, 2)
(X2, Y2) = (1, 4)
Gradient =
=
= −1
Explanation
Gradient of line joining points (3, 2), (1, 4)Gradient =
= \)
(X1, Y1) = (3, 2)
(X2, Y2) = (1, 4)
Gradient =
=
= −1
43. Simplify (3√64a3)
Correct Answer: Option D
Explanation
(3√64a3)
44. If
= m + n √ 6,
44. find the values of m and n respectively
44. find the values of m and n respectively
45. If α and β are the roots of the equation 3x2 + bx − 2 = 0. Find the value of +
Correct Answer: Option D
Explanation
+ =3x2 + 5x + 5x − 2 = 0.
Sum of root = α + β
Product of root = αβ
x2 + − = 0
αβ = −
α + β =
∴ = −
= − ×
=
46 . Find the range of the following set of numbers 0.4, −0.4, 0.3, 0.47, −0.53, 0.2 and −0.2
- A. 1.03
- B. 0.07
- C. 0.03
- D. 1.0
Explanation
0.4, −0.4, 0.3, 0.47, −0.53, 0.2, −0.2Range is the difference between the highest and lowest value
i.e Highest − Lowest
− 0.53, −0.4, −0.2, 0.2, 0.3, 0.4, 0.47
0.47 is the highest
− 0.53 is the lowest
∴ = 0.47 − (− 0.53)
∴0.47 + 0.53
= 1.0
47. Evaluate 1 − ( + 1) + (5 + 1)
- A. 4
- B. 3
- C. 2
Correct Answer: Option D
Explanation
1 − ( + 1) + (5 + 1)1 − ( × ) + (5 + )
1 − +
=
48. What is the product of 2x2 − x + 1 and 3 − 2x
- A. 4x3 − 8x2 + 5x + 3
- B. −4x3 + 8x2 − 5x + 3
- C. −4x3 − 8x2 + 5x + 3
- D. 4x3 + 8x2 − 5x + 3
Explanation
(2x2 - x + 1) × (3 - 2x);3(2x2 - x + 1) - 2x (2x2 - x + 1)
6x2 - 3x + 3 - 4x3 + 2x2 - 2x
-4x3 + 8x2 -5x + 3
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