2000 - JAMB Mathematics Past Questions and Answers - page 2
11
The 3rd term of an A.P is 4x - 2y and the 9th term is 10x - 8y. Find the common difference.
A
19x - 17y
B
8x - 4y
C
x - y
D
2x
correct option: c
n = 3, U3 = 4x - 2y,
Un = a + (n+1)d,
4x - 2y = a + 2d (1)
U9 = 10x - 8y,
10x - 8y = a + 8d (2)
Solving (1) and (2), d = 6(x-y)/6
d = x-y.
Users' Answers & CommentsUn = a + (n+1)d,
4x - 2y = a + 2d (1)
U9 = 10x - 8y,
10x - 8y = a + 8d (2)
Solving (1) and (2), d = 6(x-y)/6
d = x-y.
12
Find the inverse of p under the binary operation * defined by p*q = p + q - pq, where p and q are real numbers and zero is the identity
A
p
B
p -1
C
p/(p-1)
D
p/(p+1)
13
Evaluate (1/2 - 1/4 - 1/8 - 1/16 + ...) - 1
A
2/3
B
zero
C
-2/3
D
-1
correct option: c
S = a/(1+r), where a = 1/2, r = 1/2.
S = 1/2 3/2 = 1/2 x 3/2 = 1/3.
1/3 - 1 = -2/3
Users' Answers & CommentsS = 1/2 3/2 = 1/2 x 3/2 = 1/3.
1/3 - 1 = -2/3
14
if (x - 1), (x + 1) and (x - 2) are factors of the polynomial ax3 + bx2 + cx - 1, find a, b, c in that order.
A
-1/2, 1., 1/2
B
1/2, 1, 1/2
C
1/2, 1, -1/2
D
1/2, -1, 1/2
correct option: a
This is a polynomial of the 3rd order, thus x should have three answers. Use the factors given to get values of x as 1, -1 and -2.
Form three equations, and carry out elimination and subsequent substitution to get a = -1/2, b = 1, and c = 1/2
Users' Answers & CommentsForm three equations, and carry out elimination and subsequent substitution to get a = -1/2, b = 1, and c = 1/2
15
A trader realizes 10x - x2 naira profit from the sale of x bags on corn. How many bags will give him the desired profit?
A
4
B
5
C
6
D
7
correct option: b
y = 10x - x2
dy/dx = 10 -x
As dy/dx = 0,
10 - 2x = 0
2x = 10
x = 5
Users' Answers & Commentsdy/dx = 10 -x
As dy/dx = 0,
10 - 2x = 0
2x = 10
x = 5
16
Solve the inequality 2 - x > x2.
A
x < -2 or x > 1
B
x > 2 or x< -1
C
-1 < x < 2
D
-2 < x < 1
17
If α and β are the roots of the equation 3x2 + 5x - 2 = 0, find the value of 1/α + 1/β
A
-5/3
B
-2/3
C
1/2
D
5/2
correct option: d
1/α + 1/β = β+α/αβ
3x2 + 5x - 2 = 0
x2 + 5x/3 - 2/3 = 0
αβ = -2/3
β+α = -5/3
Thus; β+α/αβ = -2/3 -2/3 = -5/2
Users' Answers & Comments3x2 + 5x - 2 = 0
x2 + 5x/3 - 2/3 = 0
αβ = -2/3
β+α = -5/3
Thus; β+α/αβ = -2/3 -2/3 = -5/2
18
A frustrum of pyramid with square base has its upper and lower sections as squares of sizes 2m and 5m respectively and the distance between them 6m. Find the height of the pyramid from which the frustrum was obtained.
A
8.0 m
B
8.4 m
C
9.0 m
D
10.0 m
correct option: d
Users' Answers & Comments19
P is a point on one side of the straight line UV and P moves in the same direction as UV. If the straight line ST is on the locus of P and angle VUS = 60°, find angle UST.
A
310°
B
130°
C
80°
D
50°
correct option: b
Make a good sketch of the question, and follow this steps.
Since ST is parallel to UV => angle USR = 50°(alternate to VUS.
Angle UST = 180° - 50° = 130° (angle on a straight line)
Users' Answers & CommentsSince ST is parallel to UV => angle USR = 50°(alternate to VUS.
Angle UST = 180° - 50° = 130° (angle on a straight line)
20
A ship sails a distance of 50km in the direction S50°E and then sails a distance of 50km in the direction N40°E. FInd the bearing of the ship from the original position.
A
S90°E
B
N40°E
C
S95°E
D
N85°E
correct option: d
Users' Answers & Comments