2003 - JAMB Mathematics Past Questions and Answers - page 1
1
The length a person can jump is inversely proportional to his weight. If a 20 kg person can jump 1.5 m, find the constant of proportionality
A
60
B
30
C
20
D
15
2
Find the value of x and y respectively if 3x - 5y + 5 = 0 and 4x - 7y + 8 = 0
A
-5, -4
B
-4,. -5
C
4, 5
D
5, 4
correct option: d
3x - 5y + 5 = 0 → eqn1
4x - 7y + 8 = 0 → eqn2
eqn1 * 4; 12x - 20y + 20 = 0 → eqn3
eqn2 * 3; 12x - 21y + 24 = 0 → eqn4
eqn3 - eqn4 = y - 4 = 0
∴ y = 4
From eqn1,
3x - 5y + 5 = 0
3x - 5(4) + 5 = 0
3x - 20 + 5 = 0
3x - 15 = 0
3x = 15
x = 5
x and y = 5, 4 respectively
Users' Answers & Comments4x - 7y + 8 = 0 → eqn2
eqn1 * 4; 12x - 20y + 20 = 0 → eqn3
eqn2 * 3; 12x - 21y + 24 = 0 → eqn4
eqn3 - eqn4 = y - 4 = 0
∴ y = 4
From eqn1,
3x - 5y + 5 = 0
3x - 5(4) + 5 = 0
3x - 20 + 5 = 0
3x - 15 = 0
3x = 15
x = 5
x and y = 5, 4 respectively
3
Three consecutive terms of a geometric progression are given as n-2, n and n=3. Find the common ratio
A
1/4
B
1/2
C
2/3
D
3/2
correct option: d
\(r=\frac{n}{n-2}\hspace{1mm}and\hspace{1mm}r=\frac{n+3}{n}\∴\frac{n}{n-2}=\frac{n+3}{n}\n^2 = n^2 +3n - 2n-6\0=n-6\∴n=6\But\hspace{1mm}r = \frac{n}{n-2}\r=\frac{6}{6-2}\\frac{6}{4}=\frac{3}{2}\)
Users' Answers & Comments4
Triangle OPQ above is the solution of the inequalities
A
x + 1 ≥ 0, y + x ≤ 0, y - x ≥ 0
B
y + x ≤ 0, y - x ≥ 0, x -1 ≥ 0
C
x - 1 ≤ 0, y - x ≥ o, y + x ≥ 0
D
x - 1 ≤ 0, y + x ≤ 0, y - x ≤ 0
correct option: a
Lines bounding Δ OPQ
OQ; y - x = 0
y - x ≥ 0
PQ; x + 1 = 0
x + 1 ≥ = 0
PO; y + x = 0
y + x ≤ 0
∴ x + 1 ≥ 0, y + x ≤ 0, y - x ≥ 0
Users' Answers & CommentsOQ; y - x = 0
y - x ≥ 0
PQ; x + 1 = 0
x + 1 ≥ = 0
PO; y + x = 0
y + x ≤ 0
∴ x + 1 ≥ 0, y + x ≤ 0, y - x ≥ 0
5
Factorize completely 4abx - 2axy -12b2x + 6bxy
A
2x(a - 3b)(2b - y)
B
2x(3b - a)(2b - y)
C
2x(a - 3b)(y - 2b)
D
2x(2b - a)(3b - y)
correct option: a
4abx - 2axy - 12b2x + 6bxy = (4abx - 2axy) - (12b2x - 6bxy)
= 2ax(2b - y) -6bx(2b - y)
= (2ax - 6bx)(2b - y)
= 2x(a - 3b)(2b - y)
Users' Answers & Comments= 2ax(2b - y) -6bx(2b - y)
= (2ax - 6bx)(2b - y)
= 2x(a - 3b)(2b - y)
6
The sum of the first n terms of an arithmetic progresssion is 252. If the first term is -16 and the last term is 72, find the number of terms in the series
A
6
B
7
C
8
D
9
correct option: d
\(S_n = 252, a = -16\hspace{1mm}and\hspace{1mm}l = 72\S_n = \frac{n}{2}(-16+72)\252 = \frac{n}{2}(-16+72)\n=\frac{504}{56}\n=9\)
Users' Answers & Comments7
A trapezium has two parallel sides of length 5cm and 9cm. If the area is 21cm2, find the distance between the parallel sides
A
3 cm
B
4 cm
C
6 cm
D
7 cm
correct option: a
Area of Trapezium = 1/2(sum of parralel sides) * ht
21 = 1/2(5 + 9)h
42 = 14h
h = 42/14
h = 3cm
Users' Answers & Comments21 = 1/2(5 + 9)h
42 = 14h
h = 42/14
h = 3cm
8
The locus of a point P which moves on one side only of a straight line XY so that ∠XPY = 90o is
A
a circle
B
a semicircle
C
an arc of a circle through X, Y
D
the perpendicular bisector of XY
correct option: b
Users' Answers & Comments9
Find the slope of the curve y = 2x2n+ 5x - 3 at (1, 4).
A
4
B
6
C
7
D
9
10
Evaluate \(\int^{2} _{3}(x^2 - 2x)dx\)
A
4
B
2
C
4/3
D
1/3
correct option: c
\(\int^{2} _{3}(x^2 - 2x)dx\=\left[\frac{x^3}{3}-\frac{2x^2}{2}\right ]^{2}_{3}\\left[\frac{x^3}{3}-x^2 + C\right ]^{2}_{3}\\left[\frac{3^3}{3}-3^2 + C \right ]-\left[\frac{2^3}{3}-2^2 + C \right ]\9-9-\left[\frac{8}{3}-4 \right ]\=\frac{-8}{3}+4\=\frac{4}{3}\)
Users' Answers & Comments