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JAMB - Mathematics (1988)

1
Tope bought X oranges at N5.00 each and some mangoes at N4.00 each. if she bought twice as many mangoes as oranges and spent at least N65.00 and at most N130.00, find the range of values of X.
Answer
(C)
5≤X≤10
2
If \(1P03{_4} = 115_{10}\) find P
Answer
(D)
3
3
If \(\frac{1}{p}\) = \(\frac{a^2 + 2ab + b^2}{a - b}\) and \(\frac{1}{q}\) = \(\frac{a + b}{a^2 - 2ab + b^2}\) Find \(\frac{p}{q}\)
Answer
(B)
\(\frac{1}{a^2 - b^2}\)
4
If x varies inversely as the cube root of y and x = 1 when y = 8, find y when x = 3
Answer
(C)
\(\frac{8}{27}\)
5
if a = -3, b = 2, c = 4, evaluate \(\frac{a^3 - b^3 - c^{\frac{1}{2}}}{b - a - c}\)
Answer
(D)
-37
6
If (g(y)) = \(\frac{y - 3}{11}\) + \(\frac{11}{y^2 - 9}\). what is g(y + 3)?
Answer
(A)
\(\frac{y}{11} + \frac{11}{y(y + 6)}\)
7
Factorize completely \((x^2 + x)^2 - (2x + 2)^2\)
Answer
(D)
(x + 1)2 (x + 2)(x - 2)
8
Simplify \(\frac{x - y}{x^{\frac{1}{3}} - y^{\frac{1}{3}}}\)
Answer
(B)
x\(\frac{2}{3}\) + x \(\frac{1}{3}\) + y\(\frac{2}{3}\)
9
What is the solution of the equation x2 - x - 1 + 0?
Answer
(A)
x = 1.6 and x = -0.6
10

For what values of x is the curve y = \(\frac{x^2 + 3}{x + 4}\) decreasing?

Answer
(D)
0 \(\leq\) x \(\leq\) 3
11
The solutions of x2 - 2x - 1 = 0 are the points of intersection of two graphs. if one of the graphs is y = 2 + x - x2, find the second graph
Answer
(A)
y = 1 - x
12
If the sum of the 8th and 9th terms of an arithmetic progression is 72 and the 4th term is -6, find the common difference
Answer
(D)
9\(\frac{1}{3}\)
13
If 7 and 189 are the first and fourth terms of geometric progression respectively, find the sum of the first three terms of the progression
Answer
(B)
91
14
Find correct to one decimal place, 0.24633 \(\div\) 0.0306
Answer
(D)
8.1
15
In a class of 150 students, the sector in a pie chart representing the students offering Physics has angle 12o. How many students are offering Physics?
Answer
(D)
5
16
\(\begin{array}{c|c} Scores(x) & 0 & 1 & 2 & 3 & 4 & 5 & 6  \\ \hline Frequency(f) & 7 & 11 & 6 & 7 & 7 & 5 & 3\end{array}\)
In the distribution above, the mode and median respectively are
Answer
(B)
1, 2
17
if x is the addition of the prime numbers between 1 and 6; and y the H.C.F. of 6, 9, 15. Find the product of x and y
Answer
(B)
30
18
Four interior angles of a pentagon are 90o - xo, 90o + xo, 110o - 2xo, 110o + 2xo. Find the fifth interior angle
Answer
(D)
140o
19
For which of the following exterior angles is a regular polygon possible? i. 35° ii. 18° iii. 15°
Answer
(C)
ii and iii
20
Simplify \(\frac{1\frac{1}{2}}{2 \div \frac{1}{4} \text{of } 32}\)
Answer
(C)
6
21
A 5.0g of salt was weighted by Tunde as 5.1g. What is the percentage error?
Answer
(B)
2
22
Two sisters, Taiwo and Keyinde, own a store. The ratio of Taiwo's share to Kehinde's is 11:9. Later, Keyinde sells \(\frac{2}{3}\) of her share to Taiwo for N720.00. Find the value of the store.
Answer
(B)
N2,400.00
23
A basket contain green, black and blue balls in the ratio 5 : 2 : 1. If there are 10 blue balls. Find the corresponding new ratio when 10 green and 10 black balls are removed from the basket
Answer
(D)
4 : 1 : 1
24
A tax payer is allowed \(\frac{1}{8}\)th of his income tax-free, and pays 20% on the remainder. If he pays N490.00 tax, what is his income?
Answer
(C)
N2,800.00
25
Evaluate \(\frac{8^{\frac{1}{3}} \times 5^{\frac{2}{3}}}{10^{\frac{2}{3}}}\) 
Answer
(D)
3\(\sqrt{2}\)
26
If \(log_{10} 2 = 0.3010\) and \(log_{10} 3 = 0.4771\), evaluate; without using logarithm tables, \(log_{10} 4.5\)
Answer
(C)
0.6532
27
Find m such that (m + \(\sqrt{3}\))(1 - \(\sqrt{3}\))2 = 6 - 2\(\sqrt{2}\)
Answer
(C)
3
28
The thickness of an 800 pages of book is 18mm. Calculate the thickness of one leaf of the book giving your answer in meters and in standard form
Answer
(D)
4.50 x 10-5m
29
Simplify \(\frac{x + 2}{x + 1}\) - \(\frac{x - 2}{x + 2}\)
Answer
(C)
\(\frac{5x + 6}{(x + 1)(x + 2)}\)
30
Solve the following equation equation for \(x^2 + \frac{2x}{r^2} + \frac{1}{r^4}\) = 0
Answer
(C)
-\(\frac{1}{r^2}\)
31
List the integral values of x which satisfy the inequality -1 < 5 - 2x \(\geq\) 7
Answer
(A)
-1, 0, 1, 2
32
Given that 3x - 5y - 3 = 0, 2y - 6x + 5 = 0 the value of (x, y) is
Answer
(D)
(\(\frac{19}{24}, \frac{-1}{8}\))
33
The solution of the quadratic equation px2 + qx + b = 0 is
Answer
(C)
\(\frac{-q \pm \sqrt{ q^2 - 4bp}}{2p}\)
34
Simplify \(\frac{1}{x^2 + 5x + 6}\) + \(\frac{1}{x^2 + 3x + 2}\)
Answer
(C)
\(\frac{2}{(x + 1)(x + 3)}\)
35
Simplify \(\frac{4a^2 - 49b^2}{2a^2 - 5ab - 7b^2}\)
Answer
(D)
\(\frac{2a + 7b}{a + b}\)
36
If cot \(\theta\) = \(\frac{x}{y}\), find cosec\(\theta\)
Answer
(C)
\(\frac{1}{y}\)\(\sqrt{x^2 + y^2}\)
37
In triangle PQR, PQ = 1cm, QR = 2cm and PQR = 120o Find the longest side of the triangle
Answer
(B)
\(\sqrt{7}\)cm
38
If \(\cos^2 \theta + \frac{1}{8} = \sin^2 \theta\), find \(\tan \theta\).
Answer
(B)
\(\frac{3\sqrt{7}}{7}\)
39
If a metal pipe 10cm long has an external diameter of 12cm and a thickness of 1cm find the volume of the metal used in making the pipe
Answer
(B)
110\(\pi\)cm3
40
PQR is a triangle in which PQ = 10cm and QPR = 60oS is a point equidistant from P and Q. Also S is a point equidistant from PQ and PR. If U is the foot of the perpendicular from S on PR, find the length SU in cm to one decimal place
Answer
(B)
4.33
41
If x and y represent the mean and the median respectively of the following set of numbers 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, find the \(\frac{x}{y}\) correct to one decimal place
Answer
(C)
1.0
42
If two dice are thrown together, what is the probability of obtaining at least a score of 10?
Answer
(A)
\(\frac{1}{6}\)
43

In the figure, PQRS is a circle. If chords QR and RS are equal, calculate the value of x

Answer
(D)
40o
44

In the figure, PQ is a parallel to ST and QRS = 40o. Find the value of x

Answer
(A)
55o
45
In the figure, PS = 7cm and RY = 9cm. IF the area of parallelogram PQRS is 56cm2. Find the area of trapezium PQTS
Answer
(C)
120cm2