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.
Хариулт
(C)
5≤X≤10
2
If \(1P03{_4} = 115_{10}\) find P
Хариулт
(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 \(\frac{p}{q}\)
Хариулт
(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
Хариулт
(C)
\(\frac{8}{27}\)
5
if a = -3, b = 2, c = 4, evaluate \(\frac{a^3 - b^3 - c^{\frac{1}{2}}}{b - a - c}\)
Хариулт
(D)
-37
6
If (g(y)) = \(\frac{y - 3}{11}\) + \(\frac{11}{y^2 - 9}\). what is g(y + 3)?
Хариулт
(A)
\(\frac{y}{11} + \frac{11}{y(y + 6)}\)
7
Factorize completely \((x^2 + x)^2 - (2x + 2)^2\)
Хариулт
(D)
(x + 1)² (x + 2)(x - 2)
8
Simplify \(\frac{x - y}{x^{\frac{1}{3}} - y^{\frac{1}{3}}}\)
Хариулт
(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?
Хариулт
(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?
Хариулт
(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
Хариулт
(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
Хариулт
(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
Хариулт
(B)
91
14
Find correct to one decimal place, 0.24633 \(\div\) 0.0306
Хариулт
(D)
8.1
15
In a class of 150 students, the sector in a pie chart representing the students offering Physics has angle 12^o. How many students are offering Physics?
Хариулт
(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
Хариулт
(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
Хариулт
(B)
30
18
Four interior angles of a pentagon are 90^o - x^o, 90^o + x^o, 110^o - 2x^o, 110^o + 2x^o. Find the fifth interior angle
Хариулт
(D)
140^o
19
For which of the following exterior angles is a regular polygon possible? i. 35° ii. 18° iii. 15°
Хариулт
(C)
ii and iii
20
Simplify \(\frac{1\frac{1}{2}}{2 \div \frac{1}{4} \text{of } 32}\)
Хариулт
(C)
6
21
A 5.0g of salt was weighted by Tunde as 5.1g. What is the percentage error?
Хариулт
(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.
Хариулт
(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
Хариулт
(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?
Хариулт
(C)
N2,800.00
25
Evaluate \(\frac{8^{\frac{1}{3}} \times 5^{\frac{2}{3}}}{10^{\frac{2}{3}}}\)
Хариулт
(D)
3\(\sqrt{2}\)
26
If \(log_{10} 2 = 0.3010\) and \(log_{10} 3 = 0.4771\), evaluate; without using logarithm tables, \(log_{10} 4.5\)
Хариулт
(C)
0.6532
27
Find m such that (m + \(\sqrt{3}\))(1 - \(\sqrt{3}\))² = 6 - 2\(\sqrt{2}\)
Хариулт
(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
Хариулт
(D)
4.50 x 10^-5m
29
Simplify \(\frac{x + 2}{x + 1}\) - \(\frac{x - 2}{x + 2}\)
Хариулт
(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
Хариулт
(C)
-\(\frac{1}{r^2}\)
31
List the integral values of x which satisfy the inequality -1 < 5 - 2x \(\geq\) 7
Хариулт
(A)
-1, 0, 1, 2
32
Given that 3x - 5y - 3 = 0, 2y - 6x + 5 = 0 the value of (x, y) is
Хариулт
(D)
(\(\frac{19}{24}, \frac{-1}{8}\))
33
The solution of the quadratic equation px² + qx + b = 0 is
Хариулт
(C)
\(\frac{-q \pm \sqrt{ q^2 - 4bp}}{2p}\)
34
Simplify \(\frac{1}{x^2 + 5x + 6}\) + \(\frac{1}{x^2 + 3x + 2}\)
Хариулт
(C)
\(\frac{2}{(x + 1)(x + 3)}\)
35
Simplify \(\frac{4a^2 - 49b^2}{2a^2 - 5ab - 7b^2}\)
Хариулт
(D)
\(\frac{2a + 7b}{a + b}\)
36
If cot \(\theta\) = \(\frac{x}{y}\), find cosec\(\theta\)
Хариулт
(C)
\(\frac{1}{y}\)\(\sqrt{x^2 + y^2}\)
37
In triangle PQR, PQ = 1cm, QR = 2cm and PQR = 120^o Find the longest side of the triangle
Хариулт
(B)
\(\sqrt{7}\)cm
38
If \(\cos^2 \theta + \frac{1}{8} = \sin^2 \theta\), find \(\tan \theta\).
Хариулт
(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
Хариулт
(B)
110\(\pi\)cm³
40
PQR is a triangle in which PQ = 10cm and QPR = 60^oS 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
Хариулт
(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
Хариулт
(C)
1.0
42
If two dice are thrown together, what is the probability of obtaining at least a score of 10?
Хариулт
(A)
\(\frac{1}{6}\)
43
In the figure, PQRS is a circle. If chords QR and RS are equal, calculate the value of x
Хариулт
(D)
40^o
44
In the figure, PQ is a parallel to ST and QRS = 40o. Find the value of x
Хариулт
(A)
55^o
45
In the figure, PS = 7cm and RY = 9cm. IF the area of parallelogram PQRS is 56cm². Find the area of trapezium PQTS
Хариулт
(C)
120cm²