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