JAMB - Mathematics (1984)

1
Simplify \(\frac{(\frac{2}{3} - \frac{1}{5}) - \frac{1}{3} \text{of} \frac{2}{5}}{3 - \frac{1}{1 \frac{1}{2}}}\)
Răspuns
(A)
\(\frac{1}{7}\)
2
\(\frac{0.0001432}{1940000}\) = k x 10ⁿ where 1 \(\leq\) k < 10 and n is a whole number. The values K and n are
Răspuns
(A)
7.381 qnd -11
3
P sold his bicycle to Q at a profit of 10%. Q sold it to R for N209 at a loss of 5%. How much did the bicycle cost P?
Răspuns
(A)
N200
4
If the price of oranges was raised by \(\frac{1}{2}\)k per orange. The number of oranges a customer can buy for N2.40 will be less by 16. What is the present price of an orange?
Răspuns
(A)
2\(\frac{1}{2}\)
5
A man invested a total of N50000 in two companies. If these companies pay dividends of 6% and 8% respectively, how much did he invest at 8% if the total yield is N3700?
Răspuns
(E)
N35 000
6
Thirty boys and x girls sat for a test. The mean of the boys' scores and that of the girls were respectively 6 and 8. Find x if the total scores was 468
Răspuns
(C)
36
7
The cost of production of an article is made up as follows: Labour N70, Power N15, Materials N30, Miscellaneous N5. Find the angle of the sector representing Labour in a pie chart
Răspuns
(A)
210^o
8
Bola choose at random a number between 1 and 300. What is the probability that the number is divisible by 4?
Răspuns
(E)
\(\frac{37}{149}\)
9
Find, without using logarithm tables, the value of \(\frac{log_3 27 - log_{\frac{1}{4}} 64}{log_3 \frac{1}{81}}\)
Răspuns
(B)
\(\frac{-3}{2}\)
10
A variable point p(x, y) traces a graph in a two-dimensional plane. (0, 3) is one position of P. If x increases by 1 unit, y increases by 4 units. The equation of the graph is
Răspuns
(D)
4x = y + 3
11
A trader in country where their currency 'MONI'(M) is in base five bought 103₅ oranges at M14₅ each. If he sold the oranges at M24₅ each, what will be his gain?
Răspuns
(B)
1030₅
12
Rationalize \(\frac{5\sqrt{7} - 7\sqrt{5}}{\sqrt{7} - \sqrt{5}}\)
Răspuns
(C)
-\(\sqrt{35}\)
13
Simplify \(\frac{3^n - 3^{n - 1}}{3^3 \times 3^n - 27 \times 3^{n - 1}}\)
Răspuns
(C)
\(\frac{1}{27}\)
14
p varies directly as the square of q and inversely as r. If p = 36, when q = 3, when r = 4, find p when q = 5 and r = 2.
Răspuns
(D)
200
15
Factorize 6x2 - 14x - 12
Răspuns
(C)
2(x - 3)(3x + 2)
16
A straight line y = mx meets the curve y = x2 - 12x + 40 in two distinct points. If one of them is (5, 5) find the other
Răspuns
(E)
(7, 5)
17
The table below is drawn for a graph y = x³ - 3x + 1
\(\begin{array}{c|c} x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\\hline y = x^3 - 3x + 1 & 1 & -1 & 3 & 1 & -1 & 3 & 1\end{array}\)
From x = -2 to x = 1, the graph crosses the x-axis in the range(s)
Răspuns
(B)
-2 < x < -1 and 0 < x < 1
18
In a racing competition, Musa covered a distance 5x km in the first hour and (x + 10)km in the next hour. He was second to Nzozi who covered a total distance of 118km in the two hours. Which of the following inequalities is correct?
Răspuns
(C)
0 \(\leq\) x < 18
19
If 2x + 3y = 1 and x - 2y = 11, find (x + y)
Răspuns
(D)
2
20
Tunde and Shola can do a piece of work in 18 days. Tunde can do it alone in x days, whilst Shola takes 15 days longer to do it alone. Which of the following equations is satisfied by x?
Răspuns
(C)
x² - 21x - 270 = 0
21
If f(x) = 2(x - 3)\(^2\) + 3(x - 3) + 4 and g(y) = \(\sqrt{5 + y}\), find g [f(3)] and f[g(4)].
Răspuns
(A)
3 and 4
22
The quadratic equation whose roots are 1 - \(\sqrt{13}\) and 1 + \(\sqrt{13}\) is?
Răspuns
(B)
x² - 2x - 12 = 0
23
Find a factor which is common to all three binomial expressions 4a2 - 9b2, 8a3 + 27b3, (4a + 6b)2
Răspuns
(C)
2a + 3b
24
If (x - 2) and (x + 1) are factors of the expression x³ + px² + qx + 1, what is the sum of p and q
Răspuns
(B)
-3
25
A cone is formed by bending a sector of a circle having an angle of 210^o. Find the radius of the base of the cone if the diameter of the circle is 12cm.
Răspuns
(E)
3.50cm
26
The sides of a triangle are(x + 4)cm, xcm and (x - 4)cm, respectively If the cosine of the largest angle is \(\frac{1}{5}\), find the value of x
Răspuns
(A)
24cm
27
If a = \(\frac{2x}{1 - x}\) and b = \(\frac{1 + x}{1 - x}\), then a2 - b2 in the simplest form is
Răspuns
(A)
\(\frac{3x + 1}{x - 1}\)
28
Simplify (1 + \(\frac{\frac{x - 1}{1}}{\frac{1}{x + 1}}\))(x + 2)
Răspuns
(B)
x²(x + 2)
29
If pq + 1 = q² and t = \(\frac{1}{p}\) - \(\frac{1}{pq}\) express t in terms of q
Răspuns
(C)
\(\frac{1}{q + 1}\)
30
The cumulative frequency function of the data below is given below by the equation y = cf(x). What is cf(5)?
\(\begin{array}{c|c} Score(n) & Frequency(f)\\\hline 3 & 30\\ 4 & 32\\ 5 & 30\\ 6 & 35\\8 & 20 \end{array}\)
Răspuns
(E)
92
31
A right circular cone has a base radius r cm and a vertical angle 2y^o. The height of the cone is
Răspuns
(C)
r cot y^o cm
32
Two fair dice are rolled. What is the probability that both show up the same number of points.
Răspuns
(E)
\(\frac{1}{6}\)
33
The larger value of y for which (y - 1)² = 4y - 7 is
Răspuns
(B)
4
34
If sin \(\theta\) = \(\frac{x}{y}\) and 0^o < 90^o then find \(\frac{1}{tan\theta}\)
Răspuns
(D)
\(\frac{y^2 - x^2}{x}\)
35
Measurements of the diameters, in centimeters, in centimeters, of 20 copper spheres are distributed as shown below
\(\begin{array}{c|c} \text{Class boundary in cm} & \text{frequency} & \\\hline 3.35 - 3.45 & 3\\ 3.45 - 3.55 & 6\\ 3.55 - 3.65 & 7\\ 3.65 - 3.75 & 4\end{array}\)
What is the mean diameter of the copper spheres?
Răspuns
(C)
3.56cm
36
What is the volume of this regular three dimensional figure?
Răspuns
(B)
48cm²
37
Using \(\bigtriangleup\)XYZ in the figure, find XYZ
Răspuns
(D)
31^o 18'
38
Find the area of the shaded portion of the semicircular figure.
Răspuns
(B)
\(\frac{r^2}{4}(2 \pi - 3 \sqrt{3})\)
39
In the figure, PQRSTW is a regular hexagon. QS intersects RT at V. Calculate TVS
Răspuns
(A)
60^o
40
In the figure, QRS is a line, PSQ = 35o, SPR = 30o and O is the centre of the circle. Find OQP.
Răspuns
(D)
25^o