Q5053.Find the value of x for which the function $y = x^3 - x$ has a minimum value.
A$-3$
B$-\frac{3}{2}$
C$\frac{\sqrt{3}}{3}$
D$3$
Correct Answer: C
$y' = 3x^2 - 1 = 0 \Rightarrow x = \pm \frac{1}{\sqrt{3}} = \pm \frac{\sqrt{3}}{3}$. Minimum at $x = \frac{\sqrt{3}}{3}$.
JAMB (UTME)
Mathematics
1999
Q5054.Three boys play a game of luck in which their respective chances of winning are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$. What is the probability that one and only one of the boys wins the game?
Q5057.If the standard deviation of the set of numbers $3, 6, x, 7, 5$ is 2, find the least possible value of x.
A$2$
B$3$
C$4$
D$6$
Correct Answer: A
Mean = $\frac{21+x}{5}$. Variance = $\frac{1}{5} \sum (x_i - \bar{x})^2 = 4$. Solving gives $x = 2$ or $x = 7.2$. Least is 2.
JAMB (UTME)
Mathematics
1999
Q5058.How many two digit numbers can be formed from the digits 0, 1, 2, if a digit can be repeated and no number may begin with 0?
A$4$
B$12$
C$16$
D$20$
Correct Answer: A
First digit: 1 or 2 (2 choices). Second digit: 0, 1, 2 (3 choices). Total = 6. (The provided options have errors).
JAMB (UTME)
Mathematics
1999
Q5059.The grades of 36 students in a class test are as shown in the pie chart above. How many students had excellent?
A$7$
B$8$
C$9$
D$12$
Correct Answer: A
Angle for Excellent = $360 - 120 - 80 - 90 = 70^{\circ}$. Number = $\frac{70}{360} \times 36 = 7$.
JAMB (UTME)
Mathematics
1999
Q5060.The marks scored by students in a test are given in the table above. Find the median.
A$7$
B$6$
C$5$
D$4$
Correct Answer: B
Total frequency = 60. Median is average of 30th and 31st. Both are 6. Median = 6.
JAMB (UTME)
Mathematics
1999
Q5061.A student calculated the mean of 5 numbers as 45.3 while rechecking his working, he discovered that his total was short by 20.5. what is the correct mean of the 5 numbers?
A$24.8$
B$41.2$
C$49.4$
D$65.8$
Correct Answer: C
Correct sum = $45.3 \times 5 + 20.5 = 226.5 + 20.5 = 247$. Correct mean = $\frac{247}{5} = 49.4$.
JAMB (UTME)
Mathematics
1999
Q5062.The sectorial allocations to various ministries in a state budget are as follows: Agriculture - $\#25,000,000.00$, Education - $\#20,000,000.00$, Women affairs - $\#35,000,000.00$, Commerce and Industries - $\#20,000,000.00$. In a pie chart to represent this information the corresponding angle to agriculture is
A$25^{\circ}$
B$45^{\circ}$
C$50^{\circ}$
D$90^{\circ}$
Correct Answer: D
Total = $100,000,000$. Angle = $\frac{25}{100} \times 360 = 90^{\circ}$.
JAMB (UTME)
Mathematics
1999
Q5063.The mean of four numbers is 5 and the mean deviation is 3. find the fourth number if the mean deviation of the first three numbers is 2.
A$6$
B$10$
C$11$
D$17$
Correct Answer: C
The question is garbled.
JAMB (UTME)
Mathematics
1999
Q5064.In a regular pentagon, PQRST, PR intersects QS at O. calculate $\angle RQS$.
A$36^{\circ}$
B$72^{\circ}$
C$108^{\circ}$
D$144^{\circ}$
Correct Answer: A
In a regular pentagon, each interior angle is $108^{\circ}$. In triangle QRS, $QR = RS$, so $\angle RQS = \frac{180-108}{2} = 36^{\circ}$.
$P - Q = \{1, x\}$. $(P - Q) \cup R = \{1, x, 2, 3, 4, v, y\}$. (The provided answer D is a typo).
JAMB (UTME)
Mathematics
2000
Q5066.The population of a town was 240,000 in January 1998 and it increased by $2\%$ each year, what would be the population of the town in January 2000?
Q5067.If $\frac{2\sqrt{3} - 2}{\sqrt{3} + 2} = m + n\sqrt{6}$, find the values of m and n respectively
A$1, -2$
B$-2, 1$
C$-\frac{2}{5}, 1$
D$2, \frac{3}{5}$
Correct Answer: A
The question is garbled.
JAMB (UTME)
Mathematics
2000
Q5068.In a youth club with 94 members, 60 like modern music and 50 like traditional music. The number of members who like both traditional and modern music is three times who do not like any type of music. How many members like only one type of music?
A$8$
B$24$
C$62$
D$86$
Correct Answer: C
Let neither be $x$. Both = $3x$. $60 + 50 - 3x + x = 94 \Rightarrow 110 - 2x = 94 \Rightarrow 2x = 16 \Rightarrow x = 8$. Both = 24. Only one = $110 - 2(24) = 62$.
JAMB (UTME)
Mathematics
2000
Q5069.Evaluate $\frac{(2.813 \times 10^{-3}) \times 1.063}{5.637 \times 10^{-2}}$ reducing each number to two significant figures and leaving your answer in two significant figures.
A$0.056$
B$0.054$
C$0.055$
D$0.54$
Correct Answer: B
$\frac{2.8 \times 10^{-3} \times 1.1}{5.6 \times 10^{-2}} = \frac{3.08 \times 10^{-3}}{5.6 \times 10^{-2}} = 0.55 \times 10^{-1} = 0.055$. (The provided answer B is a typo).
JAMB (UTME)
Mathematics
2000
Q5070.A man wishes to keep some money in a savings deposit at $25\%$ compound interest so that after 3 years he can buy a car for $\#150,000$. how much does he need to deposit now?
Q5072.Audu bought an article for $\#50,000$ and sold it to Femi at a loss of $x\%$. Femi later sold the article to Oche at a profit of $40\%$. If Femi made a profit of $\#10,000$ find the value of x.
Q5086.Find the minimum value of the function $f(\theta) = \frac{2}{3} - \cos \theta$ for $0 \le \theta \le 2\pi$.
A$\frac{1}{2}$
B$\frac{2}{3}$
C$1$
D$2$
Correct Answer: A
Minimum when $\cos \theta$ is maximum (1). $f_{min} = \frac{2}{3} - 1 = -\frac{1}{3}$. (The provided options have errors).
JAMB (UTME)
Mathematics
2000
Q5087.A frustum of a pyramid with square base has its upper and lower sections as squares of sizes 2m and 5m respectively and the distance between them 6m find the height of the pyramid from which the frustum was obtained.
A$8.0\text{m}$
B$8.4\text{m}$
C$9.0\text{m}$
D$10.0\text{m}$
Correct Answer: D
By similar triangles, $\frac{h}{2.5} = \frac{h-6}{1} \Rightarrow h = 2.5h - 15 \Rightarrow 1.5h = 15 \Rightarrow h = 10\text{m}$.
JAMB (UTME)
Mathematics
2000
Q5088.P is a point on one side of the straight line UV and P moves in the same direction as UV. If the straight line ST is on the locus of P and $\angle VUS = 50^{\circ}$ find $\angle UST$.
A$50^{\circ}$
B$130^{\circ}$
C$100^{\circ}$
D$80^{\circ}$
Correct Answer: B
The locus is a line parallel to UV. $\angle UST = 180 - 50 = 130^{\circ}$.
JAMB (UTME)
Mathematics
2000
Q5089.A ship sails a distance of 50km in the direction $550^{\circ}E$ and then sails a distance of 50km in the direction $N40^{\circ}E$. find the bearing of the ship from its original position.
A$045^{\circ}$
B$090^{\circ}$
C$135^{\circ}$
D$180^{\circ}$
Correct Answer: B
The ship sails 50km at $55^{\circ}$ and then 50km at $50^{\circ}$. The bearing is approximately $90^{\circ}$.
JAMB (UTME)
Mathematics
2000
Q5090.An equilateral triangle of side 3cm is inscribed in a circle. Find the radius of the circle.
Q5092.In the diagram above, if $\angle RPS = 50^{\circ}$, $\angle RPQ = 30^{\circ}$ and $PQ = QR$ find the value of $\angle PRS$
A$50^{\circ}$
B$60^{\circ}$
C$70^{\circ}$
D$80^{\circ}$
Correct Answer: A
The question is incomplete.
JAMB (UTME)
Mathematics
2000
Q5093.In the diagram above, EFGH is a circle center O. FH is a diameter and GE is a chord which meets FH at right angle at the point N. if $NH = 8\text{cm}$ and $EG = 24\text{cm}$, calculate FH.
Q5096.A predator moves in a circle of radius 2 centre (0, 0), while a prey moves along the line $y = x$. If $0 \le x \le 2$, at which point(s) will they meet?
A$(1, 1)$ only
B$(1, 1)$ and $(1, 2)$
C$(\sqrt{2}, \sqrt{2})$
D$(\sqrt{2}, -\sqrt{2})$
Correct Answer: C
$x^2 + y^2 = 4$ and $y = x$. $2x^2 = 4 \Rightarrow x = \sqrt{2}$. Point is $(\sqrt{2}, \sqrt{2})$.
JAMB (UTME)
Mathematics
2000
Q5097.Find the value of $\frac{\cos^2 \theta - 1}{\sin^2 \theta}$
A$1$
B$-1$
C$0$
D$2$
Correct Answer: B
$\cos^2 \theta - 1 = -\sin^2 \theta$. Ratio = $-1$.
Q5099.A bowl is designed by revolving completely the area enclosed by $y = x^2 - 1$, $y = 0$, $y = 3$ and $x \ge 0$ around the y-axis. What is the volume of this bowl?
