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Instruction
JAMB Mathematics 1998
JAMB (UTME)
Mathematics
1998
Q5001.From the top of a vertical mast 150m high, two huts on the same ground level are observed. One due east and the other due west of the mast. Their angles of depression are $60^{\circ}$ and $45^{\circ}$ respectively. Find the distance between the huts.
A$150(1 + \sqrt{3})\text{m}$
B$50(\sqrt{3} + 3)\text{m}$
C$150\text{m}$
D$50\sqrt{3}\text{m}$
Correct Answer: A
Distance = $150 \cot 45^{\circ} + 150 \cot 60^{\circ} = 150 + 50\sqrt{3} = 50(3 + \sqrt{3})$. (The provided answer A is a typo).
Q5010.A bag contains 16 red balls and 20 blue balls only. How many white balls must be added to the bag so that the probability of randomly picking a red ball is equal to $\frac{2}{5}$?
Q5011.The pie chart above shows the monthly expenditure of a public servant. The monthly expenditure on housing is twice that of school fees. How much does the worker spend on housing if his monthly income is $\#7,200$?
A$\#1000$
B$\#2000$
C$\#3000$
D$\#4000$
Correct Answer: B
Angle for Food = $120^{\circ}$. Angle for Transport = $90^{\circ}$. Remaining = $150^{\circ}$. Housing = $2 \times$ School fees. $3 \times$ School fees = $150^{\circ} \Rightarrow$ School fees = $50^{\circ}$, Housing = $100^{\circ}$. Amount = $\frac{100}{360} \times 7200 = \#2000$.
JAMB (UTME)
Mathematics
1998
Q5012.The bar chart above shows the distribution of marks scored by 60 pupils in a test in which the maximum score was 10. if the pass mark was 5, what percentage of the pupils failed the test?
A$59.4\%$
B$50.0\%$
C$41.7\%$
D$25.0\%$
Correct Answer: A
Number of pupils who scored less than 5 = $1+3+4+7+9 = 24$. Percentage = $\frac{24}{60} \times 100 = 40\%$. (The provided answer A is a typo).
JAMB (UTME)
Mathematics
1998
Q5013.In a recent zonal championship games involving 10 teams, teams X and Y were given probabilities $\frac{2}{5}$ and $\frac{1}{3}$ respectively of winning the gold in the football event. What is the probability that either team will win the gold?
Q5014.If x, y can take values from the set $\{1,2,3,4\}$, find the probability that the product of x and y is not greater than 6.
A$\frac{5}{8}$
B$\frac{5}{16}$
C$\frac{1}{2}$
D$\frac{3}{8}$
Correct Answer: A
Total outcomes = 16. Favorable: (1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(3,1),(3,2),(4,1) = 10. Probability = $\frac{10}{16} = \frac{5}{8}$.
Instruction
JAMB Mathematics 1999
JAMB (UTME)
Mathematics
1999
Q5015.If $(a^2b^3c)^3 / a^3b^2c^5 = 1$, what is the value of $p + 2q$?
A$\frac{5}{2}$
B$-\frac{5}{4}$
C$-\frac{25}{4}$
D$4$
Correct Answer: B
The question is garbled.
JAMB (UTME)
Mathematics
1999
Q5016.Find the value of $x$ if $\frac{2}{x+2} = \frac{1}{x-2}$
A$3+2\sqrt{2}$
B$3-2\sqrt{2}$
C$3-2\sqrt{2}$
D$4+2\sqrt{2}$
Correct Answer: A
$2(x-2) = x+2 \Rightarrow 2x - 4 = x + 2 \Rightarrow x = 6$. (The provided options have errors).
JAMB (UTME)
Mathematics
1999
Q5017.A trader bought 100 oranges at 5 for $\#1.20$, 20 oranges got spoilt and the remaining were sold at 4 for $\#1.50$. Find the percentage gain or loss.
$\frac{1.725}{0.0043125} = 400$. (The provided answer C is a typo).
JAMB (UTME)
Mathematics
1999
Q5022.If $\log_{10} x = a$, evaluate $\log_5 \sqrt{x}$ in terms of $a$.
A$\frac{a}{2}$
B$\frac{a}{2} - 1$
C$\frac{a}{2} - 1$
D$\frac{a}{2} - 1$
Correct Answer: A
$\log_5 \sqrt{x} = \frac{1}{2} \log_5 x = \frac{1}{2} \times \frac{\log_{10} x}{\log_{10} 5} = \frac{a}{2 \log_{10} 5}$. (The provided options have errors).
JAMB (UTME)
Mathematics
1999
Q5023.A group of market women sell at least one of yam, plantain and maize. 12 of them sell maize, 10 sell yam and 14 sell plantain. 5 sell plantain and maize, 4 sell yam and maize, 2 sell yam and plantain only while 3 sell all the three items. How many women are in the group?
A$25$
B$19$
C$18$
D$17$
Correct Answer: A
$n(M \cup Y \cup P) = 12 + 10 + 14 - 5 - 4 - 2 - 2(3) + 3 = 25$. (The provided answer A is a typo).
Q5025.A binary operation $*$ is defined by $a * b = ab + b$ for any real number $a$ and $b$. if the identity element is zero, find the inverse of 2 under this operation.
A$\frac{2}{3}$
B$\frac{1}{2}$
C$-\frac{1}{2}$
D$-\frac{2}{3}$
Correct Answer: A
$2 * x = 0 \Rightarrow 2x + x = 0 \Rightarrow 3x = 0 \Rightarrow x = 0$. (The provided options have errors).
JAMB (UTME)
Mathematics
1999
Q5026.The first term of a geometrical progression is twice its common ratio. Find the sum of the first two terms of the progression if its sum to infinity is 8.
A$\frac{72}{25}$
B$\frac{56}{9}$
C$\frac{45}{9}$
D$\frac{56}{9}$
Correct Answer: B
$a = 2r$. $S_{\infty} = \frac{a}{1-r} = \frac{2r}{1-r} = 8 \Rightarrow 2r = 8 - 8r \Rightarrow 10r = 8 \Rightarrow r = 0.8$. $a = 1.6$. Sum of first two terms = $a + ar = 1.6 + 1.28 = 2.88 = \frac{72}{25}$. (The provided answer B is a typo).
JAMB (UTME)
Mathematics
1999
Q5027.Tope bought $x$ oranges at $\#5.00$ each and some mangoes at $\#4.00$ each. If she bought twice as many mangoes as oranges and spent at least $\#28$ and at most $\#$, find the range of the value of $x$.
A$4 < x < 5$
B$5 < x < 8$
C$5 < x < 10$
D$8 < x < 10$
Correct Answer: C
$5x + 4(2x) = 13x$. $28 \le 13x \le 130 \Rightarrow 2.15 \le x \le 10$. (The provided options have errors).
JAMB (UTME)
Mathematics
1999
Q5028.If $m n = \frac{m}{n} - \frac{n}{m}$ for $m, n \in R$, evaluate $-3 4$
A$-\frac{25}{12}$
B$-\frac{7}{12}$
C$\frac{7}{12}$
D$\frac{25}{12}$
Correct Answer: B
$-3 * 4 = \frac{-3}{4} - \frac{4}{-3} = -\frac{3}{4} + \frac{4}{3} = \frac{-9+16}{12} = \frac{7}{12}$. (The provided answer B is a typo).
JAMB (UTME)
Mathematics
1999
Q5029.Find the matrix T if $ST = I$ where $S = \begin{pmatrix} -1 & 1 \\ 1 & -2 \end{pmatrix}$ and I is the identity matrix.
By similar triangles, $\frac{l}{3} = \frac{l+4}{6} \Rightarrow 6l = 3l + 12 \Rightarrow 3l = 12 \Rightarrow l = 4$. (The provided answer B is a typo).
JAMB (UTME)
Mathematics
1999
Q5039.Find the length XZ in the triangle above
A$7\text{m}$
B$6\text{m}$
C$5\text{m}$
D$3\text{m}$
Correct Answer: A
$XZ^2 = 2^2 + 1^2 - 2(2)(1)\cos 120^{\circ} = 4 + 1 + 2 = 7$. $XZ = \sqrt{7}$. (The provided answer A is a typo).
JAMB (UTME)
Mathematics
1999
Q5040.Find a positive value of a if the coordinate of the centre of a circle $x^2 + y^2 - 2ax + 4y - a = 0$ is $(a, -2)$ and the radius is 4 units
A$1$
B$2$
C$3$
D$4$
Correct Answer: A
Centre = $(a, -2)$. Radius = $\sqrt{a^2 + 4 + a} = 4 \Rightarrow a^2 + a + 4 = 16 \Rightarrow a^2 + a - 12 = 0 \Rightarrow (a+4)(a-3) = 0 \Rightarrow a = 3$. (The provided answer A is a typo).
JAMB (UTME)
Mathematics
1999
Q5041.A man 1.7m tall observes a bird on top of a tree at an angle of $30^{\circ}$. if the distance between the man's head and the bird is 25m, what is the height of the tree?
A$26.7\text{m}$
B$14.2\text{m}$
C$(1.7 + 25\sqrt{3})\text{m}$
D$(1.7 + 25\sqrt{2})\text{m}$
Correct Answer: B
Height above man's head = $25 \sin 30^{\circ} = 12.5$. Total height = $12.5 + 1.7 = 14.2\text{m}$.
JAMB (UTME)
Mathematics
1999
Q5042.In the figure above, TZ is tangent to the circle QPZ. Find x if $TZ = 6$ units and $PQ = 9$ units.
A$-\frac{7}{4}$
B$\frac{7}{8}$
C$\frac{7}{4}$
D$\frac{7}{2}$
Correct Answer: C
$TZ^2 = TP \times TQ$. $36 = x(x+9) \Rightarrow x^2 + 9x - 36 = 0 \Rightarrow (x+12)(x-3) = 0 \Rightarrow x = 3$. (The provided answer C is a typo).
JAMB (UTME)
Mathematics
1999
Q5043.Find the tangent of the acute angle between the lines $2x + y = 3$ and $3x - 2y = 5$
Q5045.In the diagram above, EFGH is a cyclic quadrilateral in which EH // FG and FH are chords. If $\angle FHG = 42^{\circ}$ and $\angle FGH = 34^{\circ}$, calculate $\angle HEG$
