Q4854.In the figure above, $XYZ = 30^{\circ}$, $YXZ = 105^{\circ}$ and $XY = 8\text{cm}$. Calculate $YZ$.
A$16\sqrt{2}\text{ cm}$
B$8\sqrt{2}\text{ cm}$
C$4\sqrt{2}\text{ cm}$
D$2\sqrt{2}\text{ cm}$
Correct Answer: B
$\angle YZX = 180 - 30 - 105 = 45^{\circ}$. By sine rule: $\frac{YZ}{\sin 105} = \frac{8}{\sin 45} \Rightarrow YZ = 8 \times \frac{\sin 105}{\sin 45} = 8 \times \frac{0.9659}{0.7071} \approx 10.9$. (The provided options have errors).
JAMB (UTME)
Mathematics
1990
Q4855.In the figure above $PQR$ is a semicircle. Calculate the area of the shaded region.
A$125\frac{2}{7}\text{ cm}^2$
B$149\frac{2}{7}\text{ cm}^2$
C$243\frac{1}{7}\text{ cm}^2$
D$267\frac{1}{7}\text{ cm}^2$
Correct Answer: A
Area of semicircle = $\frac{1}{2} \times \frac{22}{7} \times 7^2 = 77$. Area of triangle = $\frac{1}{2} \times 6 \times 8 = 24$. Shaded area = $77 - 24 = 53$. (The provided options have errors).
JAMB (UTME)
Mathematics
1990
Q4856.A cylindrical pipe, made of metal is $3\text{cm}$, thick if the internal radius of the pipe is $10\text{cm}$. Find the volume of metal used in making $3\text{m}$ of the pipe
Q4858.Find the curved surface area of the frustum in the figure.
A$16\sqrt{10}\text{ cm}$
B$20\sqrt{10}$
C$24$
D$24$
Correct Answer: B
Slant height = $\sqrt{6^2 + (6-4)^2} = \sqrt{36+4} = \sqrt{40} = 2\sqrt{10}$. Curved surface area = $\pi(R+r)l = \frac{22}{7}(6+4) \times 2\sqrt{10} \approx 198.6$. (The provided options have errors).
JAMB (UTME)
Mathematics
1990
Q4859.The locus of a point which moves so that it is equidistant from two intersecting straight lines is the
Aperpendicular bisector of the two lines
Bangle bisector of the two lines
Cbisector of the two lines
Dline parallel to the two lines
Correct Answer: B
The locus is the angle bisector.
JAMB (UTME)
Mathematics
1990
Q4860.$4, 16, 30, 20, 10, 14$ and $26$ are represented on a pie chart. Find the sum of the angles of the sectors representing all numbers equal to or greater than $16$.
Q4873.If $U = \{S, P, L, E, N, D, O, U, R\}$, $X = \{S, P, E, N, D\}$, $Y = \{P, N, O, U, R\}$. Find $X \cap (Y' \cup Z)$
A$\{P, O, U, R\}$
B$\{S, P, D, R\}$
C$\{P, N, D\}$
D$\{N, D, U\}$
Correct Answer: C
The question is incomplete.
JAMB (UTME)
Mathematics
1996
Q4874.A survey of 100 students in an institution shows that 80 students speak Hausa and 20 students Igbo, while only 9 students speak both languages. How many students neither Hausa nor Igbo?
Let $u = \frac{1}{x}, v = \frac{1}{y}$. $2u - 3v = 2$, $4u + v = 10$. Solving gives $u = 2, v = \frac{2}{3}$. $x = \frac{1}{2}, y = \frac{3}{2}$. (The provided answer C is a typo).
JAMB (UTME)
Mathematics
1996
Q4877.Find the minimum value of $x^2 - 3x + 2$ for all real values of x.
Q4885.Two binary operations $*$ and $\oplus$ are defined as $m n = mn - n - 1$ and $m \oplus n = mn + n - 2$ for all real numbers m, n. find the values of $3 \oplus (4 5)$.
Q4889.Each of the base angles of an isosceles triangle is $58^{\circ}$ and all the vertices of the triangle lie on a circle. Determine the angle which the base of the triangle subtends at the centre of the circle.
A$64^{\circ}$
B$116^{\circ}$
C$128^{\circ}$
D$148^{\circ}$
Correct Answer: C
Vertex angle = $180 - 2(58) = 64^{\circ}$. Angle at centre = $2 \times 64 = 128^{\circ}$.
JAMB (UTME)
Mathematics
1996
Q4890.From the figure above, FK // GR and FH = GH, $\angle RFK = 34^{\circ}$ and $\angle FGH = 47^{\circ}$, calculate the angle marked x.
Q4891.The figure above shows circles of radii 3cm and 2cm with centres at X and Y respectively. The circles have a transverse common tangent of length 25cm. Calculate XY.
A$630\text{cm}$
B$626\text{cm}$
C$615\text{cm}$
D$600\text{cm}$
Correct Answer: B
$XY = \sqrt{25^2 + (3+2)^2} = \sqrt{625 + 25} = \sqrt{650} \approx 25.5$. (The provided options have errors).
JAMB (UTME)
Mathematics
1996
Q4892.A chord of a circle diameter 42cm subtends an angle of $60^{\circ}$ at the centre of the circle. Find the length of the minor arc.
Q4893.An arc of a circle subtends an angle of $70^{\circ}$ at the centre. If the radius of the circle is 6cm, calculate the area of the sector subtended by the given angle.
Volume = $\frac{1}{2} \times 6 \times 5 \times 10 = 150\text{cm}^3$. (The provided answer A is a typo).
JAMB (UTME)
Mathematics
1996
Q4895.A cone with the sector angle of $45^{\circ}$ is cut out of a circle of radius r cm. find the base radius of the cone.
A$\frac{r}{16}\text{cm}$
B$\frac{r}{8}\text{cm}$
C$\frac{r}{4}\text{cm}$
D$\frac{r}{2}\text{cm}$
Correct Answer: B
Arc length = $\frac{45}{360} \times 2\pi r = \frac{\pi r}{4}$. Circumference of cone = $2\pi R = \frac{\pi r}{4} \Rightarrow R = \frac{r}{8}$.
JAMB (UTME)
Mathematics
1996
Q4896.A point P moves so that it is equidistant from points L and M. if LM is 16cm, find the distance of P from LM when P is 10cm from L.
A$12\text{cm}$
B$10\text{cm}$
C$8\text{cm}$
D$6\text{cm}$
Correct Answer: D
P is on the perpendicular bisector. Distance from midpoint = $\sqrt{10^2 - 8^2} = \sqrt{100-64} = 6\text{cm}$.
JAMB (UTME)
Mathematics
1996
Q4897.The angle between the positive horizontal axis and a given line is $135^{\circ}$. find the equation of the line if it passes through the point (2, 3).
A$x - y = 1$
B$x + y = 1$
C$x + y = 5$
D$x - y = 5$
Correct Answer: C
Slope = $\tan 135^{\circ} = -1$. $y - 3 = -1(x - 2) \Rightarrow y - 3 = -x + 2 \Rightarrow x + y = 5$.
JAMB (UTME)
Mathematics
1996
Q4898.Find the distance between the point Q(4, 3) and the point common to the lines $2x - y = 4$ and $x + y = 2$
A$\sqrt{10}$
B$\sqrt{5}$
C$\sqrt{26}$
D$\sqrt{13}$
Correct Answer: A
Intersection: $2x - (2-x) = 4 \Rightarrow 3x = 6 \Rightarrow x=2, y=0$. Distance = $\sqrt{(4-2)^2 + (3-0)^2} = \sqrt{4+9} = \sqrt{13}$. (The provided answer A is a typo).
JAMB (UTME)
Mathematics
1996
Q4899.The angle of elevation of a building from a measuring instrument placed on the ground is $30^{\circ}$. if the building is 40m high, how far is the instrument from the foot of the building?
