JAMB UTME - Mathematics - 2018
Pregunta 1 Informe
Detalles de la respuesta
Second quadrant: Sin is positive, Cos is negative and Tan is negative
Third quadrant: Tan is positive, Sin is negative and Cos is negative
Fourth quadrant: Cos is positive, Sin is negative and Tan is negative
The correct option is the third quadrant only where Tanθ is positive and Sinθ is negative
Pregunta 2 Informe
\[ P=\left[\frac{Q(R-T)}{15}\right]^{\frac{1}{3}} \]
Make T the subject of the relation.
Detalles de la respuesta
P3=Q(R−T)15
15P3=Q(R−T)
15P3Q=R−T
T=R−15P3Q
Pregunta 4 Informe
The table shown gives the marks scored by a group of student in a test. Use the table to answer the question given.
| Mark | 0 | 1 | 2 | 3 | 4 | 5 |
| Frequency | 1 | 2 | 7 | 5 | 4 | 3 |
What is the probability of selecting a student from the group that scored 2 or 3?
Detalles de la respuesta
Pregunta 5 Informe
Detalles de la respuesta
Pr(product of x and y NOT > 6) = 816 = 12
Pregunta 6 Informe
The table shown gives the marks scored by a group of student in a test. Use the table to answer the question given.
| Mark | 0 | 1 | 2 | 3 | 4 | 5 |
| Frequency | 1 | 2 | 7 | 5 | 4 | 3 |
What is the median mark?
Detalles de la respuesta
Median is the middle number
= Nth2
Term = 22th2 = 11th term
Going in ascending order, 11th term is 3, going in descending order 11th term is 3
Median = 3 + 32 = 62 = 3
Pregunta 7 Informe
Detalles de la respuesta
= 6×5×4×3×2×12×1
= 360
Pregunta 8 Informe
Find the values of x for which
\( \frac{x+2}{4} - \frac{2x-3}{3} < 4 \)
Detalles de la respuesta
3x+6−(8x−12)12<4
−5x+1812<4
−5x+18<48
−5x<30
x>−6
Pregunta 9 Informe
Detalles de la respuesta
a2=122+92
a=√122+92
a=15 m
b2=152+82
b=√152+82
b=17 m
cosθ=ab=1517
Pregunta 10 Informe
Detalles de la respuesta
Pregunta 11 Informe
A trader realises 10x - x\(^{2}\) Naira profit from the sale of x bags of corn. How many bags will give him the maximum profit?
Detalles de la respuesta
Maximum profit can be achieved when the differential of profit with respect to number of bags(x) is 0
i.e. δpδx = 0
δpδx = 10 - 2x = 0
10 = 2x
Then x = 102 = 5
Pregunta 12 Informe
Detalles de la respuesta
HCF of 80, 64, 48 = 16
960 ÷ 16 = 60
Pregunta 13 Informe
Detalles de la respuesta
Pregunta 14 Informe
\[ \frac{0.00256 \times 0.0064}{0.025 \times 0.08} \]
Detalles de la respuesta
Explanation:
=0.0000163840.002
=0.008192
Pregunta 15 Informe
Which one of the following gives the members of the set \(A^c \cap B \cap C\)?
Detalles de la respuesta
B = {r, s. t, u}
C = {t, u, v, w, x}
A1 n B n C = elements common to the three sets = none = empty set = Φ
Pregunta 16 Informe
If \[ N=\begin{pmatrix}3 & 5 & -4 \\ 6 & -3 & -5 \\ -2 & 2 & 1\end{pmatrix} \] , find \(|N|\).
Detalles de la respuesta
3(-3 + 10) - 5(6 - 10) - 4(12 - 6)
3(7) - 5(-4) - 4(6) = 17
Pregunta 17 Informe
In the figure below, /MX/ = 8cm, /XN/ = 12cm, /NZ/ = 4cm and ∠ XMN = ∠ XZY. Calculate /YM/
Detalles de la respuesta
∠ XMN = ∠ XZY
Angle X is common
So, ∠ XNM = ∠ XYZ
Then from the angle relationship
XMXZ = XNXY = MNZY
XM = 8, XZ = 12 + 4 = 16,
XN = 12, XY = 8 + YM
816 = 12(8+YM)
Cross multiply
8(8 + YM) = 192
64 + 8YM = 192
8YM = 128
YM = 1288
= 16cm
Pregunta 18 Informe
Detalles de la respuesta
Every 6 months that can be counted on the eight month of the third year is 5
(i.e. 2 times in the first year, 2 times in the second year and once in the third year)
His salary then = initial salary + increment
= 540 + 5(36)
= 540 + 180
= ₦720.00
It can also be solves using a sequence in form of an AP
Pregunta 19 Informe
Detalles de la respuesta
Pregunta 20 Informe
Detalles de la respuesta
Using 90 as the angle for transport
So, x + 2x + 120 + 90 = 360
3x + 210 = 3605
3x = 360 - 210
= 150
x = 1503 = 50
So the angle for housing is 2x = 2 × 50
= 100
Amount spent on housing = 100360 × 7200
= ₦2000
Pregunta 21 Informe
Solve for t in the equation \( \frac{3}{4}t + \frac{1}{3}(21 - t) = 11 \)
Detalles de la respuesta
Multiply through by the LCM of 4 and 3 which is 12
12 x(34 t) + 12 x (13 (21 - t)) = (11 x 12)
9t + 4(21 - t) = 132
9t + 84 - 4t = 132
5t + 84 = 132
5t = 132 - 84 = 48
t = 485
t = 9 35
Pregunta 22 Informe
Detalles de la respuesta
So the answer is 1.0
Pregunta 23 Informe
Detalles de la respuesta
Pregunta 24 Informe
The table below shows the frequency of children of age x years in a hospital:
| x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| f | 3 | 4 | 5 | 6 | 7 | 6 | 5 | 4 |
Use the table to answer the question below:
What is the modal age?
Detalles de la respuesta
Pregunta 25 Informe
Detalles de la respuesta
Pregunta 26 Informe
Detalles de la respuesta
Pregunta 27 Informe
Detalles de la respuesta
siny=300 m600 m=12
y=sin−10.5
y=30∘
x=180∘+(90∘−30∘)
x=180∘+60∘
x=240∘
Pregunta 28 Informe
Detalles de la respuesta
Pregunta 29 Informe
If the simple interest on a sum of money invested at 3% per annum for \(2\frac{1}{2}\) years is ₦123, find the principal.
Detalles de la respuesta
Pregunta 30 Informe
Use the cumulative frequency curve to answer the question.
Estimate the median of the date represented on the graph.
Detalles de la respuesta
Pregunta 31 Informe
Detalles de la respuesta
Pregunta 32 Informe
Simplify \(25^{\frac{1}{2}} \times 8^{-\frac{2}{3}}\)
Detalles de la respuesta
2512 × 8−23
= √25 x (3√8 ) -2
= 5 x 2-2
= 5 x 122 =
54 = 114
Pregunta 33 Informe
Detalles de la respuesta
Pregunta 34 Informe
Detalles de la respuesta
Pregunta 35 Informe
The figure below is a Venn diagram showing the elements arranged within sets A, B, C, \( \epsilon \).
Use the figure to answer this question
What is \( n((A \cup B)^c) \)?
Detalles de la respuesta
B = (r, s, t, u)
A U B = Elements in both A and B = (p, q, r, s, t, u, v)
(A U B)1 = elements in the universal set E but not in (A U B)= (w, x, y, z)
n(A U B) 1 = number of the elements in (A U B)1 = 4
Pregunta 36 Informe
If \( P = \left[\frac{Q(R-T)}{15}\right]^{\frac{1}{3}} \) make T the subject of the relation
Detalles de la respuesta
P3 = Q(R−T)15
Cross multiplying
15P3 = Q(R - T)
Divide both sides by Q
15P3Q = R - T
Rearranging gives
T = R - 15P3Q
= RQ−15P3Q
Pregunta 37 Informe
Use the quadratic equation curve to answer this question.
What is the 80th percentile?
Detalles de la respuesta
Pregunta 38 Informe
The probabilities that John and James pass an examination are \( \frac{3}{4} \) and \( \frac{3}{5} \) respectively. Find the probability of both boys failing the examination.
Detalles de la respuesta
= 34 x 35
= 920
Pr(John and James failed)= 1 - Pr(John and James passed)
1 – 920
= 1120
Pregunta 39 Informe
if \(y = 23_{\mathit{five}} + 101_{\mathit{three}}\) find y leaving your answer in base two
Detalles de la respuesta
23five = 2 x 51 + 3 x 50
= 10 + 3 = 13
101five = (1 x 32) + (0 x 31) + (1 x 30)
= 9 + 0 + 1 = 10
So, y = 13 + 10 = 23
To convert 23 to base 2 (as in the diagram above)
y = 23
= 10111five
Pregunta 40 Informe
Detalles de la respuesta
= 90100 x 20000 =18000
At the end of second year, its value = 90% of 18000
= 90100 x 18000 = ₦16,200
