JAMB UTME - Mathematics - 2018
Swali 1 Ripoti
Maelezo ya Majibu
Swali 2 Ripoti
Maelezo ya Majibu
Swali 3 Ripoti
Maelezo ya Majibu
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
Swali 4 Ripoti
In the figure below, /MX/ = 8cm, /XN/ = 12cm, /NZ/ = 4cm and ∠ XMN = ∠ XZY. Calculate /YM/
Maelezo ya Majibu
∠ 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
Swali 5 Ripoti
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 \( n((A \cup B)^c) \)?
Maelezo ya Majibu
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
Swali 6 Ripoti
Use the quadratic equation curve to answer this question.
What is the 80th percentile?
Maelezo ya Majibu
Swali 7 Ripoti
If \[ N=\begin{pmatrix}3 & 5 & -4 \\ 6 & -3 & -5 \\ -2 & 2 & 1\end{pmatrix} \] , find \(|N|\).
Maelezo ya Majibu
3(-3 + 10) - 5(6 - 10) - 4(12 - 6)
3(7) - 5(-4) - 4(6) = 17
Swali 8 Ripoti
Use the cumulative frequency curve to answer the question.
Estimate the median of the date represented on the graph.
Maelezo ya Majibu
Swali 9 Ripoti
Maelezo ya Majibu
= 90100 x 20000 =18000
At the end of second year, its value = 90% of 18000
= 90100 x 18000 = ₦16,200
Swali 10 Ripoti
If \( P = \left[\frac{Q(R-T)}{15}\right]^{\frac{1}{3}} \) make T the subject of the relation
Maelezo ya Majibu
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
Swali 11 Ripoti
Maelezo ya Majibu
Swali 12 Ripoti
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?
Maelezo ya Majibu
Swali 13 Ripoti
Maelezo ya Majibu
Swali 14 Ripoti
Find the values of x for which
\( \frac{x+2}{4} - \frac{2x-3}{3} < 4 \)
Maelezo ya Majibu
3x+6−(8x−12)12<4
−5x+1812<4
−5x+18<48
−5x<30
x>−6
Swali 16 Ripoti
Maelezo ya Majibu
Pr(product of x and y NOT > 6) = 816 = 12
Swali 17 Ripoti
Maelezo ya Majibu
Swali 18 Ripoti
Maelezo ya Majibu
= 6×5×4×3×2×12×1
= 360
Swali 19 Ripoti
Solve for t in the equation \( \frac{3}{4}t + \frac{1}{3}(21 - t) = 11 \)
Maelezo ya Majibu
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
Swali 20 Ripoti
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?
Maelezo ya Majibu
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
Swali 21 Ripoti
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?
Maelezo ya Majibu
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
Swali 22 Ripoti
Maelezo ya Majibu
Swali 23 Ripoti
Simplify \(25^{\frac{1}{2}} \times 8^{-\frac{2}{3}}\)
Maelezo ya Majibu
2512 × 8−23
= √25 x (3√8 ) -2
= 5 x 2-2
= 5 x 122 =
54 = 114
Swali 24 Ripoti
\[ P=\left[\frac{Q(R-T)}{15}\right]^{\frac{1}{3}} \]
Make T the subject of the relation.
Maelezo ya Majibu
P3=Q(R−T)15
15P3=Q(R−T)
15P3Q=R−T
T=R−15P3Q
Swali 25 Ripoti
Maelezo ya Majibu
HCF of 80, 64, 48 = 16
960 ÷ 16 = 60
Swali 26 Ripoti
Maelezo ya Majibu
siny=300 m600 m=12
y=sin−10.5
y=30∘
x=180∘+(90∘−30∘)
x=180∘+60∘
x=240∘
Swali 27 Ripoti
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.
Maelezo ya Majibu
Swali 28 Ripoti
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?
Maelezo ya Majibu
Swali 29 Ripoti
Maelezo ya Majibu
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
Swali 30 Ripoti
Maelezo ya Majibu
Swali 31 Ripoti
Maelezo ya Majibu
Swali 32 Ripoti
\[ \frac{0.00256 \times 0.0064}{0.025 \times 0.08} \]
Maelezo ya Majibu
Explanation:
=0.0000163840.002
=0.008192
Swali 33 Ripoti
if \(y = 23_{\mathit{five}} + 101_{\mathit{three}}\) find y leaving your answer in base two
Maelezo ya Majibu
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
Swali 34 Ripoti
Maelezo ya Majibu
So the answer is 1.0
Swali 35 Ripoti
Which one of the following gives the members of the set \(A^c \cap B \cap C\)?
Maelezo ya Majibu
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
Swali 36 Ripoti
Maelezo ya Majibu
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
Swali 37 Ripoti
Maelezo ya Majibu
a2=122+92
a=√122+92
a=15 m
b2=152+82
b=√152+82
b=17 m
cosθ=ab=1517
Swali 38 Ripoti
Maelezo ya Majibu
Swali 39 Ripoti
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.
Maelezo ya Majibu
= 34 x 35
= 920
Pr(John and James failed)= 1 - Pr(John and James passed)
1 – 920
= 1120
Swali 40 Ripoti
