JAMB UTME - Mathematics - 2014
Question 1 Report
Answer Details
Question 2 Report
The gradient of a line joining \((x,4)\) and \((1,2)\) is \(\frac{1}{2}\). Find the value of \(x\)
Answer Details
12=2−41−x
1 - x = 2(2 - 4)
1 - x = 4 - 8
1 - x = -4
-x = -4 - 1
x = 5
Question 3 Report
Evaluate the inequality \( \frac{x}{2} + \frac{3}{4} \leq \frac{5x}{6} - \frac{7}{12} \)
Answer Details
12x2+1234≤125x6−12712
6x + 9 ≤ 10x - 7
6x - 10x ≤ - 7 - 9
-4x ≤ -16
-4x/-4 ≥ -16/-4
x ≥ 4
Question 4 Report
Answer Details
P=KQR
When Q = 36, R = 16, P = 27
Then substitute into the equation
27=K3616
K=27×1636
K=12
So the equation connecting P, Q and R is
P=12QR
Question 5 Report
Answer Details
Question 6 Report
Answer Details
Question 7 Report
Answer Details
= [(2 - t) + (4 + t) + (3 - 2t) + (2 + t) + (t - 1) ÷ ] 5
= [11 - 1 + 3t - 3t] ÷ 5
= 10 ÷ 5
= 2
Question 8 Report
| Numbers | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 18 | 22 | 20 | 16 | 10 | 14 |
The table above represents the outcome of throwing a die 100 times. What is the probability of obtaining at least a 4?
Answer Details
Then n(E) = 16 + 10 + 14 = 40
Hence, prob (E) = n(E)n(S)
=40100
=25
Question 9 Report
Answer Details
Question 10 Report
Answer Details
Question 11 Report
If \( \sin \theta = \frac{12}{13} \), find the value of \( 1 + \cos \theta \)
Answer Details
Question 12 Report
Simplify \( \frac{2\sqrt{2}-\sqrt{3}}{\sqrt{2}+\sqrt{3}} \)
Answer Details
=2√2(√2)+(2√2)(−√3)−√3(√2)−√3(−√3)(√2)2−(√3)2
=2×2−2√6−√6+32−3
=4−3√6+3−1
=7−3√6−1
=7−1−3√6−1
=−7+3√6
=3√6−7
Question 13 Report
Answer Details
Question 14 Report
Answer Details
Question 16 Report
If \(y = 4x^3 - 2x^2 + x\), find \(\frac{\delta y}{\delta x}\)
Answer Details
δyδx = 3(4x2) - 2(2x) + 1
= 12x2 - 4x + 1
Question 17 Report
Answer Details
=7!(7?3)!3!
=7!4!3!ways
Question 18 Report
Answer Details
x * 2 = 12 - x
Thus by comparison,
x = x, y = 2
But x * y = x * 2
xy = 12 - x
x2 = 12 - x
x2 + x - 12 = 0
x2 + 4x - 3x - 12 = 0
x(x + 4) - 3(x + 4) = 0
(x - 3)(x + 4) = 0
x - 3 = 0 or x + 4 = 0
So x = 3 or x = -4
Question 19 Report
What is the common ratio of the G.P. \( (\sqrt{10}+\sqrt{5})+(\sqrt{10}+2\sqrt{5})+\ldots \)?
Answer Details
r=Tn+1Tn=T2T1
r=√10+2√5√10+√5
r=√10+2√5√10+√5×√10−√5√10−√5
=(√10)(√10)+(√10)(−√5)+(2√5)(√10)+(2√5)(−√5)(√10)2−(√5)2
10−√50+2√50−1010−5
√505
√25×25
5√25
√2
Question 20 Report
Answer Details
When y = 0, 0 - 4x + 3 = 0
Then -4x = -3
x = 3/4
So the line cuts the x-axis at point (3/4, 0).
When x = 0, y - 4(0) + 3 = 0
Then y + 3 = 0
y = -3
So the line cuts the y-axis at the point (0, 3)
Hence the midpoint of the line y - 4x + 3 = 0, which lies between the x-axis and the y-axis is;
[12(x1+x2),12(y1+y2)]
[12(34+0),12(0+−3)]
[12(34),12(−3)]
[38,−32]
Question 21 Report
Answer Details
Question 22 Report
In the figure above, KL//NM, LN bisects < KNM. If angles KLN is \(54^\circ\) and angle MKN is \(35^\circ\), calculate the size of angle KMN.
Answer Details
35∘ + < KMN + 108∘ = 180∘ (sum of angles of △ )
< KMN + 143∘ = 180∘
< KMN = 180∘ - 143∘
= 37∘
Question 23 Report
Answer Details
The equation of the line perpendicular to the given line takes the form 3x - 4y = k
Thus, substitution x = -2 and y = 3 in 3x - 4y = k gives;
3(-2) - 4(3) = k
-6 - 12 = k
k = -18
Hence the required equation is 3x - 4y = -18
3x - 4y + 18 = 0
Question 24 Report
Question 25 Report
The pie chart above shows the monthly distribution of a man's salary on food items. If he spent ₦8,000 on rice, how much did he spent on yam?
Answer Details
Question 26 Report
In the figure above, what is the equation of the line that passes the y-axis at (0,5) and passes the x-axis at (5,0)?
Answer Details
Question 27 Report
Answer Details
Question 28 Report
Question 29 Report
Answer Details
Question 30 Report
Find the value of x in the figure above.
Answer Details
Question 31 Report
Find y, if
\[ \begin{pmatrix} 5 & -6 \\ 2 & -7 \end{pmatrix} \begin{pmatrix} 5 \\ 2 \end{pmatrix} = \begin{pmatrix} 7 \\ -11 \end{pmatrix} \]Answer Details
By matrices multiplication;
5x - 6y = 7 ........(1)
2x - 7y = -11 ......(2)
2 x (1): 10x - 12y = 14 .......(3)
5 x (2): 10x - 35y = -55 ......(4)
(3) - (4): 23y = 69
y = 69/23 = 3
Question 32 Report
If P = {1,2,3,4,5} and \( \cup \) Q = {1,2,3,4,5,6,7}, list the elements in Q
Question 33 Report
Answer Details
Let E denote the event of choosing a number divisible by 3
Then E = {12, 15, 18, 21, 24, 27, 30} and n(E) = 7
Prob (E) = n(E)n(E)
Prob (E) = 721
Prob (E) = 13
Question 34 Report
Answer Details
Then 2log75 + log750
= 2(1.8751) + 2.8751
= 3.7502 + 2.8751
= 6.6253
Question 35 Report
Evaluate \( \int (2x+3)^{\frac{1}{2}}\delta x \)
Answer Details
let u = 2x + 3, δyδx=2
δx=δu2
Now ∫(2x+3)12δx=∫u12.δx2
=12∫u12δu
=12u32×23+k
=13u32+k
=13(2x+3)32+k
Question 36 Report
From the Venn diagram above, the shaded parts represent
Answer Details
Question 37 Report
Find the value of
\[ \begin{vmatrix} 0 & 3 & 2 \\ 1 & 7 & 8 \\ 0 & 5 & 4 \end{vmatrix} \]Answer Details
= 0(28 - 40) - 3(4 - 0) + 2(5 - 0)
= 0(-12) - 3(4) + 2(5)
= 0 - 12 + 10
= -2
Question 38 Report
Answer Details
6160 = 22/7 x 28 x 28 x h
h=616022×4×28
h=2.5m
Question 39 Report
| Values | 0 | 1 | 2 | 3 | 4 |
| Frequency | 1 | 2 | 2 | 1 | 9 |
Find the mode of the distribution above
Answer Details
Question 40 Report
If y = cos 3x, find \( \frac{\delta y}{\delta x} \)
Answer Details
Question 41 Report
Answer Details
Question 42 Report
Answer Details
Explanation:
-4x - (-1)12 = -12
-4x + 12 = -12
-4x = -12 - 12
-4x = - 24
x = 6
Question 43 Report
Answer Details
x-2 = 2/25 x 1/8
x-2 = 2/200
x-2 = 1/100
1/x2 = 1/100
x2 = 100
x = 10
Question 44 Report
Answer Details
Question 45 Report
Answer Details
Question 46 Report
Answer Details
= 43 x 10-5 x 2 x 103
= 43 x 2 x 10-5+3
= 86 x 10-2
= 8.6 x 101 x 10-2
= 8.6 x 10-1
Question 47 Report
Answer Details
f(1) = (1)3 + 4(1)2 + k(1) - 6 = 0 (factor theorem)
1 + 4 + k - 6 = 0
5 - 6 + k = 0
-1 + k = 0
k = 1
Question 48 Report
Evaluate \( \int \sin 2x \, dx \)
Answer Details
