JAMB UTME - Mathematics - 2008
Question 1 Report
Answer Details
at turning pt, dydx = 0
∴ 2x - 3 = 0
∴ x = 32
d2ydx2 = ddx (ddx )
= 270
∴ ymin = 232 - 332 + 2
= 94 - 92 + 2
= -14
Question 2 Report
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Question 3 Report
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= x + x2
dy/dx = 1 + 2x
As dy/dy → 0
1 + 2x = 0
2x = -1
X = -1/2
Y = x(1+x)
= -1/2(1 - 1/2) at x = -1/2
= -1/2(1/2)
= -1/4
Question 4 Report
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Question 5 Report
Question 6 Report
Question 7 Report
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D = √(x2−x1)2+(y2−y1)2
D = √(−3−(−1)2+(−5−(−6)2
D = √(−3+1)2+(−5+6)2
D = √(−2)2+12
D = √4+1
D = √5
Question 8 Report
Answer Details
Arrange in ascending order:
0, 0, 1, 1, 2, 4, 4, 4, 4
Position of median = N+1 / 2 = 9+1 / 2 = 5th
Median = 2
Question 9 Report
If \( \frac{1+\sqrt{2}}{1-\sqrt{2}} \) is expressed in the form of x+y√2 find the values of x and y
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Question 10 Report
In the diagram < OPQ is
Question 11 Report
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Question 12 Report
If \( \log X^{\frac{1}{2}} \) 64 = 3, find the value of x.
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recall that X = 10p
log10X = P
64 = X12
43 = X12
43×12 = X12×13
4 = X12
(4)2 = X12×2
x = 16
Question 13 Report
Find the range of values of x which satisfy the inequalities \(4x - 7 \leq 3x\) and \(3x - 4 \leq 4x\)
Answer Details
4X - 3X ≤ 7 and 3X - 4X ≤ 4
X ≤ 7 and -X ≤ 4 = X ≥ -4
Range -4 ≤ x ≤ 7
Question 14 Report
Find the area of the figure given
Answer Details
A = 12πr2 + LB
A = 12×2277×(52)2+(15×5)
= 12×227×254+75
A = 27528+751
275+210028=237528
A = 84.8cm2
Question 15 Report
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10!3!2!2!
Question 16 Report
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n(E) only = 20-10 = 10
n(M∩E) = 10
∴M∪E = 20+10+10
= 40
Question 17 Report
Evaluate \( \frac{\left(\frac{3}{8} \div \frac{1}{2} + \frac{1}{2}\right)}{\left(\frac{1}{8} \times \frac{2}{3} + \frac{1}{3}\right)} \)
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Question 18 Report
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P = k/q
K = q2P
= 428
∴P = 128/q
32 = 128/q
q2 = 128/32
q2 = 4
q = √4 = +/-2
Question 19 Report
Answer Details
x2 - 5x + 6 = 0
(X-2)(X-3) = 0
X-2 = 0 implies X = 2
X-3 = 0 implies X = 3
∴ x ≤ 2, x ≥ 3
Question 20 Report
Find the values of x and y respectively if
\[ \begin{pmatrix} 1 & 0\\ -1 & -1\\ 2 & 2 \end{pmatrix} + \begin{pmatrix} x & 1\\ -1 & 0\\ y & -2 \end{pmatrix} = \begin{pmatrix} -2 & 1\\ -2 & -1\\ -30 & 0 \end{pmatrix} \]Answer Details
therefore, (x, y) = (-3, -5) respectively
Question 21 Report
In the diagram above ∠OPQ is
Answer Details
∴ a+a+74 = 180
2a + 74 = 180
2a = 180-74
2a = 106
a = 53
∴∠OPQ = 53∘
Question 22 Report
Find the capacity in liters of a cylindrical well of radius 1 meter and depth 14 meters
[π = 22/7]
Answer Details
1m = 100cm
14cm = 1400cm
∴V=227×100x100x14001000=44,000liters
Question 23 Report
Find the area of the figure above
[π = 22/7]
Answer Details
=L×h+12πr25×15+12×227×(52)2=75+(22×25)2×7=75+92328=84.8cm
Question 24 Report
Question 25 Report
Question 26 Report
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implies x is a factor ∴ x = 4
f(4) implies 2(4)2 - k(4) - 12 = 0
32 - 4k - 12 = 0
-4k + 20 = 0
-4k = -20
k = 5
Question 27 Report
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(X 1/2)3 = 64
(X 1/2)3 = 4 3
X 1/2 = 4
X = 42
X = 16
Question 28 Report
A binary operation on the set of real numbers excluding -1 is such that sor all \(m, n \in R\), \(m \Delta n = m + n + mn\). Find the identity element of the operation.
Answer Details
m Δ e = e Δ m = m
m Δ e = m
m + e + me = m
e + me = m - m
e + me = 0
e(1 + m) = 0
e = 01+m = 0
Question 29 Report
Question 30 Report
Answer Details
[sinx]π2π2
= sinπ2 - (-sin π2 )
= sin π2 + sin π2
= 2 sin π2
= 2 sin 1.5714
= 2(0.2704)
= 0.5
= 1
Question 31 Report
Answer Details
2Y = -3X - 1
−32X−12
Gradient of 3X + 2Y +1 = 0 is -3/2
Gradient of a line perpendicular to 3X + 2Y + 1 = 0
=−1÷32=−1×−23=23
Question 32 Report
Answer Details
1xX2 + 2xX1 + 5xX0 = 20
X2 + 2X + 5 = 20
X2 + 2X - 15 = 0
(X + 5)( X - 3) = 0
X + 5 implies X = -5
X - 3 implies X = 3
But X cannot be negative
∴X = 3
Question 33 Report
\[ \begin{pmatrix} -2 & 1 \\ 2 & 3 \end{pmatrix} + \begin{pmatrix} p & q \\ r & s \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}. \] What is the value of r?
Answer Details
2p + 3r = 0.......(ii)
r - 1 + 2p ........(iii)
2p + 3(1 + 2p) = 0
2p + 3(1 + 2p) = 0
2p + 3 + 6p = 0
3 - 8p = 0 → 8p = 3
p = 38
6 = 1 - 2 38
= 1 - 68
8−68 = 28
= 14
Question 34 Report
Evaluate \( \int_{1}^{2} (6x^{2} - 2x)\,dx \)
Answer Details
= [2(2)3 - (2)2] – [2(1)3 - (1)2]
= [16-4] – [2-1]
= 12 – 1
= 11
Question 35 Report
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S = 280o2
= 140
< O = 360 - 280 = 80o
60 + 80 + 140 + a = 360o
(< in a quad); 280 = a = 360
a = 360 - 280
a = 80o
Question 36 Report
The result of rolling a fair die 150 times is as summarized in the table given.
| Number | 1 | 2 | 3 | 4 | 5 | 6 |
| Frequency | 12 | 18 | \(x\) | 30 | \(2x\) | 45 |
What is the probability of obtaining a 5?
Answer Details
12 + 18 + x + 30 + 2x + 45 = 150
3x + 105 = 150
3x = 150 - 105
3x = 45
x = 453
x = 15
probability of 5 = 30150
= 15
Question 37 Report
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Question 38 Report
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X-3 = Ky2
K = X-3 / y2
= 5-2/22
= 2/4
= 1/2
∴X-3 = 1/2y2
X-3 = 1/2(6)2
X-3 = 1/2 x 30/1
X-3 = 18
X = 21
Question 39 Report
Answer Details
(4x+3y+3x-2y)(4x+3y-(3x-2y))
(4x+3y+3x-2y)(4x+3y-3x+2y)
(x+5y)(7x+y)
Question 40 Report
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Range = 3x+2 - (x-3)
= 3x+2 - x - 3
= 2x + 5
Question 41 Report
Question 42 Report
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A = 2 letters
C = 3 letters
E = 2 letters
Can be arranged in 10! / (2!3!2!) ways
Question 43 Report
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y = {n + 1 : n = 2, 3, 4, 5}
find x ∩ y
x = (n2 + 1)(22 + 1)(32 + 1)
y = (2 + 1) (3 + 1)(5 + 1)
x = {1, 5, 10}
y = {3, 4, 6}
x ∩ y = Φ
Question 44 Report
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x tan 20o = 68
x = 68tan20 = 680.364
x = 186.8
= 187m
Question 45 Report
simplify \(16^{-\frac{1}{2}} \times 4^{-\frac{1}{2}} \times 27^{\frac{1}{3}}\)
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Question 46 Report
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Let e be the identity element
∴mΔe = eΔm = m
m+e+me = m
e+me = m-m
e+me = 0
e(1+m) = 0
e = 0 / (1+m)
e = 0
Question 47 Report
The solution of the quadratic inequality \(x^2 + x - 12 \ge 0\) is
Answer Details
For the condition to hold, each of (x - 3) and (x + 4) must be of the same sign
.i.e. x - 3 ≥ 0 and x + 4 ≥ 0
or x - 3≤ 0 and x + 4 ≤ 0
when x ≥ 3, the condition is satisfied
when x ≥ -4, the condition is not satisfied.
when x ≤ 3, the condition is not satisfied
when x ≤ -4 , the condition is not satisfied. Thus, the solution of the inequality is x ≥ 3 or x ≤ -4 ,
Question 48 Report
Make Q the subject of formula when \(L = \frac{4}{3}M\sqrt{PQ}\)
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Question 49 Report
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2*3 = 2(2) - 3(3) + 2
=4-9+2
= -3
But -3 does not belong to positive integer
Question 50 Report
The bar chart above shows the number of times the word a, and , in, it, the , to appear in a paragraph in a book. What is the ratio of the least frequent word?
Answer Details
= 3/12
= 1/4
