JAMB UTME - Mathematics - 2004
Question 1 Report
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= logx26 - 3logx33 = log5(0.2)3
= logx(64/27) = log5(1/5)3
logx(64/27) = log5(1/125)
let logx(64/27) = y
∴xy = 64/27
and log5(1/125) = y
∴ 5y = 1/125
5y = 125-1
5y = 5-3
∴ y = -3
substitute y = -3 in xy = 64/27
implies x-3 = 64/27
1/x3 = 64/27
64x3 = 27
x3 = 27/64
x3 = 3√27/64
x = 3/4
Question 2 Report
Find the value of x in the figure above
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Question 3 Report
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Question 4 Report
Question 5 Report
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Question 6 Report
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Question 7 Report
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Question 8 Report
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Question 9 Report
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Question 11 Report
Simplify \( \frac{1}{\sqrt{3}+2} \) in the form \( a+b\sqrt{3} \)
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Question 12 Report
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Question 13 Report
Evaluate \( \frac{\frac{1}{10}\times\frac{2}{3}+\frac{1}{4}}{\frac{\frac{1}{2}}{\frac{3}{5}}-\frac{1}{4}}} \)
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Explanation:
Question 14 Report
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| Each interior Angle of the polygon = | (n-2) | 180 |
| _n |
| = | (6-2) | 180 |
| _6 |
= 4 x 30
= 120∘
i.e ∠PQR = 120∘ ∴ RQD = 120/2 = 60∘ also
∴ Δ QOR is equilateral Δ ∴ QO = 7cm
∴ PO = QO = RO ...... = 7cm radius of the circumference of the circle = 2πr
= 2 x 22/7 x 7/1
= 44 cm
Question 15 Report
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Question 16 Report
In the diagram above, PQ = 4 cm and TS = 6 cm. If the area of parallelogram PQTU is 32 cm2, find the area of the trapezium PQRU
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Question 17 Report
The graph above shows the cumulative frequency curve of the distribution of marks in a class test. What percentage of the students scored more than 20 marks?
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% of students scoring more than 20 marks
= 725 x 100% = 28%
Question 18 Report
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Question 19 Report
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Question 20 Report
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this implies that (3√42x)3 = (16)3
42x = 42*3
42x = 46
∴ 2x = 6
x = 3
Question 21 Report
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Question 22 Report
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Question 23 Report
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Question 24 Report
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dy/dx = 3x(1/3)x - sin (x/3)
= - sin x/3
But x = 3π/2 ∴ -sin(x/3) = -sin(3π/6)
= -sin (3 * 180)/6
= - sin 90
= -1
Question 25 Report
In the diagram above, KLMN is a cyclic quadrilateral. /KL/ = /KN/, ∠NKM = 55o and ∠KML = 40o. Find ∠LKM.
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Question 26 Report
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substitute x = -3 in 3x3 + 5x2 - 11x + 4
3(-3)3 + 5(-3)2 - 11(-3) + 4
-81 + 45 + 33 + 4
-81 + 82
= 1
Question 27 Report
What are the integer values of x which satisfy the inequality \( -1 < 3 - 2x \le 5 \)?
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Question 28 Report
If the operation * on the set of integers is defined by \(p * Q = \sqrt{pq}\), find the value of \(4 * (8 * 32)\).
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Question 29 Report
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xo = 35 + 29 (Exterior angle = sum of two interior opposite angles)
x = 55o (∠ at the center twice ∠ at circumference) y = 110o
∠PSO = ∠SPO (base ∠S of 1sc Δ b/c PO = SO)
∴ ∠PSO = (180 - 110)/2
= 35o
Question 30 Report
Find the sum to infinity of the series 1/2 , 1/6, 1/18, .....
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Question 32 Report
The shaded area in the diagram above is represented by
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Gradient (m) of the line = (y2 - y1) / (x2 - x1) = (0-6) / (2-0) = -6/2
= -3
Equation of the line y-y1 = m(x-x1)
y - 6 = -3(x - 0)
y - 6 = -3x
y + 3x = 6
inequality; from the y axis, the shaded region is below the line
∴ y + 3x ∠ 6 and line is a broken line
Question 33 Report
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Question 34 Report
I. Rectangular bars of equal width
II. The height of each rectangular bar is proportional to the frequency of the corresponding class interval.
III. Rectangular bars have common sides with no gaps in between
A histogram is described completely by
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Question 35 Report
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y = K/x
K = xy
K = (1/2) * 4 ( when y = 4 and x = 1/2)
K = 2
∴y = 2/x
10 = 2/x (when y = 10)
10x = 2
x = 2/10
x = 1/5
Question 36 Report
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Question 37 Report
Evaluate \( \int_{1}^{3}(X^2 - 1)\,dx \)
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Question 38 Report
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P7 = 4516 - 3056
P7 = 1426
convert 1426 = 1 * 62 + 4 * 61 + 2 * 60
= 36 + 24 + 2
= 62
Convert 6210 to base 7
62/7 = 8 R 6
8/7 = 1 R 1
1/7 = 0 R 1
∴P7 = 1167
Question 39 Report
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∴ [A]
Question 41 Report
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y = 4x3 - 2x2
dy/dx = 12x2 - 4x
at x = -1
dy/dx = 12(-1)2 - 4(-1)
= 12 + 4
= 16
Question 42 Report
An unbiased die is rolled 100 times and the outcome is tabulated above.
What is the probability of obtaining a 5?
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P(obtaining 5) = 20/100
= 1/5
Question 43 Report
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Question 44 Report
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Question 45 Report
The pie chart above shows the distribution of the crops harvested from a farmland in a year. If 3000 tonnes of millet is harvested, what amount of beans is harvested
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= 360 -300
= 60∘
if 150∘ represents 3000 tonnes
1∘ 3000/150
60∘ will represents (3000/150) * (60/1)
= 1200 tonnes
Question 46 Report
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Question 47 Report
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Question 48 Report
