JAMB UTME - Mathematics - 2003
Question 1 Report
In the diagram, STUV is a straight line. < TSY = < UXY = 40o and < VUW = 110o. Calculate < TYW
Answer Details
< TUW = 180∘ - 110∘ = 70∘
In △ XTU, < XUT + < TXU = 180∘
i.e. < YTS + 70∘ = 180
< XTU = 180 - 110∘ = 70∘
Also < YTS + < XTU = 180 (< s on a straight line)
i.e. < YTS + < XTU - 180(< s on straight line)
i.e. < YTS + 70∘ = 180
< YTS = 180 - 70 = 110∘
in △ SYT + < YST + < YTS = 180∘ (Sum of interior < s)
SYT + 40 + 110 = 180
< SYT = 180 - 150 = 30
< SYT = < XYW (vertically opposite < s)
Also < SYX = < TYW (vertically opposite < s)
but < SYT + < XYW + < SYX + < TYW = 360
i.e. 30 + 30 + < SYX + TYW = 360
but < SYX = < TYW
60 + 2(< TYW) = 360
2(< TYW) = 360∘ - 60
2(< TYW) = 300∘
TYW = 3002 = 150∘
< SYT
Question 2 Report
Question 3 Report
The locus of a point P which moves on one side only of a straight line XY so that ∠XPY = \(90^\circ\) is
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Question 4 Report
In the diagram above, PQ is parallel to RS. What is the value of ? + ? + ??
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γ + S = 180(Allied angles)
α + P = 180(Allied angles)
p = 180 - α
β = P + S
β = 180 - α + 180 - γ
β = 360 - α - γ
β + α + γ = 360
Question 5 Report
The histogram above shows the ages of the victims of a pollution. How many people were involved in the pollution?
Question 6 Report
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Question 7 Report
An arc of a circle subtends an angle of \(30^\circ\) on the circumference of a circle of radius 21cm. Find the length of the arc.
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∴ θ = 60∘
Length of arc =θ360×2πr=60360×2×227×211=22cm
Question 8 Report
On the pie chart, there are four sectors of which three angles are \(45^\circ\), \(90^\circ\) and \(135^\circ\). If the smallest sector represents N28.00, how much is the largest sector?
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Question 9 Report
The result of tossing a fair die 120 times is summarized above. Find the value of x
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2x + 80 = 120
2x = 120 - 80
2x = 40
x = 20
Question 10 Report
ematics and Physics?
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(32-x) + (24-x) + (x) + (4 who offer neither) = 40
=> 60 - x = 40
=> -x = -20
Therefore x = 20.
Question 11 Report
XYZ is a circle enter o and a radius 7cm. Find the area of the shaded region. θ = 45 x 2 = 90
Answer Details
θ = 90
Area of sector = θ/360 x πr2
= 90/360 x 22/7 x 7 x 7
= 77/2cm2
Area of triangle = 1/2 ab sin θ
= 1/2 x 7 x 7 sin 90
= 1/2 x 7 x 7 x 1
= 49/2
Area of shaded region = 77/2 - 49/2
| 1 | 1 |
| 2 |
= 28/2
= 14cm2
Question 12 Report
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Question 13 Report
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OQ; y - x = 0
y - x ≥ 0
PQ; x + 1 = 0
x + 1 ≥ = 0
PO; y + x = 0
y + x ≤ 0
∴ x + 1 ≥ 0, y + x ≤ 0, y - x ≥ 0
Question 14 Report
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Question 16 Report
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Question 17 Report
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Question 18 Report
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Question 19 Report
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Question 20 Report
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Question 21 Report
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Question 23 Report
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Question 24 Report
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Question 25 Report
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Question 26 Report
Find the range of values of \(x\) which satisfy the inequalities \(4x - 7 \le 3x\) and \(3x - 4 \le 4x\)
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Question 27 Report
Given:
U = {Even numbers between 0 and 30}
P = {Multiples of 6 between 0 and 30}
Q = {Multiples of 4 between 0 and 30}
Find (P∪Q)c
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Question 28 Report
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Since PQ = QR, Δ PQR is a right angle isosceles triangle
=> The bearing of P from R = 180 + 45
= 225∘
Question 29 Report
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Question 30 Report
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Mid point QR = (x2+x1)/2 . (y2+y1)/2
= 2+0/2 . 1+0/2
| Gradient of Qr = | y2-y1 |
| x2-x1 |
| = | 1-0 |
| 2-0 |
= 1/2
| Gradient of PM(M)= | -1 |
| 1/2 |
= -2
Equation of Pm = y - y1 = m(x-x1)
i.e y - 1/2 = -2(x-1)
2y - 1 = -4(x-1)
2y - 1 = -4x + 4
2y + 4x = 5
Question 31 Report
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Question 33 Report
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Question 34 Report
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Question 35 Report
Find the mean of the distribution above
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Question 36 Report
Find the range of the value of \(x\) satisfying the inequalities \(5 + x \le 8\) and \(13 + x \ge 7\)
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5 + x ≤
8 and 13 + x ≥
7
5 + x ≤
8
X ≤
8 – 5
X ≤
3
And 13 + x ≥
7
X ≥
7 – 15
X ≥
-7
Combining the two together
-6 ≤
x ≤
3
Question 37 Report
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Question 38 Report
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4x - 7y + 8 = 0 → eqn2
eqn1 * 4; 12x - 20y + 20 = 0 → eqn3
eqn2 * 3; 12x - 21y + 24 = 0 → eqn4
eqn3 - eqn4 = y - 4 = 0
∴ y = 4
From eqn1,
3x - 5y + 5 = 0
3x - 5(4) + 5 = 0
3x - 20 + 5 = 0
3x - 15 = 0
3x = 15
x = 5
x and y = 5, 4 respectively
Question 39 Report
Evaluate \( \log_{\sqrt{2}} 4 + \log_{\frac{1}{2}} 16 - \log_{4} 32 \)
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Question 40 Report
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Question 41 Report
Evaluate \( \int_{3}^{2}(x^2-2x)\,dx \)
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Question 42 Report
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Question 43 Report
If \( \frac{9^{2x-1}}{27^{x+1}} = 1 \) find the value of x.
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32(2x-1) = 33(x+1)
Solving by equating index: 2(2x-1) = 3(x+1), => x = 5
Question 44 Report
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Question 45 Report
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