JAMB UTME - Mathematics - 2002
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Frage 3 Bericht
Using the graph find the values of \(p\) and \(q\) if \(px + qy \ge 4\)
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y2?y1x2?x1?m
y?0x+4?12
2y ? ? x + 4, -x + 2y ? 4 = px + qy ? 4
p = -1, q = 2
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Frage 5 Bericht
Simplify \( \frac{3}{5} \div \left(\frac{2}{7} \times \frac{4}{3} \div \frac{4}{9}\right) \)
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Frage 6 Bericht
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Frage 7 Bericht
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Frage 8 Bericht
In the diagram, XZ is the diameter of the circle XYZW, with centre O and radius \( \frac{15}{2} \)cm. If XY = 12cm, find the area of the triangle XYZ
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Frage 9 Bericht
Find the range of values of x for which \( \frac{(x+2)}{4}-\frac{2x-3}{3}<4 \)
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Frage 14 Bericht
In the diagram above, PST is a straight line, PQ = QS = RS. If ∠RST = \(72^\circ\), find x
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In Δ QRS, ∠RQS = ∠PSQ + X(Extr ∠ = sum of two intr. opp ∠s)
∴ ∠RQS = X + X
= 2X
Also ∠QRS = 2X(base ∠s of isoc Δ QRS in Δ PRS,
72 = ∠RPS + ∠PRS(Extr, ∠ = sum of two intr. opp ∠s)
∴ 72 = x + 2x
72 = 3x
x = 72/3
x = 24∘
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Frage 20 Bericht
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Frage 21 Bericht
In the diagram above, a cylinder is summounted by a hemisphere bowl. Calculate the volume of the solid.
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Frage 22 Bericht
In the diagram are two concentric circles of radii r and R respectively with centre O. If \(r = \frac{2}{5}R\), express the area of the shaded portion in terms of \(\pi\) and R
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Ashaded portion = πR2−π(23R)2=πR2−4πR225
= πR2(1−23)=2125πR2
Frage 23 Bericht
In the diagram PQ is parallel to RS. What is the value of \( \alpha + \beta + \gamma \)
Frage 25 Bericht
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Frage 30 Bericht
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Frage 31 Bericht
In the diagram above, \(XZ\) is the diameter of the circle \(XZW\), with center \(O\) and radius \(15/2\) cm. If \(XY = 12\) cm, find the area of the triangle \(XYZ\)
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Frage 32 Bericht
The triangle PQR above is
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= 52∘
∠QPR + 76 + 52 = 180(extr ∠ = sum of intr. opp ∠s)
∠QPR + 128 = 180
∠QPR = 180 - 128
= 52∘
∴ΔPQR is an isosceles triangle
Frage 33 Bericht
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Frage 34 Bericht
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Frage 35 Bericht
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Frage 36 Bericht
In the diagram, a cylinder is surmounted by a hemispherical bowl. Calculate the volume of the solid
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N.B h = r
V = πx(3)2 x 20 = 23×π×(3)3
180π+18π=198cm3
Frage 37 Bericht
Make \(r\) subject of the formula given that \(\frac{x}{r+a}=\frac{a}{r}\)
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Frage 38 Bericht
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Frage 39 Bericht
In the diagram above are two concentric circles of radii r and R respectively with center O. If r = 2/3R, express the area of the shaded portion in terms of π and R
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Frage 41 Bericht
Find the derivative of y = sin2(5x) with respect to x.
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Frage 42 Bericht
Without using tables, evaluate (343)1/3 x (
0.14)-1 x (25)-1/2
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Frage 44 Bericht
The slope of the tangent to the curve \(y = 2x^2 - 2x + 5\) at the point \((1, 6)\) is
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Frage 50 Bericht
The venn diagram above shows the numbers of students offering music and history in a class of 80 students. If a student is picked at random from the class, what is the probability that he offers Music only?
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70 - x = 60
- x = 60 - 70
- x = - 10
∴ x = 10
Music only = 30 - x
= 30 - 10
20
P(music only) = 20/80
= 1/4
= 0.25
