2004 - JAMB Mathematics Past Questions and Answers - page 5

41
A farmer planted 5000 grains of maize and harvested 5000 cobs, each bearing 500 grains. What is the ratio of the number of grains sowed to the number harvested?
A
1 : 250 000
B
1 : 25 000
C
1 : 500
D
1 : 5 000
correct option: c

5000 : 5000 * 500

5000 : 2500000

5 : 2500

1 : 500

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42
The shadow of a pole 5√3m high is 5m. Find the angle of elevation of the sun.
A
45o
B
75o
C
30o
D
60o
correct option: d

Tan θ = 5√3/5

Tan θ = √3

θ = 60o

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43
The shaded area in the diagram above is represented by
A
{(x,y) : y - 3x < -6}
B
{(x,y) : y + 3x < 6}
C
{(x,y) : y + 3x < -6}
D
{(x,y) : y - 3x < 6}
correct option: b

Coordinates of the line are (x1 y1)(0,2) respectively and (x2 y2)(2,0) respectively

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

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44
PQRSTV is a regular polygon of side 7 cm inscribed in a circle. Find the circumference of the circle PQRSTV.
A
56 cm
B
22 cm
C
42 cm
D
44 cm
correct option: d
Each interior Angle of the polygon = (n-2)180
_n

= (6-2)180
_6

= 4 x 30

= 120o

i.e ∠PQR = 120o ∴ RQD = 120/2 = 60o 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

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45
The shaded region in the venn diagram above is
A
Po \(\cap\)(Q \(\cap\) R)
B
P \(\cap\) Q
C
Po\(\cup\)(Q\(\cap\)R)
D
Po \(\cup\)(Q \(\cup\)R)
correct option: a
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46
The shaded area in the diagram above is represented by
A
{(x, y) : y + 3x < 6}
B
{(x , y) : y + 3x < -6}
C
{(x, y) : y - 3x < 6}
D
{(x, y) : y - 3x < 6}
correct option: a

when x = 0, y = 0 (\to) (0, 6)

when y = 0, x = 2 (\to) (2, 0)

y + 3x < 6

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47
P, R and S lie on a circle centre O as shown in the diagram while Q lies outside the circle. Find < PSO
A
35o
B
40o
C
45o
D
55o
correct option: a

< PRS = 20o + 35o = 55o

< POS = 2 < PRS

2 x 55o = 10o

< OPS = < PSO = x

In (\bigtriangleup)POS

OP = OS(radii)

(\bigtriangleup)POS is an isosceles

2x + 110o = 180o

2x = 180o - 110o = 70o

x = (\frac{70^o}{2})

= 35o

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48
In the diagram above, PQ = 4cm and TS = 6cm. If the area of parallelogram PQTU is 32cm2, find the area of trapezium PQRU
A
24cm2
B
48cm2
C
60cm2
D
72cm2
correct option: a
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49
The pie chart above shoes the distribution of the corps harvested from a farmland in a year, If 3,000 tonnes of millet is harvested, what amount of beans is harvested?
A
9000 tonnes
B
6000 tonnes
C
1500 tonnes
D
1200tonnes
correct option: d

beans angle = 360o - (60o + 90o + 150o)

360o - 300o = 60o

150o - 3000 tonnes

60o - (\frac{60}{150} \times 3000) tonnes

= 1,200 tonnes

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50
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?
A
68%
B
28%
C
17%
D
8%
correct option: b

(\begin{array}{c|c} \text{class-marks(x)} & \text{(freq. (f)} & \text{cum. freq.}\hline 9 & &3.....3\14 & & 6....3 + 6 = 9\ 19 & & 9.....9 + 9 = 18\ 24 & & 3.....18 + 3 = 21\ 29 & & 2.....21 + 2 = 23\ 34 & & 2.....23 + 2 = 25\ & & 25\end{array})

% of students scoring more than 20 marks

= (\frac{7}{25}) x 100% = 28%

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