2007 - JAMB Mathematics Past Questions & Answers - page 1

1
A particle p moves between points S and T such that angle SPT is always constant. Find the locus of P.
A
it is a straight line perpendicular to ST.
B
it is a quadrant of a circle with ST as diameter
C
it is a perpendicular bisector of ST
D
it is a semi-circle with ST as diameter
CORRECT OPTION: d
The locus of P is a semi-circle with ST as diameter.
2
The area of a square is 444 sqcm. Find the length of the diagonal.
A
12\(\sqrt{2}\) cm
B
11\(\sqrt{3}\)cm
C
13 cm
D
12 cm
CORRECT OPTION: a
Area S2 = 144sqcm

s = \(\sqrt{144}\) = 12 cm

Length of diagonal = \(\sqrt{12^2 + 12^2}\)

= \(\sqrt{144}\) + 144

= \(\sqrt{228}\)

= 12\(\sqrt{2}\)cm
3
Find the value of \(\frac{tan60^o - tan30^o}{tan60^o + tan30^o}\)
A
1
B
\(\frac{1}{2}\)
C
\(\frac{3}{\sqrt{3}}\)
D
\(\frac{2}{\sqrt{3}}\)
CORRECT OPTION: b
\(\frac{tan60^o - tan30^o}{tan60^o + tan30^o}\) = \(\frac{\sqrt{3} - \frac{1}{\sqrt{3}}}{\sqrt{3} - \frac{1}{\sqrt{3}}}\)

= \(\frac{3 - 1}{3 + 1}\)

= \(\frac{2}{4}\)

= \(\frac{1}{2}\)
4
Calculate the length of an arc of a circle of diameter 14cm, which subtends an angle of 90o at the centre of the circle
A
14\(\pi\) cm
B
7\(\pi\) cm
C
5\(\pi\) cm
D
4\(\pi\) cm
CORRECT OPTION: d
Length of an arc \(\frac{\theta}{360^o}\pi d\)

= \(\frac{90^o}{360^o}\) x \(\pi\) x 4cm

= 4\(\pi\) cm
5
What is the value of k if the mid-point of the line joining (1 - k, -4) and (2, k - 1) is (-k, k)?
A
-4
B
-1
C
-2
D
-3
CORRECT OPTION: d
The midpoint (-k, k) = (\(\frac{1 - k + 2}{2}, \frac{-4 + k + 1}{2}\))

\(\Rightarrow\) -k = \(\frac{3 - k}{2}\)

-2k = 3 - k

-2k + k = 3

k = -3
6
\(\begin{array}{c|c} \text{Age in years} & 10 & 11 & 12\\ \hline \text{No. of pupils} & 6 & 27 & 7\end{array}\)
the table above shows the number of pupil in each age group in a class. What is the probability that a pupil chosen at random is at least 11 years old?
A
\(\frac{27}{40}\)
B
\(\frac{3}{30}\)
C
\(\frac{17}{20}\)
D
\(\frac{33}{40}\)
CORRECT OPTION: c
Total number of pupils = 6 + 27 + 7 = 40

Number of pupils that are at least 11 years old = 27 + 7

= 34

therefore prob. (at least 11 years) = \(\frac{34}{17}\)

= \(\frac{17}{20}\)
7
If 5, 8, 6 and 2 occur with frequencies 3, 2, 4 and 1 respectively, find the product of the modal and the median number
A
40
B
30
C
48
D
36
CORRECT OPTION: d
The mode = 6

therefore the array is 21, 53, 64, 82

The median = 6

The product = 6 x 6 = 36
8
In how many ways can 6 subjects be selected from 10 subjects for an examination?
A
218
B
210
C
215
D
216
CORRECT OPTION: b
No. of ways \(^{10}C_{6}\) = \(\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5}{6 \times 5 \times 4 \times 3 \times 2 \times 1}\)

= 210
9
in a basket, there are 6 grapes, 11 bananas and 13 oranges. If one fruit is chosen at random, what is the probability that the fruit is either a grape or banana?
A
\(\frac{5}{30}\)
B
\(\frac{6}{30}\)
C
\(\frac{11}{30}\)
D
\(\frac{17}{30}\)
CORRECT OPTION: d
Total fruits = 6 + 11 + 13 = 30

prob. (Grape) = \(\frac{6}{30}\) = \(\frac{1}{5}\)

prob. (Banana) = \(\frac{11}{30}\)

prob. (a grape or a banana) = \(\frac{1}{5}\) + \(\frac{11}{30}\)

= \(\frac{17}{30}\)
10
a senatorial candidate had planned to visit seven cities prior to a primary election. However, he could only visit four of the cities. How many different itineraries could be considered?
A
840
B
720
C
640
D
520
CORRECT OPTION: a
No of ways = \(^{7}P_{4}\)

= 7 x 6 x 5 x 4

= 840
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