# 2007 JAMB Mathematics Past Questions & Answers - page 1

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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

**Solution**

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

**Solution**

^{2}= 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

**Solution**

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

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

= \(\frac{1}{2}\)

4
Calculate the length of an arc of a circle of diameter 14cm, which subtends an angle of 90

^{o}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

**Solution**

= \(\frac{90^o}{360^o}\) 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

**Solution**

\(\Rightarrow\) -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?

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

**Solution**

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

**Solution**

therefore the array is 2

^{1}, 5

^{3}, 6

^{4}, 8

^{2}

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

**Solution**

= 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

**Solution**

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

**Solution**

= 7 x 6 x 5 x 4

= 840

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