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JAMB Mathematics Past Questions & Answers - Page 33

161.

A surveyor walks 500m up a hill which slopes at an angle of 30 $^o$ . Calculate the vertical height through which he rises

A.

252m

B.

500m

C.

250m

D.

255m

View answer & explanation

Correct answer is C

$\frac{h}{500}$ = sin 30 $^o$

= 500 sin 30 $^o$

= 500 x $\frac{1}{2}$

= 250m

162.

The mean age group of some students is 15years. When the age of a teacher, 45 years old, is added to the ages of the students, the mean of their ages become 18 years. Find the number of students in the group.

A.

7

B.

9

C.

15

D.

42

View answer & explanation

Correct answer is B

x $\frac{\sum x}{N}$

15 = $\frac{\sum x }{N}$

$\sum x$ = 15N........(i)

y = $\frac{\sum y}{Ny} = \frac{\sum x + 45}{N + 1}$

$\frac{18}{1} = \frac{15N + 45}{N + 1}$

18(N + 1) = 15N + 45

18N + 18 = 15N + 45

18N - 15N = 45 - 18

3N = 27

N = $\frac{27}{3}$

= 9

163.

The sum of the interior angle of pentagon is 6x + 6y. Find y in terms of x.

A.

y = 6 - x

B.

y = 90 - x

C.

y = 120 - x

D.

y = 150 - x

View answer & explanation

Correct answer is B

Sum of interior angles = (2n - 4) 90 $^o$

For perntagon, n = 5

Sum of interior angles = 6 x 90 $^o$ = 540 $^o$

6x + 6y = 540 $^o$

6(x + y) = 540 $^o$

x + y = $\frac{540^o}{6}$ = 90 $^o$

y = 90 $^o$

y = 90 - x

164.

In a class of 40 students, 32 offer mathematics, 24 offer physics and 4 offer neither mathematics nor physics. How many offer both mathematics and physics?

A.

4

B.

8

C.

16

D.

20

View answer & explanation

Correct answer is D

40 = 32 - x + x + 24 + 4

40 = 60 - x

x = 60 - 40

x = 20

165.

Three consecutive terms of a geometric progression are give as n - 2, n and n + 3. Find the common ratio

A.

$\frac{3}{2}$

B.

$\frac{2}{3}$

C.

$\frac{1}{2}$

D.

$\frac{1}{4}$

View answer & explanation

Correct answer is A

$\frac{h}{n - 2} = \frac{n + 3}{n}$

n $^2$ = (n + 3) (n - 2)

n $^2$ = n $^2$ + n - 6

n $^2$ + n - 6 - n $^2$ = 0

n - 6 = 0

n = 6

Common ratio: $\frac{n}{n - 2} = \frac{6}{6 - 2} = \frac{6}{4}$ = $\frac{3}{2}$

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