Year : 
2001
Title : 
Mathematics
Exam : 
NECO - BECE

Paper 1 | Objectives

1 - 10 of 35 Questions

# Question Ans
1.

If s = \(\sqrt{(\frac{a^2}{x^2} - \frac{b^2}{y^2})}\)what does y equal?

A. \(\sqrt{\frac{(b^2 - a^2)}{(s^2 - x^2)}}\)

B. \(\sqrt{\frac{(b^2 - a^2)}{(s^2 \times 2)}}\)

C. \(\sqrt{\frac{x^2 - a^2 - b^2}{s}}\)

D. \(\frac{x^2 - a^2 - b^2}{s}\)

E. \(\sqrt{\frac{(b^2 x^2)}{(a^2 - s^2 x^2)}}\)

Detailed Solution

s = \(\sqrt{(\frac{a^2}{x^2} - \frac{b^2}{y^2})}\)
s\(^2\) = \(\frac{a^2}{x^2} - \frac{b^2}{y^2}\)
\(\frac{b^2}{y^2}\) = \(\frac{a^2}{x^2}\) - s\(^2\)
\(\frac{b^2}{y^2}\) = \(\frac{a^2 - s^2 x^2}{x^2}\)
\(\frac{1}{y^2}\) = \((\frac{a^2 - s^2 x^2}{x^2}) \times \frac{1}{b^2}\)
\(\frac{1}{y^2}\) = \(\frac{a^2 - s^2 x^2}{b^2 x^2}\)
\(\therefore\) y\(^2\) = \(\frac{b^2 x^2}{a^2 - s^2 x^2}\)
y = \(\sqrt{\frac{b^2 x^2}{a^2 - s^2 x^2}}\)
2.

Mr Aborowa bought a car for N200,000.00 and later sold it for N170,000.00. What is the percentage loss?

A. 117.60%

B. 117.60%

C. 117.60%

D. 17.65%

Detailed Solution

Using these:
Loss = C.p - S.p
: Percentage Loss = ( Loss X 100) ÷ C.p
= %17.65
3.

Find the 19th term of the A.P. \(\frac{5}{6}\), \(\frac{8}{6}\), \(\frac{11}{6}\).................

A. 7\(\frac{1}{2}\)

B. 9

C. 9\(\frac{1}{2}\)

D. 9\(\frac{5}{6}\)

E. 10

Detailed Solution

first term (a) = \(\frac{5}{6}\)
common difference = \(\frac{8}{6}\) - \(\frac{5}{6}\) → \(\frac{3}{6}\) or \(\frac{1}{2}\)
A.P formula → T\(_n\) = a + (n - 1)d
T\(_n\) = \(\frac{5}{6}\) + (19 - 1)\(\frac{1}{2}\)
T\(_n\) = \(\frac{5}{6}\) + 9
→ 9\(\frac{5}{6}\)
4.

Simplify 27\(^{-\frac{1}{3}}\) \(\times\) 64\(^{-\frac{1}{3}}\) \(\times\) 4\(^{\frac{1}{3}}\)

A. 48

B. 12

C. \(\frac{4}{3}\)

D. \(\frac{1}{12}\)

E. \(\frac{1}{48}\)

D

5.

The bearing of a point Y from point x is 150°. What is the bearing of X from Y?

A. 330°

B. 240°

C. 150°

D. 120°

E. 30°

A

6.

If the mean of 3, 5, 8, k, 14 and 17 is 11, what is the value of k

A. 58

B. 38

C. 19

D. 11

E. 967

Detailed Solution

To calculate Mean:
add up all the numbers ⇒ 3+5+8+k+14+17 = 47 + k
then divide by how many numbers there are ⇒ 6
The Mean is already given as 11
11 = (47 + k) / 6
Cross multiply to solve for k
: k = (6 X 11) - 47
k = 19
7.

From the kip of a storey-buliding, the angle of depression of a mango on a tree 20 m away from the base of the storey-building is 68°. if the mango is 4.5 m above the ground, what is the height of the storey-building to the nearest metre?

A. 55m

B. 54m

C. 50m

D. 49m

E. 45m

B

8.

The mean age of 12 boys involved survey is 19 years, 3 months. lf the-age of one of the boys is 22 years, what is the mean age of the other-boys?

A. 10.5 years

B. 19.0 years

C. 35.4 years

D. 264.0 years

E. 423.5 years

B

9.

If cos x = - \(\frac{5}{13}\) where 180° < X < 270°, what is the value of tan x -sin x ?

A. \(\frac{111}{13}\)

B. \(\frac{321}{65}\)

C. -\(\frac{216}{65}\)

D. \(\frac{112}{13}\)

E. \(\frac{131}{65}\)

10.

Given that (3 - y) ÷ 2x = (6y + 7) ÷ (4x - 5), find the value of x when y = 2

A. \(\frac{64}{5}\)

B. 6

C. \(\frac{5}{34}\)

D. \(\frac{-5}{34}\)

E. \(\frac{-64}{5}\)

D

1.

If s = \(\sqrt{(\frac{a^2}{x^2} - \frac{b^2}{y^2})}\)what does y equal?

A. \(\sqrt{\frac{(b^2 - a^2)}{(s^2 - x^2)}}\)

B. \(\sqrt{\frac{(b^2 - a^2)}{(s^2 \times 2)}}\)

C. \(\sqrt{\frac{x^2 - a^2 - b^2}{s}}\)

D. \(\frac{x^2 - a^2 - b^2}{s}\)

E. \(\sqrt{\frac{(b^2 x^2)}{(a^2 - s^2 x^2)}}\)

Detailed Solution

s = \(\sqrt{(\frac{a^2}{x^2} - \frac{b^2}{y^2})}\)
s\(^2\) = \(\frac{a^2}{x^2} - \frac{b^2}{y^2}\)
\(\frac{b^2}{y^2}\) = \(\frac{a^2}{x^2}\) - s\(^2\)
\(\frac{b^2}{y^2}\) = \(\frac{a^2 - s^2 x^2}{x^2}\)
\(\frac{1}{y^2}\) = \((\frac{a^2 - s^2 x^2}{x^2}) \times \frac{1}{b^2}\)
\(\frac{1}{y^2}\) = \(\frac{a^2 - s^2 x^2}{b^2 x^2}\)
\(\therefore\) y\(^2\) = \(\frac{b^2 x^2}{a^2 - s^2 x^2}\)
y = \(\sqrt{\frac{b^2 x^2}{a^2 - s^2 x^2}}\)
2.

Mr Aborowa bought a car for N200,000.00 and later sold it for N170,000.00. What is the percentage loss?

A. 117.60%

B. 117.60%

C. 117.60%

D. 17.65%

Detailed Solution

Using these:
Loss = C.p - S.p
: Percentage Loss = ( Loss X 100) ÷ C.p
= %17.65
3.

Find the 19th term of the A.P. \(\frac{5}{6}\), \(\frac{8}{6}\), \(\frac{11}{6}\).................

A. 7\(\frac{1}{2}\)

B. 9

C. 9\(\frac{1}{2}\)

D. 9\(\frac{5}{6}\)

E. 10

Detailed Solution

first term (a) = \(\frac{5}{6}\)
common difference = \(\frac{8}{6}\) - \(\frac{5}{6}\) → \(\frac{3}{6}\) or \(\frac{1}{2}\)
A.P formula → T\(_n\) = a + (n - 1)d
T\(_n\) = \(\frac{5}{6}\) + (19 - 1)\(\frac{1}{2}\)
T\(_n\) = \(\frac{5}{6}\) + 9
→ 9\(\frac{5}{6}\)
4.

Simplify 27\(^{-\frac{1}{3}}\) \(\times\) 64\(^{-\frac{1}{3}}\) \(\times\) 4\(^{\frac{1}{3}}\)

A. 48

B. 12

C. \(\frac{4}{3}\)

D. \(\frac{1}{12}\)

E. \(\frac{1}{48}\)

D

5.

The bearing of a point Y from point x is 150°. What is the bearing of X from Y?

A. 330°

B. 240°

C. 150°

D. 120°

E. 30°

A

6.

If the mean of 3, 5, 8, k, 14 and 17 is 11, what is the value of k

A. 58

B. 38

C. 19

D. 11

E. 967

Detailed Solution

To calculate Mean:
add up all the numbers ⇒ 3+5+8+k+14+17 = 47 + k
then divide by how many numbers there are ⇒ 6
The Mean is already given as 11
11 = (47 + k) / 6
Cross multiply to solve for k
: k = (6 X 11) - 47
k = 19
7.

From the kip of a storey-buliding, the angle of depression of a mango on a tree 20 m away from the base of the storey-building is 68°. if the mango is 4.5 m above the ground, what is the height of the storey-building to the nearest metre?

A. 55m

B. 54m

C. 50m

D. 49m

E. 45m

B

8.

The mean age of 12 boys involved survey is 19 years, 3 months. lf the-age of one of the boys is 22 years, what is the mean age of the other-boys?

A. 10.5 years

B. 19.0 years

C. 35.4 years

D. 264.0 years

E. 423.5 years

B

9.

If cos x = - \(\frac{5}{13}\) where 180° < X < 270°, what is the value of tan x -sin x ?

A. \(\frac{111}{13}\)

B. \(\frac{321}{65}\)

C. -\(\frac{216}{65}\)

D. \(\frac{112}{13}\)

E. \(\frac{131}{65}\)

10.

Given that (3 - y) ÷ 2x = (6y + 7) ÷ (4x - 5), find the value of x when y = 2

A. \(\frac{64}{5}\)

B. 6

C. \(\frac{5}{34}\)

D. \(\frac{-5}{34}\)

E. \(\frac{-64}{5}\)

D