JAMB Mathematics Past Questions & Answers - Page 56

276.

A binary operation \(\otimes\) is defined by \(m \otimes n = mn + m - n\) on the set of real numbers, for all m, n \(\in\) R. Find the value of 3 \(\otimes\) (2 \(\otimes\) 4).

A.

6

B.

25

C.

15

D.

18

Correct answer is C

\(m \otimes n = mn + m - n\)

3 \(\otimes\) (2 \(\otimes\) 4)

2 \(\otimes\) 4 = 2(4) + 2 - 4 = 6

3 \(otimes\) 6 = 3(6) + 3 - 6  = 15

277.

The angle of elevation of the top of a tree from a point on the ground 60m away from the foot of the tree is 78°. Find the height of the tree correct to the nearest whole number.

A.

148m

B.

382m

C.

282m

D.

248m

Correct answer is C

\(\tan 78 = \frac{h}{60}\)

\(h = 60 \tan 78\)

\(h = 60 \times 4.705 = 282.27m\)

\(\approxeq\) 282m to the nearest whole number.

278.

Make q the subject of the formula in the equation \(\frac{mn}{a^2} - \frac{pq}{b^2} = 1\)

A.

\(q = \frac{b^2(mn - a^2)}{a^2 p}\)

B.

\(q = \frac{m^2 n - a^2}{p^2}\)

C.

\(q = \frac{mn - 2b^2}{a^2}\)

D.

\(q = \frac{b^2 (n^2 - ma^2)}{n}\)

Correct answer is A

\(\frac{mn}{a^2} - \frac{pq}{b^2} = 1\)

\(\frac{mn}{a^2} - 1 = \frac{pq}{b^2}\)

\(\frac{mn - a^2}{a^2} = \frac{pq}{b^2}\)

\(pq = \frac{b^2 (mn - a^2)}{a^2}\)

\(q = \frac{b^2(mn - a^2)}{a^2 p}\)

279.

The number line represents

A.

0 > x \(\geq\) -7

B.

-7 \(\leq\) x < -1

C.

-7 < x \(\leq\) -1

D.

-7 < x < -1

Correct answer is C

No explanation has been provided for this answer.

280.

In the diagram above, RST is a tangent to circle VSU center O ∠SVU = 50° and UV is a diameter. Calculate ∠RSV.

A.

90°

B.

50°

C.

45°

D.

40°

Correct answer is D

< VSU = 90° (angle in a semi-circle)

\(\therefore\) < SUV = 180° - 90° - 50°

= 40°

< RSV = 40° (angle which chord makes tangent = angle in alternate segment)