JAMB Mathematics Past Questions & Answers - Page 166

826.

Simplify 10² + log₁₀5

500

2 log₁₀ 5

log₁₀5 x 10¹⁰⁰

View answer & explanation

Correct answer is E

10² + log₁₀5 = log₁₀ 10¹⁰⁰ + log₁₀5

= log₁₀5 x 10¹⁰⁰

827.

Given log 2 = 0.69, log3 = 1, 10 and log7 = 1.90, all to a fixed base, find log 10.5 to the same base without using tables.

1.03

2.31

3.69

10.5

View answer & explanation

Correct answer is B

log 10.5 = log \(\frac{21}{2}\)

= log 21 - log 2

= log(3 x 7) - log 2

= log 3 + log 7 - log 2

= 1.10 + 1.90 - 0.69

= 3 - 0.69

= 2.31

828.

Solve the equation for the positive values of \(\theta\) less than 360^o. 3 tan \(\theta\) + 2 = -1

135^o or 315^o

45^o or 135^o

315^o or 180^o

315v + 45^o

360^o or 315^o

View answer & explanation

Correct answer is A

3 tan \(\theta\) + 2 = -1

3 tan \(\theta\) \(\frac{-3}{3}\) = -1

\(\theta\) = tan -1(-1)

\(\theta\) = 360^o - 45^o

= 315^o

\(\theta\) = 180 - 45^o = 135^o

829.

Find the area of the curved surface of a cone whose base radius is 6cm and whose height is 8cm. (take \(\pi\) = \(\frac{22}{7}\))

188.57cm²

1320cm²

188cm²

188.08cm²

10cm²

View answer & explanation

Correct answer is A

S = curved surface area = \(\pi\)rL

= \(\frac{22}{7}\) x 6 x 10

= 188.57cm²

830.

Simplify the given expression \(\sqrt{\frac{1 - cos x}{1 + cos x}}\)

\(\frac{1 - cos x}{sin x}\)

1 - cos x

sin x

1 + cos x

\(\frac{1 + cos x}{sin x}\)

View answer & explanation

Correct answer is A

\(\sqrt{\frac{1 - cos x}{1 + cos x}}\) = a

a² = \(\frac{1 - cosx}{1 + cosx}\)

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

= \(\frac{(1 - cosx)^2}{cos^2 x}\)

a² = \(\frac{(1 - cos x)^2}{sin^2 x}\)

a = \(\frac{1 - cos x}{sin x}\)