JAMB Mathematics Past Questions & Answers - Page 185

921.

PQR is the diagram of a semicircle RSP with centre at Q and radius of length 3.5cm. If QPT = 60o. Find the perimeter of the figure PTRS. \(\pi\) = \(\frac{22}{7}\)

A.

25cm

B.

18cm

C.

36cm

D.

29cm

E.

25.5cm

Correct answer is A

Circumference of PRS = \(\frac{\pi}{2}\) = \(\frac{22}{7}\) x \(\frac{7}{1}\) x \(\frac{1}{2}\)

= 11cm

Side PT = 7cm, Side TR = 7cm

Perimeter(PTRS) = 11cm + 7cm + 7cm

= 25cm

922.

Simplify \(\sqrt[3]{\frac{27a^{-9}}{8}}\).

A.

\(\frac{9a^2}{2a^3}\)

B.

\(\frac{3}{2a^3}\)

C.

\(\frac{2}{3a^2}\)

D.

\(\frac{3a^2}{2}\)

Correct answer is B

\(\sqrt[3]{\frac{27a ^{-9}}{8}}\) = \(\frac{3a^{-3}}{2}\)

= \(\frac{3}{2}\) x \(\frac{1}{a^3}\)

= \(\frac{3}{2a^3}\)

923.

On a square paper of length 2.524375cm is inscribed square diagram of length 0.524375cm. Find the area of the paper not covered by the diagram. correct to 3 significant figures.

A.

6.00cm2

B.

6.10cm2

C.

6cmv

D.

6.09cm2

E.

4.00cm2

Correct answer is B

Area of the paper = area of square = L x B or S2

where s = S x k

Area of the paper = (2.524)2

area of the diagram = (0.524)2

area not covered = (2.524)2 - (0.524)2

= 6.370576 - 0.274576

= 6.096

= 6.10cm2 (2 s.f)

925.

A ship H leaves a port P and sails 30 km due south. Then it sails 60km due west. What is the bearing of H from P?

A.

20o 34'

B.

243o 26'

C.

116o 34'

D.

63o 26'

E.

240o 56'

Correct answer is B

Let the bearing of H from P be represented by x°.

\(\tan \theta = \frac{30}{60} = 0.5\)

\(\theta = \tan^{-1} (0.5) = 26.565°\)

\(x = 180° + (90 - 26.565)\)

\(x = 180 + 63.435 = 243.435°\)

= \(243° 26'\)