Mathematics Questions & Answers - Free Online Practice

826.

The population of students in a school is 810. If this is represented on a pie chart, calculate the sectoral angle for a class of 72 students

32^o

45^o

60^o

75^o

View answer & explanation

Correct answer is A

In a school with students' population 810, the sectoral angle for a class of 72 students is

= \(\frac{72}{810}\) x 360º

= 32º

827.

The angle of elevation of an aircraft from a point K on the horizontal ground 30\(\alpha\). If the aircraft is 800m above the ground, how far is it from K?

400.00m

692.82m

923.76m

1,600.99m

View answer & explanation

Correct answer is D

In \(\bigtriangleup\)KBC, sin 30 = \(\frac{800}{IKCI}\)

IKCL = \(\frac{800}{sin30^o}\)

= \(\frac{800}{0.5}\)

= 1600m

828.

PQRT is square. If x is the midpoint of PQ, Calculate correct to the nearest degree, LPXS

53^o

55^o

63^o

65^o

View answer & explanation

Correct answer is C

In the diagram given,

tan\(\alpha\) = \(\frac{1}{0.5}\) = 2

\(\alpha\) = tan - 1(2) = 63.43^o

= 63^o

829.

Given that tan x = \(\frac{2}{3}\), where 0^o d" x d" 90^o, Find the value of 2sinx.

\(\frac{2\sqrt{13}}{13}\)

\(\frac{3\sqrt{13}}{13}\)

\(\frac{4\sqrt{13}}{13}\)

\(\frac{6\sqrt{13}}{13}\)

View answer & explanation

Correct answer is C

tan x = \(\frac{2}{3}\)(given), is illustrated in a right-angled \(\Delta\)

thus m² = 2² + 3²

= 4 + 9 = 13

m = \(\sqrt{13}\)

Hence, 2sin x = 2 x \(\frac{2}{m}\)

2 x\(\frac{2}{\sqrt{13}}\)

= \(\frac{4}{\sqrt{13}}\)

= \(\frac{4}{\sqrt{13}} = \frac{\sqrt{13}}{\sqrt{13}}\)

= \(\frac{4\sqrt{13}}{13}\)

830.

\(\begin{array}{c|c}
x & 0 & 1\frac{1}{4} & 2 & 4\\
\hline
y & 3 & 5\frac{1}{2} & &
\end{array}\)
The table given shows some values for a linear graph. Find the gradient of the line

View answer & explanation

Correct answer is B

Ler: (x1, y1) = (0, 3)

(x2, y2) = (\(\frac{5}{4}, \frac{11}{2}\))

Using gradient, m = \(\frac{y_2 - y_2}{x_2 - x_1}\)

= \(\frac{\frac{11}{2} - 3}{\frac{5}{4} - 0}\)

= \(\frac{11 - 6}{2} + \frac{5}{4}\)

= \(\frac{5}{} + \frac{5}{4}\)

= \(\frac{5}{2} \times \frac{4}{5}\)

= 2