WAEC Mathematics Past Questions & Answers - Page 71

351.

In the diagram, \(\bar{YW}\) is a tangent to the circle at X, |UV| = |VX| and < VXW = 50o. Find the value of < UXY.

A.

70o

B.

80o

C.

105o

D.

110o

Correct answer is B

In the diagram above, x1 = 50(angles in alternate segment)

x1 = x2(base angles of isos. \(\Delta\))

< UXY + x2 + 50o = 180o(sum of angles on a straight line)

< UXY + 50o + 50o = 180p

< UXY + 100o = 180o

< UXY = 180o - 100o

= 80o

352.

\(\begin{array}{c|c}
Age(years) & 13 & 14 & 15 & 16 & 17 \\
\hline
Frequency & 10 & 24 & 8 & 5 & 3
\end{array}\)
Find the median age

A.

13

B.

14

C.

15

D.

16

Correct answer is B

Median = \(\frac{N}{2}\)th age

= \(\frac{50}{2}\)th age

= 25th age

= 14 years

354.

If cos \(\theta\) = x and sin 60o = x + 0.5 0o < \(\theta\) < 90o, find, correct to the nearest degree, the value of \(\theta\)

A.

32o

B.

40o

C.

60o

D.

69o

Correct answer is D

sin 60o = x + 0.5 0o(given)

0.8660 = x + 0.5

0.8660 - 0.5 = x

x = 0.3660

cos\(\theta\) = x(given)

cos\(\theta\) = 0.3660

Hence, \(\theta\) = cos-1(0.3660)

= 68.53o

= 69o (nearest degree)

355.

A straight line passes through the point P(1,2) and Q
(5,8). Calculate the length PQ

A.

\(4\sqrt{11}\)

B.

\(4\sqrt{10}\)

C.

\(2\sqrt{17}\)

D.

\(2\sqrt{13}\)

Correct answer is D

|PQ| = \(\sqrt{(x_2 - X- 1) + (y_2 - y_1)^2}\)

= \(\sqrt{(5 - 1)^2 + (8 - 2)^2}\)

= \(\sqrt{4^2 + 6^2}\)

= \(\sqrt{16 + 36}\)

= \(\sqrt{52}\)

= 2\(\sqrt{13}\)