Mathematics Questions & Answers - Free Online Practice

3,526.

In the diagram O is the center of the circle, if ∠QRS = 62^o, find the value of ∠SQR.

14^o

28^o

31^o

45^o

90^o

View answer & explanation

Correct answer is B

< QSR = 90° (angle in a semi-circle)

\(\therefore\) < SQR = 180° - (90° + 62°)

= 28°

3,527.

In the diagram above, TPS is a straight line, PQRS is a parallelogram with base QR and height 8cm. |QR| = 6cm and the area of triangle QST is 52cm2. Find the area of ΔQPT

39cm²

28cm²

24cm²

21cm²

19cm²

View answer & explanation

Correct answer is B

Area of \(\Delta\)QST = 52cm\(^2\); height = 8cm
b=base length; but A = 1/2 b x h
=52=1/2 x b x 8cm = 104 =8b
b=104/8 = 13cm; ST= 13cm; PS = 6cm
TP = 13 - 6 = 7cm;
area of \(\Delta\)QST = 1/2 b x h
= 1/2 x 7 x 8/1 = 28cm\(^2\)

3,528.

If the second and fourth term of a G.P are 8 and 32 respectively,what is the sum of the first four terms?

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Correct answer is D

ar = 8 .....(1)

ar³ = 32 .....(2)

divide (2) by (1)

r² = 4 r = 2 ∴ a = 4

S =

a(rⁿ - 1)/r - 1

S =

4(2⁴ - 1)/2 - 1

= 60

3,529.

If 3loga + 5loga - 6loga = log64, what is a?

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Correct answer is C

loga³ + loga⁵ - loga⁶

log(

a³ * a⁵/a⁶

) = loga⁶⁴

a² = 64 a = 8

3,530.

The surnames of 40 children in a class arranged in alphabetical order. 16 of the surnames begins with O and 9 of the surname begins with A, 14, of the letters of the alphabet do not appear as the first letter of a surname

If more than one surname begins with a letter besides A and O, how may surnames begin with that letter

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Correct answer is E

14 of the letters of the alphabet do not appear as the first letter of surname
∴ the no. of letters that appeared = 26-14 = 12 alphabets
15 surnames begin with 10 letters beside O and A
∴ 6 surnames begin with a letter