## Mathematics (2017) Study Mode

Try this quiz in CBT Mode

Question 1
A
{2, 3}
B
{2, 3, 4}
C
{3, 4, 6}
D
{2}
Explanation.

T = {evenn numbers from 1 to 12}
N = {common factors of 6,8 and 12}
Find T ∩ N
T = {2, 4, 6, 8, 10, 12}
N = {2}
T ∩ N = {2} i.e value common to T & N

Question 2
A

$$\frac{1}{3}$$

B

$$\frac{2}{8}$$

C

$$\frac{3}{7}$$

D

$$\frac{1}{8}$$

Explanation.
2, 1, $$\frac{1}{2}$$, $$\frac{1}{4}$$.....

There are 4 terms in the series
Therefore the next number will be the 5th term

Tn = ar$$^{n - 1}$$ (formular for geometric series)

a = first term = 2

r = common rate = $$\frac{\text{next term}}{\text{previous term}}$$ = $$\frac{1}{2}$$

n = number of terms

T5 = 5th term = ?

T5 = ar$$^{5 - 1}$$

= ar$$^4$$

= 2 $$\times$$ (ar$$^{n - 1}$$)4

= 2 $$\times$$ $$\frac{1}{16}$$

= $$\frac{1}{8}$$

Question 3
A
$$\frac{3}{4}$$
B
$$\frac{3}{10}$$
C
$$\frac{1}{4}$$
D
$$\frac{1}{20}$$
Explanation.
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

E1 = {3, 6, 9, 12, 15, 18}

E2 = {4, 8, 12, 16, 20}

Probability of E2 = $$\frac{5}{20}$$ i.e $$\frac{\text{Total number in}E_2}{\text{Entire number in set}}$$

Probability of set E2 = 1 ? $$\frac{5}{20}$$

= $$\frac{15}{20}$$

= $$\frac{3}{4}$$

Question 4
A

2.6cm

B

3.5cm

C

3.6cm

D

7.0cm

Explanation.
Curved surface area of cylinder = 2πrh

110 = 2 $$\times$$ $$\frac{22}{7}$$ $$\times$$ r $$\times$$ 5

r = $$\frac{110 \times 7}{44 \times 5}$$

= 3.5cm

Question 5
A

q - $$\frac{8}{7}$$

B

7 - $$\frac{q}{4}$$

C

8 - $$\frac{q}{2}$$

D

7 + $$\frac{q}{8}$$

Explanation.
Y = Px2 + q

Y = 2x2 - 1

Px2 + q = 2x2 - 1

Px2 = 2x2 - 1 - q

p = $$\frac{2x^2 - 1 - q}{x^2}$$

at x = 2

P = $$\frac{2(2)^2 - 1 - q}{2^2}$$

= $$\frac{2(4) - 1 -q}{4}$$

= $$\frac{8 - 1 - q}{4}$$

P = $$\frac{7 - q}{4}$$

Question 6
A

$$\frac{\sqrt{3}}{2\sqrt{2}}$$

B

-3 - $$\frac{1}{2}$$

C

$$\frac{1}{2}$$-2

D

1 + $$\frac{\sqrt{2}}{2}$$

Explanation.
hypotenuse
sin = $$\frac{1}{2}$$

$$\sin45 = \frac{1}{\sqrt{2}}$$

= $$\frac{2}{2}$$

= (sin45 + sin30)

= $$\frac{1}{\sqrt{2}} + \frac{1}{2}$$

= $$\frac{\sqrt{2}}{2}$$ + $$\frac{1}{2}$$

= $$\frac{\sqrt{2} + 1}{2}$$

= $$\frac{1 + \sqrt{2}}{2}$$

Question 7
A
$$\frac{- \pi}{2}$$
B
-1
C
D
$$\frac{ \pi}{2}$$
Explanation.
y = xsinx

$$\frac{dy}{dx}$$ = $$1 \sin x + x \cos x$$

= $$\sin x + x \cos x$$

At x = $$\frac{\pi}{2}$$

= sin$$\frac{\pi}{r}$$ + $$\frac{\pi}{2} \cos {\frac{\pi}{2}}$$

= 1 + $$\frac{\pi}{2}$$ $$\times$$ 10

= 1

Question 8
A

24oC

B

20oC

C

34oC

D

30oC

Explanation.
t α h, t = 20, h

t = ? h = 60

t = kh where k is constant

20 = 50k

k = $$\frac{20}{50}$$

k = $$\frac{2}{5}$$

when h = 60, t = ?

t = $$\frac{2}{5}$$ $$\times$$ 60

t = 24oC

Question 9
A
B
C
2$$\frac{2}{3}$$
D
3$$\frac{2}{3}$$
Explanation.

No official Explanation yet!

Question 10
A
$$\frac{\text{NSL}}{M}$$
B
$$\frac{N^2SL}{M^2}$$
C
$$\frac{N^2SL}{M}$$
D
$$\frac{NSL}{M^2}$$
Explanation.
M = $$\frac{\sqrt{SL}}{T}$$,

make T subject of formula square both sides

M2 = $$\frac{N^2SL}{T}$$

TM2 = N2SL

T = $$\frac{N^2SL}{M^2}$$