## Mathematics (2017) Study Mode

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1.

Given T = { even numbers from 1 to 12 }
N = {common factors of 6, 8 and 12}
Find T ∩ N

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A.
{2, 3}
B.
{2, 3, 4}
C.
{3, 4, 6}
D.
{2}
Explanation. Give a better 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

2.

What is the next number in the series 2, 1, $$\frac{1}{2}$$, $$\frac{1}{4}$$...

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A.

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

B.

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

C.

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

D.

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

Explanation. Give a better 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 $$\times$$ $$\frac{1}{16}$$

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

3.
If U = {x : x is an integer and 1 ? x ? }
E1 = {x: x is a multiple of 3}
E2 = {x: x is a multiple of 4} and an integer is picked at random from U, find the probability that it is not in E2
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A.
$$\frac{3}{4}$$
B.
$$\frac{3}{10}$$
C.
$$\frac{1}{4}$$
D.
$$\frac{1}{20}$$
Explanation. Give a better 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 ? $$\frac{5}{20}$$

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

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

4.

The curved surface area of a cylinder 5cm high is 110cm2. Find the radius of its base
π = $$\frac{22}{7}$$

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A.

2.6cm

B.

3.5cm

C.

3.6cm

D.

7.0cm

Explanation. Give a better 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

5.

If two graphs Y = px2 + q and y = 2x2 - 1 intersect at x =2, find the value of p in terms of q

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A.

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

B.

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

C.

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

D.

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

Explanation. Give a better 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 = $$\frac{7 - q}{4}$$

6.

Evaluate ($$\sin$$45o + $$\sin$$30o ) in surd form

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A.

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

B.

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

C.

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

D.

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

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

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

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

= (sin45 + sin30)

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

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

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

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

7.
If y = x Sin x, find $$\frac{dy}{dx}$$ when x = $$\frac{\pi}{2}$$
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A.
$$\frac{- \pi}{2}$$
B.
-1
C.
1
D.
$$\frac{ \pi}{2}$$
Explanation. Give a better 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

8.

If temperature t is directly proportional to heat h, and when t = 20oC, h = 50 J, find t when h = 60J

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A.

24oC

B.

20oC

C.

34oC

D.

30oC

Explanation. Give a better 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

9.
Evaluate 1 - ($$\frac{1}{5}$$ x $$\frac{2}{3}$$) + ( 5 + $$\frac{2}{3}$$)
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A.
4
B.
3
C.
2$$\frac{2}{3}$$
D.
3$$\frac{2}{3}$$

10.
Given m = N$$\frac{\sqrt{SL}}{T}$$ make T the subject of the formula
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A.
$$\frac{\text{NSL}}{M}$$
B.
$$\frac{N^2SL}{M^2}$$
C.
$$\frac{N^2SL}{M}$$
D.
$$\frac{NSL}{M^2}$$
Explanation. Give a better Explanation
M = $$\frac{\sqrt{SL}}{T}$$,

make T subject of formula square both sides

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

TM2 = N2SL

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

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