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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. q-image

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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