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1.
Integrate \(\frac{2x^3 + 2x}{x}\) with respect to x
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A.
\(\frac{2x^3}{3}\) - 2x + k
B.
x3 + 2x + k
C.
\(\frac{2x^3}{3}\) + 2x + k
D.
x3 - 2x + k
Explanation. Give a better Explanation
\(\int\) \(\frac{2x^3 + 2x}{x}\) = \(\int\) \(\frac{2x^3}{x}\) + \(\frac{2x}{x}\) = \(\int\) (2x2 + 2) dx

\(\frac{2x^2+1}{2 + 1}\) + 2x + k

= \(\frac{2x^3}{3}\)+ 2x + k


2.
If the mean of 4, y, 8 and 10 is 7. Find Y?
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A.
6
B.
10
C.
7
D.
9
Explanation. Give a better Explanation
\(\frac{4 + y + 8 + 10}{4}\) = 7

22 + y = 4 x 7
22 + y = 28
y = 28 - 22 = 6


3.

Find the derivative of y = ( \(\frac{1}{3}\)X + 6)

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A.

2( \(\frac{1}{3}\)X + 6 )

B.

\(\frac{2}{3}\) ( \(\frac{1}{3}\)X + 6)

C.

\(\frac{2}{3}\) ( \(\frac{1}{3}\)X + 6)2

D.

\(\frac{1}{3}\) ( \(\frac{1}{3}\)X + 6)2

Explanation. Give a better Explanation

Y = ( \(\frac{1}{3}\)X + 6)2

\(\frac{dy}{dx}\) = 2( \(\frac{1}{3}\)X + 6) \(\frac{1}{3}\)

= \(\frac{2}{3}\) ( \(\frac{1}{3}\)X + 6)



4.
In a school of 150 students, 80 offer French while 60 offer Arabic and 20 offer neither. How many students offer both subjects?
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A.
45
B.
10
C.
35
D.
30
Explanation. Give a better Explanation
80 - x + x + 60 - x + 20 = 150
160 - x = 150
x = 160 - 150 = 10


5.
If the 2nd term of a G.P is \(\frac{8}{9}\) and the 6th term is 4\(\frac{1}{2}\). Find the common ratio.
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A.
2
B.
\(\frac{3}{2}\)
C.
\(\frac{2}{3}\)
D.
3
Explanation. Give a better Explanation
T2 = \(\frac{8}{9}\), T6 = 4\(\frac{1}{2}\)
ar = \(\frac{8}{9}\)
ar5 = \(\frac{9}{2}\)

\(\frac{ar}{ar^5}\) = \(\frac{8}{9}\) x \(\frac{2}{9}\)

\(\frac{1}{r^4}\) = \(\frac{16}{81}\)

r = \(\sqrt[4]{18/16}\) = \(\frac{3}{2}\)


6. q-image

From the diagram above, find the value of < OTQ

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A.

230o

B.

55o

C.

115o

D.

65o

Explanation. Give a better Explanation
< OTQ = \(\frac{130}{2}\)
= 65o


7.
The sum of the interior angles of a polygon is a given as 1080o. Find the number of the sides of the polygon.
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A.
5
B.
7
C.
6
D.
8
Explanation. Give a better Explanation
\(\frac{(n - 2) 180}{180}\) = \(\frac{1080}{180}\)

(n - 2) = 6
n = 6 + 2 = 8


8. q-image

In the diagram above, l1 is parallel to l2, Find the value of < PMT

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A.

82o

B.

36o

C.

72o

D.

118o

Explanation. Give a better Explanation
< MPT = 180o - 118o = 62o

< PML = 62o ( Alternative angle)

y + 2y + 10o + 62o = 180o (Angles on a straight line)

3y = 180 - 72
\(\frac{3y}{3}\) = \(\frac{108}{3}\)
y = 36o

< PMT = 2y + 10 = 2(36) + 10 = 82o


9. q-image

From the diagram above, Find the value of < ROP

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A.

110o

B.

70o

C.

95o

D.

85o

Explanation. Give a better Explanation
< ROP = 95o (Exterior angle of cyclic quadrilateral)


10. q-image

The venn diagram shows a class of 50 students with the games they play. How many students play only two games?

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A.

15

B.

16

C.

20

D.

18

Explanation. Give a better Explanation

Number of students that plays only two games = 4 + 8 + 3  = 15



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