## MATHEMATICS (2016) Study Mode

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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.

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.

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.

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.

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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