# Mathematics (2018) | Study Mode

Question 41
A
-5.3
B
0.5
C
3
D
8
##### Explanation

The minimum value is the lowest value of the curve on y axis which gives a value of -5.3

Question 42
A
-1 1$$\frac{1}{2}$$
B
-1
C
1
D
5
##### Explanation

log$$_2$$ 8 log$$_3$$ $$\frac{1}{9}$$

= log $$_2$$ 2$$^3$$ log$$_3$$ 9$$^{-1}$$

= log$$_2$$ 2$$^3$$ log$$_3$$ 3$$^{-2}$$

Based on law of logarithm

= 3 log$$_2$$ 2 (-2 log$$_3$$ 3)

But log$$_2$$ 2 = 1,

log$$_3$$ 3 = 1

So, = 3 + 2

= 5

Question 43
A
Second only
B
Third only
C
Fourth only
D
First and third only
##### Explanation

First quadrant: Sin, Cos and Tan are all positive

Second quadrant: Sin is positive, Cos is negative and Tan is negative

Third quadrant: Tan is positive, Sin is negative and Cos is negative

Fourth quadrant: Cos is positive, Sin is negative and Tan is negative

The correct option is the third quadrant only where Tan is positive and Sin is negative

Question 44
A
36
B
40
C
44
D
50
##### Explanation

The total number of students is f = 3 + 4 + 5 + 6 + 7 + 6 + 5 + 4

= 40

Question 45
A
2
B
3
C
4
D
7
##### Explanation

A = (p, q, r, t, u, v)

B = (r, s, t, u)

A U B = Elements in both A and B = (p, q, r, s, t, u, v)

(A U B)1 = elements in the universal set E but not in (A U B)= (w, x, y, z)

n(A U B) 1 = number of the elements in (A U B)1 = 4

Question 46
A
A straight line of length 4cm
B
C
perpendicular to point P at 4cm
D
a circle of diameter 4cm
##### Explanation

Locus is the path traced at by a point which moves in accordance with a certain law. It is also the set of all possible position occupied by an object The path traced from all possible location of 4cm from a given point P form a circle of radius 4cm with centre P.

Question 47
A
14$$^o$$
B
21$$^o$$
C
32$$^o$$
D
39$$^o$$
##### Explanation

Sin(5x - 28) = Cos(3x - 50)..i

But Sin = Cos(90 - )

So Sin(5x - 28) = Cos(90 - [5x - 28])

Sin(5x - 28) = Cos(90 - 5x + 28)

Sin(5x - 28) = Cos(118 - 5x)ii

Combining i and ii

Cos(3x - 50) = Cos(118 - 5x)

3x - 50 = 118 - 5x

Collecting the like terms

3x + 5x = 118 + 50

8x = 168

x = $$\frac{168}{8}$$

x = 21$$^o$$

Question 48
A
20
B
19
C
17
D
15
##### Explanation

Prime numbers are numbers that has only two factors (i.e 1 and itself). They are numbers that are only divisible by 1 and their selves. First four Prime numbers greater than 10 are 11, 13, 17 and 19

Average = sum of numbers / number

= $$frac{(11 + 13 + 17 + 19)}{4}$$

= $$\frac{60}{4}$$

= 15

Question 49
A
4
B
5
C
6
D
7
##### Explanation

The modal age is the age with the highest frequency, and that is age 5 years with f of 7

Question 50
A
0.040
B
0.049
C
0.050
D
0.49
##### Explanation

0.04945 to 2s.f is 0.05

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