# Mathematics 2009 | Study Mode

Question 11
A
I and II
B
I and III
C
II and III
D
I, II and III
##### Explanation
STW = S(This means that all the elements of s are in T and also in W.)
STW = W (imply W is a universal set for S and T) TW = S imply all the elements of S are in T and W)
S T W
I, II, and III

Question 12
A
$$\frac{p^2 t}{s^3}$$
B
$$\frac{p^3 t}{s^3}$$
C
$$\frac{p^3 t}{s^2}$$
D
$$\frac{p^ t}{s^3}$$
##### Explanation
$$P=\sqrt{\frac{rs^3}{t}}\\= P^2 =\frac{rs^3}{t}\\ tp^2 = rs^3\\ r = \frac{p^2 t}{s^3}$$

Question 13
A
15x2 - 11x 12
B
15x2 + 11x 12
C
12x2 - x 12
D
12x2 + 11x 15
##### Explanation
If 4/3 and -3/5 are roots of a polynomial
Imply x = 4/3 and - 3/5
3x = 4 and 5x = -3
3x-4 = 0 and 5x+3 = 0 are factors
(3x-4)(5x+3) = 0 product of the factors
15x2 + 9x 20x 12 = 0 By expansion
15x2 - 11x 12 = 0

Question 14
A
y = 2+7x+4x2
B
y = 2-7x+4x2
C
y = 2+7x-4x2
D
y = 2-7x-4x2
##### Explanation
x = -2 and x = 1/4
x = -2 and 4x = 1
x+2 and 4x-1
(x+2)(4x-1) = 0
4x2 - x + 8x -2 = 0
4x2 + 7x 2 = 0 but y intercept is positive. Multiply the equation by -1
-4x2 - 7x + 2 = 0
y = 2 7x 4x2

Question 15
A
6/35
B
10/21
C
21/10
D
35/6
##### Explanation
$$W U\\ W = KU\\ K = \frac{W}{U}\\ K = \frac{5}{3}\\ W = \frac{5}{3}U\\ \frac{2}{7} = \frac{5}{3}U\\ U = \frac{2}{7} \times \frac{3}{5}\\ U = \frac{6}{35}$$

Question 16
A
x < -1 or x > 1
B
-1 < x < 1
C
x > 0
D
x < -1
##### Explanation
x2 > 0
(x+1)(x-1) > 0
x > -1 or -1
x < -1 or x > 1

Question 17
A
-5 < x < $$\frac{7}{3}$$
B
-5 $$\leq$$ x $$\leq$$ $$\frac{7}{3}$$
C
-5 < x $$\leq$$ $$\frac{7}{3}$$
D
-5 $$\leq$$ x < $$\frac{7}{3}$$
##### Explanation
3x - 7 $$\leq$$ 0 and x + 5 > 0
3x $$\leq$$ 7 and x > -5
x $$\leq$$ $$\frac{7}{3}$$
Range -5 < x $$\leq$$ $$\frac{7}{3}$$

Question 18
A
n(3n - 0.5)
B
n(3n + 2)
C
n(3n + 2.5)
D
n(3n + 5)
##### Explanation
a = 5, d = 6, n = n
Sn = n/2(2a + (n-1)d)
= n/2(2(5) + (n-1)6)
= n/2(10 + 6n-6)
= n/2(6n+4)
= 6n2/2 + 4n/2
= 32 + 2n
= n(3n + 2)

Question 19
A
10
B
9
C
10/9
D
9/10
##### Explanation
$$a=1, r=\frac{9}{10}\\ S_n = \frac{a}{1-r}\\ S_n = \frac{1}{1-\frac{9}{10}}\\ =1\div \frac{1}{10}\\ =1\times \frac{10}{1}\\ 10$$

Question 20
A
-6
B
-8
C
-10
D
-12
##### Explanation
m * n = n - (m+2)
= -5 - (3+2)
= -5-5
= -10

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