# Mathematics (2017) | Study Mode

Question 41
A

9

B

-9

C

6

D

-6

##### Explanation

x * y is an operation on 3x + 2y - 1

Find 3A - 1

x = 3, y = -1

3 * - 1 on 3x + 2y - 1

3(3) + 2(-1) -1

= 9 - 2 - 1

= 6

Question 42
A

3-Feb

B

2-Jan

C

-1

D

3-Feb

##### Explanation

Gradient of line joining points (3, 2), (1, 4)

Gradient = $$\frac{\text{Change in Y}}{\text{Change in X}}$$

= $$\frac{y_2 - Y_1}{x_2 - x_1}$$

(X1, Y1) = (3, 2)

(X2, Y2) = (1, 4)

Gradient = $$\frac{4 - 2}{1 + 3}$$

= $$\frac{2}{-2}$$

= -1

Question 43
A

4a

B

$$\frac{1}{8a}$$

C

8a

D

$$\frac{1}{4a}$$

##### Explanation

(3-64a3)$$^{-1}$$

$$\frac{1}{(3-64a^3)}$$

= $$\frac{1}{4a}$$

Question 44
A

1, - 2

B

- 2, n = 1

C

$$\frac{-2}{5}$$, 1

D

$$\frac{2}{3}$$

##### Explanation

$$\frac{2 \sqrt{3} - \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}}$$= m + n-6

$$\frac{2 \sqrt{3} - \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}}$$ x $$\frac{\sqrt{3} - 2 \sqrt{2}}{\sqrt{3} - \sqrt{2}}$$

$$\frac{2 \sqrt{3} (\sqrt{3} - 2 \sqrt{2}) - \sqrt{2}(\sqrt{3} - 2 \sqrt{2})}{\sqrt{3}(\sqrt{3} - 2 \sqrt{2}) + 2 \sqrt{2}(\sqrt{3} - 2 \sqrt{2})}$$

$$\frac{2 \times 3 - 4\sqrt{6} - 6 + 2 \times 2}{3 - 2 \sqrt{6} + 2 \sqrt{6} - 4 \times 2}$$

= $$\frac{6 - 4 \sqrt{6} - \sqrt{6} + 4}{3 - 8}$$

= $$\frac{0 - 4 \sqrt{6} - 6}{5}$$

= $$\frac{10 - 5 \sqrt{6}}{5}$$

= - 2 + -6

- m + n$$\sqrt{6}$$ = - 2 + -6

m = - 2, n = 1

Question 45
A

$$\frac{-5}{3}$$

B

$$\frac{-2}{3}$$

C

$$\frac{1}{2}$$

D

$$\frac{5}{2}$$

##### Explanation

$$\frac{1}{\alpha}$$ + $$\frac{1}{\beta}$$ = $$\frac{\beta -\alpha}{\alpha \beta}$$

3x2 + 5x + 5x - 2 = 0.

Sum of root = +

Product of root =

x2 + $$\frac{5x}{3}$$ - $$\frac{2}{3}$$ = 0

= - $$\frac{-2}{3}$$

+ = $$\frac{5}{3}$$

- $$\frac{\alpha + \beta}{\alpha \beta}$$ = - $$\frac{\frac{5}{3}}{\frac{2}{3}}$$

= - $$\frac{2}{3}$$ $$\times$$ $$\frac{3}{3}$$

= $$\frac{5}{2}$$

Question 46
A

1.03

B

0.07

C

0.03

D

1

##### Explanation

0.4, -0.4, 0.3, 0.47, -0.53, 0.2, -0.2

Range is the difference between the highest and lowest value

i.e Highest - Lowest

- 0.53, -0.4, -0.2, 0.2, 0.3, 0.4, 0.47

0.47 is the highest

- 0.53 is the lowest

- = 0.47 - (- 0.53)

-0.47 + 0.53

= 1.0

Question 47
A

4

B

3

C

2$$\frac{2}{3}$$

D

3 $$\frac{2}{3}$$

##### Explanation

1 - ($$\frac{1}{5}$$ + 1$$\frac{2}{3}$$) + (5 + 1$$\frac{2}{3}$$)

1 - ($$\frac{1}{5}$$ $$\times$$ $$\frac{5}{3}$$) + (5 + $$\frac{5}{3}$$)

1 - $$\frac{1}{3}$$ + $$\frac{20}{3}$$

= $$\frac{22}{3}$$

Question 48
A

4x3 - 8x2 + 5x + 3

B

-4x3 + 8x2 - 5x + 3

C

-4x3 - 8x2 + 5x + 3

D

4x3 + 8x2 - 5x + 3

##### Explanation

(2x2 - x + 1) $$\times$$ (3 - 2x);

3(2x2 - x + 1) - 2x (2x2 - x + 1)

6x2 - 3x + 3 - 4x3 + 2x2 - 2x

-4x3 + 8x2 -5x + 3

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