# Mathematics (2017) | Study Mode

Question 21
A

7

B

-7

C

- 7$$\sqrt{3}$$

D

7$$\sqrt{3}$$

##### Explanation
4$$\sqrt{27}$$ + 5$$\sqrt{12}$$ - 3$$\sqrt{75}$$

= 4$$\sqrt{3}$$ $$\times$$ 9 + 5$$\sqrt{3}$$ $$\times$$ 4 - 3$$\sqrt{3}$$ $$\times$$ 25

= 4 $$\times$$ 3$$\sqrt{3}$$ + 5 $$\times$$ 2$$\sqrt{3}$$ - 3 $$\times$$ 5$$\sqrt{3}$$

= 12$$\sqrt{3}$$ + 10$$\sqrt{3}$$ - 15$$\sqrt{3}$$

= (12 + 10 - 15)$$\sqrt{3}$$

= 7$$\sqrt{3}$$

Question 22
A
three times as much
B
the same
C
twice as much
D
half as much
##### Explanation
Let the speed of the 1st trip be x miles/hr

and the speed of the 2nd trip be 3x miles/hr

Speed = distance/time

? Time taken to cover a distance of 50 miles on the 1st trip

= $$\frac{50}{xhr}$$

time taken to cover a distance of 300 miles on the next trip

= $$\frac{300}{3xhr}$$

= $$\frac{100}{xhr}$$

?the new time compared with the old time is twice as much

Question 23
A

40o

B

55o

C

50o

D

60o

##### Explanation
Sum of angle at a point = 360o

2x + 3x + 4x = 360

9x = 360

x = $$\frac{360}{9}$$

x = 40o

Question 24
A
2x2 -x + 1
B
2x2 - x -1
C
2x2 + x + 1
D
2x2 + x -1

Question 25
A
60%
B
32%
C
25%
D
20%
##### Explanation
Total Cost Price = N(250,000 + 70,000)

= N 32,000

Selling Price = N 400,000(Given)

Gain = Selling Price - Cost Price

= 400,000 - 300,000

= 80,000

% gain = $$\frac{\text{Gain}}{\text{Cost Price}}$$ $$\times$$ 100

= $$\frac{80,000}{320,000}$$ $$\times$$ 100

Gain % = 25%

Question 26
A

$$\frac{10!}{2!2!2!}$$

B

$$\frac{10!}{4!2!}$$

C

$$\frac{10!}{4!2!2!}$$

D

$$\frac{10!}{2!2!}$$

##### Explanation

EXCELLENCE

It is a ten letter word = 10!

Since we have repeating letters, we have to divide to remove the duplicates accordingly. There are 4 Es, 2 Cs, 2 Ls

? there are
$$\frac{10!}{4!2!2!}$$ ways to arrange

Question 27
A

3.3 x 104

B

3.3 x 10-3

C

3.3 x 10-4

D

3.3 x 10-8

##### Explanation
$$\frac{0.00000231}{0.007}$$ to standard form

= $$\frac{231 \times 10^{-8}}{7 \times 10^{-3}}$$

= 33 $$\times$$ 10$$^{-8 - (-3)}$$

= 33 $$\times$$ 10$$^{- 8 + 3}$$

= 33 $$\times$$ 10-5

Question 28
A

5%

B

10%

C

8%

D

7%

##### Explanation
Actual measurement = 10cm

approximated value of measurement = 10.5cm

% error = $$\frac{\text{Actual measurement - Approximated}}{\text{Actual measure}}$$ $$\times$$ 100

= $$\frac{10 - 10.5}{10}$$ $$\times$$ 100

= $$\frac{-0.5}{10}$$ $$\times$$ 100

ignore -sign i.e take absolute value

= $$\frac{0.5}{10}$$ $$\times$$ 100

= 5 %

Question 29
A

N 4,900

B

N 500

C

N 4,700

D

N 400

##### Explanation
Principal = P, Simple Interest = I, Amount = A

Amount = Principal + Simple Interest

I = $$\frac{PRT}{100}$$

R = rate, T = time

I = $$\frac{P \times 5 \times 2}{100}$$

I = $$\frac{10P}{100}$$

I = $$\frac{P}{10}$$

Amount A = P + I

5500 = P + $$\frac{P}{10}$$

Multiply through by 100

5500 = 10P + P

5500 = 11P

p = $$\frac{5500}{11}$$

p = N 500

Question 30
A

N 35, 000

B

N 40,000

C

N 25,000

D

N 20,000

##### Explanation

Total angle at a point = 3600

To get the angle occupied by fertilizer we have,

40 + 50 + 80 + 70 + 30 + fertilizer(x) = 360

270 + x = 360

x = 360 -270

x = 90o

Total amount allocated to the farm
= N 80,000

Amount allocated to the fertilizer

= $$\frac{\text{fertilizer (angle) Total amount}}{\text{total angle}}$$

= $$\frac{90}{360}$$ 80,000

= N20,000

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