# Mathematics (2015) | Study Mode

Question 31
A

21cm2

B

21cm2

C

15cm2

D

17cm2

##### Explanation

The area of cross section = (2 - 102)

= (11 + 10)(11 - 10)

(21)(1)

= 21cm2

Question 32
A

x = 2 or 1

B

x = 3 or -1

C

x = 1 or 0

D

x = 1 or 2

##### Explanation

x2 - 2x - 3 = 0

-3x + x = - 2x

- 3x $$\times$$ x = - 3x2

(x2 - 3x)(x - 3) = 0

(x - 3)(x + 1) = 0

Either (x - 3) = 0 or (x + 1) = 0

x = 3 or - 1

Question 33
A

3.13cm2

B

145cm2

C

314cm2

D

214cm2

##### Explanation

Explanation

V = r2h

V = ?, h = 4cm, r = 5cm

V = 3.14(5)2 (4)

V = 3.14(25)(4)

V = 3.14 $$\times$$ 1200

= 314cm2

Question 34
A

-Cos x + 2xSin x + C

B

-Cos x + 2

C

x2Cos x + 2xSin x + 2Cos x+ C

D

-x2Cos x + 2xSinx + 2Cos x + C

##### Explanation

Let u= x2

du = 2xdx

Let v = sinx

-dv = - sin x i.e. v = cos x

- udv = uv - - vdu

- x2 Sin xdx = - x2 Cos x - - (- Cos x)2 $$\times$$ dx

x2 Cos x + 2 - x cos x1 dx

= - x2 Cos x + 2 - x Cos x2 dx

2 - u Cos xdx

Let u = x

du = dx

dv = Cos x

-dv = - Cos x

- x2 Sin x1 dx = - x2 Cos x + 2Sin x - 2Cos x + C

- x2 Sin xdx

= - x2 Cos x + 2xSin + 2Cos x + C

Question 35
A

$$\frac{2}{15}$$

B

$$\frac{3}{4}$$

C

$$\frac{7}{15}$$

D

$$\frac{1}{15}$$

##### Explanation

Prob(A) = $$\frac{1}{5}$$ , Prob(B) = $$\frac{1}{4}$$, Prob (A B) = $$\frac{1}{15}$$, Prob (A B) = ?

Note:

I. the probability is either event of A or B or both.

The formula using is prob (A $$\cup$$ B) = -prob(A) + prob(A) $$\cup$$ prob(A B)

II. But if the probability of both outcomes A and B

The formula using is Prob(A B) $$\cup$$ prob(A) + prob(B) + prob (A $$\cup$$ B)

In this question, A or B, Prob (A $$\cup$$ B): A and B, Prob (A $$\cup$$ B)

prob (A $$\cup$$ B) = prob(A) + prob(B) $$\cup$$ Prob (A B) is used.

prob (A $$\cup$$ B) = $$\frac{1}{15}$$ + $$\frac{1}{3}$$ + $$\frac{1}{15}$$

= (3 + 5 + 1) 15

= $$\frac{7}{15}$$

Question 36
A

1/T

B

2T

C

5/T

D

T/5

##### Explanation

4-(390625T - 8)
[(390625T - 8)]

[((390625) $$\times$$ T - 8)]

(- 390625 $$\times$$ T - 4 )

(625 $$\times$$ T -)

(54 $$\times$$ T -4)

= (54) $$\times$$ (T - 4 )

= 5 $$\times$$ T - 1

= 5 $$\times$$ 1/T

= 5/T

Question 37
A
x6 = 123.346
B
x6 = 424.56
C
x6 = 122.436
D
x6 = 124.456
##### Explanation
(159.75)10 = (y)6

$$\begin{array}{c|c} 6 & 159 \\ \hline 6 & 26 \text{ rem 3} \\ 6 & 4 \text{ rem 2} \\ & 0 \text{ rem 4} \\ \end{array}\uparrow$$

15910 = 4236

Then Convert 0.75 to base 6

0.75 x 6 =4.5 i.e 4.5 - 3.00 = 1.5
0.5 x 6 = 3.00 423 + 1.5 =424.5

159.75 = (424.5)6

(159)10 = (424.5)6

Question 38
A

15%

B

25%

C

35%

D

10%

##### Explanation

Percentage Loss = (actual loss ) (Cost price) $$\times$$ 100

Actual loss = Cost Price - Selling Price (sold price)

= N800 - N520 = N280

Percentage loss = (280 800) $$\times$$ 100 = 35%

His loss percent = 35%

Question 39
A

$$3 \frac{5}{6}$$

B

$$4 \frac{5}{6}$$

C

$$2 \frac{1}{6}$$

D

$$\frac{1}{3}$$

##### Explanation

6 - 2 + 1

73/12 - 11/4 + 3/2

[(73 - 33 + 18) (12)]

58/12

29/6

$$4\frac{5}{6}$$

Question 40
A
3m
B
2.4m
C
3.2m
D
5.1m