mathexit 1Q1112

8/11/2019 mathexit 1Q1112

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DIRECTIONS: Solve each problem and choose the best answer from the choices given. Detailed solution

should be shown and all final answers should be encircled. Write out your solution as shown below:

Sample Item:

1.

What is the x-intercept of the line passing through A(1,4) and B(4,1)?

a.

4

b. 4.5

c. 5

d.

6

In your answer sheet write:

1.

C

Solution:

5

0=yletintercept,-for xSolving

5

1-x4-y

1-x1-4

4-14-y

-x-x

--y

-x

-

-x

-y

:form pointtwousing

1=y4= x1)B(4,

4=y1= x4)(1,A

1

12

121

12

12

1

1

22

11

x

y x

x x

y y y

x

y y

x

y

EXAMINATION STARTS HERE!

1.

Find x in the equation shown: 4x2

+ 48x + 144 = 400

a. 16, 4 b. -16, 4 c. -32, 8 d. -4, 16

Answer: b

Solution: 4x2 + 48x + 144 = 400

4x2 + 48x – 256 = 0

x2 + 12x – 64 = 0

(x + 16)(x – 4) = 0, x = -16, x = 4

MATH23X

EXIT EXAMINATION1st Quarter SY 2011–2012

8/11/2019 mathexit 1Q1112


2. The age of a crocodile at the Manila Zoo 13 years ago was 1/3 of its age 7 years

from now. How old is the crocodile at present?

a. 15 b. 21 c. 23 d. 27

Answer: c

Solution:

Let x = present age, x – 13 = age 13 years ago, x+ 7 = age 7 years from now

x + 7 = 3x – 39

-2x = -46

x = 23

So, the crocodile is 23 years old at present.

3.

An airplane flying with the wind can cover a certain distance in 2 hours. The return trip againstthe wind takes 2.5 hours. How fast is the plane and what is the speed of the air, if the one-way

distance is 600 miles? (Let x-speed of the plane, y-speed of the wind)

a.

x = 40, y = 260 b. x = 30, y = 270 c. x = 270, y = 30 d. x = 230, y = 70

Answer: c

Solution: ,

2x + 2y = 600 ---------------- > x + y = 300

5x – 5y = 1200 -------------- > x – y = 240

-----------------------

2x = 540

x = 270

y = 300 – 270 = 30

speed of the plane: x = 270 , speed of the wind : y = 30

4.

How many gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 9

gallons of 30% alcohol solution?

a. 3 gallons of 20% solution and 6 gallons of 50% solution

b. 6 gallons of 20% solution and 6 gallons of 50% solution

c. 5 gallons of 20% solution and 3 gallons of 50% solution

d. 6 gallons of 20% solution and 3 gallons of 50% solution

Answer: d

Solution:

(0.20)(x) + (0.50)(9-x) = (0.30)(9)2x +45 – 5x = 27

-3x = -18

x = 6 gallons -------- > amount of 20% alcohol solution

y = 9 – x = 3 gallons --------- > amount of 50% alcohol solution

8/11/2019 mathexit 1Q1112


5.

How many different second order determinant can be formed from four different numbers?

a. 4 b. 8 c. 16 d. 24

Answer: d

Solution:

4! = 4 x 3 x 2 x 1 = 24

6.

The angle of elevation of the top of an incomplete vertical pillar at a horizontal distance of 100

meters from its base is 45 degrees. If the angle of elevation of the top of the complete pillar at

the same point is to be 60 degrees, then the height of the incomplete pillar is to be increased by

how much?

a.

73.21 b. 100 c. 173.21 d. 26.79

Answer: a

Solution:

7.

The function f is defined for 0 ≤ x ≤ 360, f(t) = 3sin(2t-1). What is the period of the waveform?

a. π/4 b. 2 c. π d. π/2

Answer: c

Solution:

Compare f(t) = a sin(bt – c) + d with f(t) = 3 sin(2t – 1), then b = 2

8.

If an equilateral triangle is circumscribed about a circle of radius 12 cm, determine the side of

the triangle.

a. 34.64 b. 41.57 c. 83.14 d. 20.78

Answer: b

Solution:

8/11/2019 mathexit 1Q1112


9.

Solve for x: 2 log5(x-4) = 4

a.

29 b. 21 c. 4 d. 25

Answer: a

Solution:

2 log5(x – 4) = 4

log5(x – 4)2 = 4

(x – 4)2 = 54

x2 – 8x + 16 = 625

x2 – 8x – 609 = 0

(x – 29)(x + 21) = 0 --------- > x = 29 , x = -21 (extraneous)

10.

The two vertices of a triangle are A(2,4) and B(-2,3). Find the locus of the third vertex of the

triangle if its area is 2 square units.a. 4x-y = 12 b. 4x + 4y = 10 c. x + 4y = 12 d. x – 4y = -10

Answer: d

Solution:

11.

What are the coordinates of the center of the curve x2 + y2 -2x -4y -31 = 0?

a.

(-1, -1) b. (-2, -2) c. (1, 2) d. (2, 1)

Answer: d

Solution:

2,1

621

5314412

3142

03142

222

22

22

22

Center

circle y x

y y x x

y y x x

y x y x

8/11/2019 mathexit 1Q1112


12.

Find the eccentricity of the curve 9x2 – 4y

2 -36x +8y = 4.

a. 1.76 b. 1.80 c. 1.86 d. 1.92

Answer: b

Solution:

80.12

605.3

605.3;13

9

4

hyperbola19

1

4

2

491429

14494124449

483649

222

2

2

22

22

22

22

a

c

e

cbac

b

a

yx

yx

yyxx

yxyx

13.

If the edge of a cube is increased by 30%, by how much is the surface area of one side of the

cube is increased?

a.

30% b. 33% c. 60% d. 69%

Answer: d

Solution:

xy AA

x

x

xyx

y

69.1

30.1

A

A

30.1; A

A

,proportionandratioBy

30%byincreasedissidethewhencubetheof area= A

cubetheof areainitial= A

edgeincreased=y

edgeinitial=x

2

x

y

2

2

x

y

y

x

Therefore, the surface area on one side increased by 69%.

14.

A conical vessel has a height of 24 cm and a base diameter of 12 cm. It holds water to a depth of

18 cm above its vertex. Find the volume (in cu cm) of its content.

a.

188.40 c. 298.40 c. 381.70 d. 412.60

Answer: c

Solution:

70.381185.43

1

3

1

5.4,24

6

18

x

: proportionandratioBy

waterof depthcm18,coneof height=cm24,coneof diameter=cm12

22

V hr V

x

8/11/2019 mathexit 1Q1112


15.

A 10m-diameter hemispherical rubber ball is filled with liquid to a depth of 4m. Determine the

surface area of the ball which is not in contact with the liquid.

a.

5π b. 10π c. 20π d. 120π

Answer: b

Solution:

Z = 2πRh = 2π(5)(1) = 10π

16.

Find the value of k such that the function defined by { is continuous at

every real number.

a.

3 b. 4 c. 5 d. 7

Answer: c

Solution: must exist, so = )

3(4) + 7 = k(4) – 1

4k – 1 = 19

4k = 20

k = 5

17.

If f’(2) = g’(2) = f(2) = g(2) = 2, then what is the value of ?

a.

8 b. 12 c. 16 d. 20

Answer: a

Solution:

Using product rule, (fg)’(2) = f(2)g’(2) + f’(2)g(2) = (2)(2) + (2)(2) = 4 + 4 = 8

18.

Find the equation of the tangent line to the curve y = x3 at the point (2,8).

a.

12x – y – 16 = 0 b. x + 12y – 98 = 0 c. 12x + y -98 = 0 d. x – 12y + 16 = 0

Answer: a

Solution:

f(x) = x3 -------- > f’(x) = 3x2

mT = f’(2) = 3(22) = 12

using point slope of a line: y = mT(x – x1) + y1

y = 12(x – 2) + 8

y = 12x – 24 + 8

12x – y – 16 = 0

19.

Find in the equation .

a.

b.

c.

d.

Answer: a

8/11/2019 mathexit 1Q1112


Solution:

20.

Evaluate: ∫

a.

68/3 b. 70/3 c. 92/3 d. 86/3

Answer: d

Solution:

∫ ∫

+

21.

Evaluate: ∫ √

a.

b.

c. d.

Answer: b

Solution:

Let u = 3 – 5x5, du = -25x

4dx

∫ √ ∫

* +

=

22.

The region bounded by the lines y = 3 – 2x, y = 2 and the coordinate axes is revolved about the

y-axis . Find the volume of the solid formed.

a.

6π/5 b. 5π/6 c. 13π/6 d. 7π/6

Answer: c

Solution:

V = ∫ =

8/11/2019 mathexit 1Q1112


23.

Find the area of the region bounded by the curve y2 = 4x, the line y = 2 and the y-axis.

a.

1/3 b. 2/3 c. 1/6 d. 5/6

Answer: b

Solution:

A = ∫ ( √

)

24.

Find a vector orthogonal to both of the vectors u = <2, -1, 3> and v = <-7, 2, -1>.

a.

-5i – 19j – 3k b. 5i + 19j + 3k c. 5i – 19j + 3k d. -5i + 19j – 3k

Answer: a

Solution:

u x v = | |= -5i – 19j – 3k

25.

Evaluate ∫ ∫ .

a.

11/3 b. 11 c. 5/12 d. 12

Answer: b

Solution:

∫ ∫ ∫ ∫

∫

mathexit 1Q1112

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