Pre-test: PreCalculus

7/26/2019 Pre-test: PreCalculus

1/8

Holy Cross College of CalinanCalinan, Davao City

S.Y.: 2016 - 2017STEM: Pre-Calculus

PRETEST

Name: Date: Score:I - MULTIPLE CHOICE

GENRAL INSTRUCTION: Write the letter of your answer on the space provided before the number.

1. What type of conic section is being described by the equation?

y= 14x2

A. Circle

B. Ellipse

C. Hyperbola

D. Parabola

2. Which among the graph describes the given equation?

x2 +y2 = 25

A.

B.

C.

D.

3. Based on the given information, what is the standard form of the circle?

Center: (15,5)and Radius: 1

A. (x 15)2 + (y+ 5)2 = 1B. (x+ 15)2 + (y+ 5)2 = 1

C. (x 15)2 + (y+ 5)2 = 9D. (x 15)2 + (y 5)2 = 1

4. What is the center and radius of the given circle?

2y+y2 = 18x 57 x2

A. Center: (9, 1); Radius: 5B. Center: (10, 0); Radius: 5

C. Center: (9, 1); Radius: 5D. Center: (2, 10); Radius: 5


2/8


x2 + y2

9 = 1

A.

B.

C.

D.

6. Based on the given information, what is the standard form of the given ellipse?

9x2 + 100y2

126x

400y

59 = 0

A. (x 7)2 + (y2)29 = 1B. (

x7)29 +

(y2)2100 = 1

C. (x7)2

100 + (y2)2

9 = 1

D. (x7)2100 +

(y2)24 = 1

7. What is the foci of the given ellipse?

x2

144 + y2

169 = 1

A. (5, 0), (5, 0)B. (0, 5), (0,5)

C. (1, 7), (1,3)D. (1, 6), (1,4)

8. What is the eccentricity of the given ellipse?

x2

64 + y2

81 = 1

A.139

B. 13

C.179

D.119

9. What is the vertices of the given ellipse?

(x1)2150 +

(y8)2140 = 1

A. (1,

8 + 5

6)

,(1

,8 5

6)

B. (1, 8 + 56), (1, 8 56) C. (8,1 + 5

6)

,(8

,1 5

6)

D. (1 + 5

6, 8), (1 56, 8)

Page 2


3/8


y2

16 x2

16 = 1

A.

B.

C.

D.

11. Based on the given information, what is the standard form of the given hyperbola?

x2 16y2 + 6x+ 128y 391 = 0

A. (x+4)2

9 (y3)2

144 = 1

B. (x+4)2

144 (y+3)2

9 = 1

C. (x+3)2

144 (y4)2

9 = 1

D. (x+4)2

144 (y3)2

9 = 1

12. What is the foci of the given hyperbola?

(y3)2100 +

(x+5)2

196 = 1

A. (5, 3 +

34), (5, 3

34)

B. (5 + 2

74, 3), (5 2

74, 3)

C. (5,3 + 2

74), (5,3 2

74)

D. (5, 3 + 2

74), (5, 3 2

74)

13. What are the vertices of the given hyperbola?

(x+4)2

9 y2

36 = 1

A. (1, 0), (7, 0)B. (0, 7), (0, 1)

C. (4, 3), (4,3)D. (4, 6), (4,6)

14. What is the eccentricity of the given hyperbola?

(y8)2150

(x+7)2

35 = 1

A.111030

B.31313

C.2597

D.103

Page 3


4/8


y= x2

A.

B.

C.

D.

16. Based on the given information, what is the standard form of the given parabola?

y2 +x+ 20y+ 91 = 0

A. x= y2 + 16y+ 95B. x= y2 18y 91

C. x= y2 20y 91D. x= y2 + 20y 109

17. What is the focus of the given parabola?

y= 13x2 + 6x+ 20

A. ( 334 ,7)B. (9, 558)

C. (8, 354 )D. (9,254 )

18. What is the vertex of the given parabola?

y= 3x2 48x 198

A. (8,6)B. (8,6)

C. (6, 8)

D. (6,8)

19. What is the directrix of the given parabola?

y= 12x2 + 6x+ 9

A. y= 192B. x= 17

2

C. x= 132D. y=

13

2

20. What is the solution of the given system of equations?

2y2 + 27x y 17 = 03x+y+ 1 = 0

A. (1, 2)

B. No solution.

C. (9, 1)

D. (1, 2), (10, 4)

Page 4


5/8

21. What is the solution of the given system of equations.

x2 +y2 3x 7y 18 = 0x+y+ 3 = 0

A. (3, 0), (6, 3)B. (2,1)

C. (2,1), (6, 3)D. (3, 0), (2,1)

22. What is the number of terms nin the given arithmetic series?

ni=1(10i 13) = 741

A. 13

B. 15

C. 12

D. 11

23. Which among the summation notation best describes the given series?

301 + 302 + 303 + 304 + 305 + 306

A.6

i=1(n+ 300)B.4

i=15nC.4

i=1n

D.4

i=13n

24. What is the coeffecient of nmin expansion (7n m)2?

A. -14

B. 1

C. -7

D. 49

25. What is the 2nd term in expansion of (b+ 4)4?

A. 4b3

B. 16b3

C. b4

D. 96b2

26. Which of the following is equivalent to (y x)2?

A. y2 5yx+ 3x2B. y2 2yx+ 5x2

C. y2 5yx+ 5x2D. y2 2yx+x2

27. What is -225 in radian measure?

A. 54B. 2318

C.119D.4336

28. What is 43 in degree measure?

A. -500

B. -235C. -480

D. -240

29. What is the measure of an angle between 0 and 360 which is coterminal with -430?

A. 30

B. 290C. 130

D. 200

Page 5


6/8

30. Which among the graph represents the given equation?

y = 4 sin(4+ 76 )

A.

B.

C.

D.

31. What is the exact value of cos225? Use Angle-Sum Identity.

A.6+

2

4

B. 624

C.2

6

4

D. 624

32. What is the exact value of tan 75? Use Angle-Difference Identity.

A.2

3

B. 2

3

C. 2 +

3

D.

3 2

33. What is the exact value of cos 0? Use Double-Angle Identity.

A. 0

B.

3

C.32

D. 1

34. What is the exact value of sin 105? Use Half-Angle Identity.

A.

3 2

2

B. 12

C.

3

D.6+

2

4

35. What is the measure of the indicated angle to the nearest degree?

A. 65

B. 23C. 67

D. 21

Page 6


7/8

36. For 0


8/8

II - PROVING

Prove the following Mathematical statement using Principle of Mathematical Induction. (6 points)

1 + 2 + 3 +...+n = n(n+1)

2 ; for all n N

You dont have to know everything.You simply need to know where to find it when necessary.

Documents

Pre-test: PreCalculus