Algebra 2 Honors Final Review Multiple Choice 1. Which ...

Algebra 2 ? Honors

Final Review

Multiple Choice

1. Which expression is equivalent to: x8 y 6 ?

a) xy

b) x 4 y3

c) x16y-12

2. Solve: x2 ? 5x ? 24 = 0

a)x =6 or x = -4 b)x =8 or x = -3

d) undefined e) NOT c)x =12 or x = -7 d)x =12 or x =7 e) NOT

3. An arch is modeled by the equation h w2 40 where h is the height in feet and w is the width in feet. What is the maximum height of the arch? a) 10 feet b) 25 feet c) 30 feet d) 40 feet e) NOT

4. Which function describes the values in the table?

a) y x

b) y 3 x

c) y x2

d) y 3x2

e) NOT

x y -1 undefined 0 0 1 3 2 4.24 3 5.20 4 6

5. Which expression is equivalent to (x2 50 y )(1 x y 2 ) 4

a) 1 x3 x2 y 2 25 x y 7.07 y

4

2

b) 1 x2 x2 y 2 25 x y 50 y 2

4

2

c) 1 x3 x2 y 2 25 x y 50 y 2 y

4

2

d) 1 x3 x2 y 2 25 x y 50 y 2

4

2

6. Which of the following is the axis of symmetry of the graph y = 3 ( x ? 4 )2 + 2?

a) x = 2 b) y = 3 c) x = 3 d) x = 4 e) y = x

7. What are the solutions of 2x3 + 10x2 + 12x = 0?

a) 2, 10, 12 b) 0, 3 c) 0, -2, -3 d) 0, 2, 3 e) -1, 0, 6

e) NOT

8. If M is the midpoint of AB , and the coordinates of M and A respectively are

( -4.2, -1.9 ) and ( -3.4, 2.5 ), then the coordinates of B are:

a) ( -3.8, -0.6 ) b) ( -5, 6.9 ) c) ( -3.8, 0.3 ) d ) ( -5, -6.3 ) e) ( 1.3, -3.45 ) 9. Solve the equation: 4( x + 2 )2 - 32 = 0. Approximate to the nearest hundredth.

a) 9.31 or -13.31 b) 4.83 or -0.83 c) 0.83 or 4.83 d) 3.66 or -7.66 e)

none of these 10. Solve the equation: 6x2 = 78. Approximate to the nearest hundredth.

a) ? 8.83 b) ? 3.61 c) ? 12 d) ? 21.63 e) none of these

11. Write the quadratic equation in vertex ( h, k ) form. Give the coordinates of the vertex and

the equation of the axis of symmetry. y = x2 + 4x ? 9

a) y = ( x ? 2 )2 ? 7; x = -2; ( 2, 7 )

b) y = ( x ? 2 )2 ? 5; x = -2; ( 2, 5 )

c) y = ( x + 2 ) 2 ? 5; x = -2, ( -2, -5)

d) y = ( x + 2 )2 ? 13 ; x = -2; ( -2, -13 )

e) none of these 12. Solve the following quadratic equation: 5x2 ? 16x + 3 = 0.

a) 17 , 1 55

b) 3, 1 5

c) 3, 1 5

d) 17 , 1 55

e) none of these

Mrs. Poyner/Ms. Eisen

Final Review

page 1

Algebra 2 ? Honors

Final Review

Multiple Choice

13. Find the axis of symmetry and the vertex for the function y = -5x2 + 20x ? 14 a) x = -2; ( -2, -6 ) b) x = 2; ( 2, 6 ) c) x = -2; ( -2, 6 ) d) x = 2; ( 2, -6 ) e) none of these

14. Find the axis of symmetry and the vertex for the function y = x2 + 6x ? 5 a) x = 3; ( 3, -4 ) b) x = 3; ( 3, 31 ) c) x = -3; ( -3, 4 ) d) x = -3; ( -3, -14 ) e) none of these

15. Find the quadratic equation that fits the set of data points exactly, in the form y ax2 bx c with values of a, b, and c correct to three decimal places.

( 1, 14.1 ), ( 7, 12.8 ), and ( 11, 14.9 ) a) y = -0.063 x2 + 1.650 x ? 4.312 c) y = 0.074 x2 ? 0.810 x + 14.836

b) y = -0.171 x2 + 1.150 x + 13.121 d) y = 0.308 x2 ? 3.610 x + 17.403

e) none of these

16. The turnstiles at the entrance to the State Fair kept track of the number of people entering the

fairgrounds, for the first seven hours following the opening of the fair. Find a quadratic equation

that models the data shown.

Time (hr)

01 2 3 4 5 6

People (1000s) 5.8 5.59 5.44 5.35 5.33 5.37 5.46

a) y = 0.043 x2 ? 0.118 x + 4.21

b) y = 0.075 x2 ? 0.146 x + 7.17

c) y = 0.031 x2 ? 0.241x + 5.80 d) y = 0.042 x2 ? 0.199 x + 4.60 e) none of these

17. Solve the quadratic inequality x2 + 3x ? 28 < 0

a) ,7 4, b) ,4 7, c) (-4, 7 ) d) ( -7, 4 ) e) none of these

18. If y varies jointly as x and the inverse of z, and y = -5 when x = -5 and z = 6, find y when x =

5 and z = -8.

a) 8 15

b) 15 4

c) 20 3

d) 3 20

e) none of these

19. The wattage rating of an appliance is given as W, in watts, and varies jointly as the

resistance, R, in ohms, and the square of the current, I, in amperes. If the wattage is 18 watts

when the resistance is 50 ohms and the current is 0.6 amperes, find the wattage when the

resistance is 100 ohms and the current 0.3 amperes.

a) 30 watts b) 60 watts c) 9 watts d) 3000 watts e) none of these

20. Find the center and the radius of the circle that has a diameter with the given endpoints.

Diameter CD , C ( 6, -3 ) and D( -4, 7 )

a) center ( 1, 2 ); radius 5 2

b) center ( 1, 2 ); radius 2 13

c) center ( 5, -5 ); radius 185 d) center ( 5, -5 ); radius 187 e) none of these

21. Solve: x2 ? 4x + 2 = 0

a) 2 2

b) 2 6

c) 2 2

d) 2 6 e) none of these

22. 2x ( x ? 2 ) = -4 a) i b)1 i 6 c)1 2i d)1 i e) NOT

23. If the equation x2 - 4x + k = 1 has exactly one solution for the value of x, then k = a) 5 b) 4 c) 2 d) -1 e) none of these

Mrs. Poyner/Ms. Eisen

Final Review

page 2

Algebra 2 ? Honors

Final Review

Multiple Choice

24. A ball is thrown vertically upward withan initial velocity of 80 ft/sec. Its height after t

seconds is given by the function h(t) 80t 16t 2 . The maximum height of the ball is:

a) 200 ft b) 100 ft c) 2.5 ft d) 5 ft e) none of these 25. If ( x ? 2 ) is a factor of x3 ? x2 ? x ? 2, then f( 2 )=

a) -2 b) 0 c) 1 d) 2 e) none of these 26. What is the remainder when ( 2x2 ? 5x ? 1 ) is divided by ( x ? 3 )?

a) -4 b) -2 c) 0 d) 2 e) none of these 27. What is the vertex of the parabola whose equation is y = 3x2 ? 2 x + 3?

a) 1 , 8 3 3

b) ( 0.3, 2.6 )

c) 1 , 5 2 2

d) ( 0.2, 3.2 )

e) none of these

28. TRUE or FALSE: The imaginary roots of the polynomial equations with real coefficients occur in conjugate pairs.

29. If b 0 , which of the exponents or powers property is not written correctly?

a) b0 1

b)

1 (9bn )

bn 9

c) bm bn bmn

d)

an bn

(a)n b

e) NOT

30. Solve: x 2 ? 6 x ? 27 = 0

a) x = 9 or x = -3 b) x = -9 or x = -3 c) x = 9 or x = 3 d) x = - 9 or x = 3 e)

NOT

31. Solve: x2 ? 1 = 8 a) x = -3 b) x = 3 c) x = 3 d) x = 9 e) NOT

32. Find the solutions of the equation -3 x2 + 10 x ? 8 = 0

a) x 3 ,2 b) x 4 ,2

4

3

33. Solve: c 2 ? 3 c = 4

c) x 4 ,2 3

d) x 4, 2 3

e) NOT

a) c = -1 and c = 4

b) c = -1 and c = -4

c) c = 1 and c = 4

d) c = 1 and c = -4 e) NOT

34. Solve 4 3x 7 x8 8x

a) x = - 11 3

b) x = - 11 , 8 3

c) x = - 13 6

d) x = -2, 25 e) NOT

35. Let the function f be defined by f (x) x2 18 . If m is a positive number such that

f (2m) 2 f (m), what is the value of m?

36. If g(n) n2 n and h(n) n2 n , which of the following is equal to h(m 1)? a) g(m) b) g(m) + 1 c) g(m) ? 1 d) h(m) + 1 e) h(m) ? 1 37. In the xy-coordinate system, ( p,0) is one of the points of intersection of the graphs of y x2 9 and y x2 9 . If p is positive, what is the value of p? a) 3 b) 6 c) 9 d) 18 e) 81

Mrs. Poyner/Ms. Eisen

Final Review

page 3

Algebra 2 ? Honors

Final Review

Multiple Choice

38. The figure shows the graph of a quadratic function h whose maximum value is h(2).

y

1 x

1

If h(a) 0 , which of the following could be the value of a?

a) -1 b) 0 c) 2 d) 3 e) 4 39. If x## is defined as x## = x2 ? x for all values of x, and A## = (A ? 2)##, then what is the

value of A? a) 1

b) 1

c) 3

d) 6

e) 3

2

2

5

40. At time t = 0, a ball was thrown upward from an initial height of 6 feet. Until the ball hit the ground, its height, in feet, after t seconds was given by the function h(t) c (d 4t)2 in which

c and d are positive constants. If the ball reached its maximum height of 106 feet at time t = 2.5 seconds, what was the height, in feet, of the ball at time t = 1 second?

3

41. For the function f (x) (x 1) 4 what are all values of x for which f(x ) is a real number?

a) all real numbers

b) x -1

c) x 0

d) x 3 4

e) x 1

42. If x and t are positive numbers that satisfy the equation value of x ?

t

x2 t 2 2t x what is the

43. If 16x 4 and 5xy 625 then y = a) 2 b) 5 c) 12.5 d) 3.5 e) 1

44. In the equation x2 kx 54 0 one root is equal to twice the other root. The value(s) of k

is (are):

a) 5.2

b) 15.6

c) -5.2

d) 15.6

e) 22.0

45. If 3x3 x2 12x 4 (x 2i)(3x 1)Q(x) for all x, then Q(x) a) x ? 2 b) x + 2 c) x ? 2i d) x + 2i e) x + i

Mrs. Poyner/Ms. Eisen

Final Review

page 4

Algebra 2 ? Honors

Final Review

Multiple Choice

46. If f (x) ax2 bx c for all x and if f (3) 0 and f (1) 0 then b + c = a) -5 b) -1 c) 1 d) 5 e) 0

47. If h varies as V and inversely as the square of r, which of the following statements must be true? a) If r increases by 2, V increases by 4. b) If both r and h are doubled, then V is doubled. c) If r is doubled and h is divided by 4, then V stays the same. d) If r is doubled and h is divided by 2, then V stays the same. e) None of the above statements must be true.

48. If the equation x2 2(k 2)x 9k 0 has equal roots, then k= a) 1 or 4 b) 0 or 4 c) 4 only d) -1 or 4 e) 2 or -4 49. What is the remainder when 3x4 2x3 20x2 12 is divided by x 2 ? a) -4 b) -28 c) -6 d) -36 e) -60

50. If A varies as the square of B and inversely as the cube of C, then if B is tripled and C is

doubled, the value of A is

a) multiplied by 3

b) multiplied by 9 8

c) multiplied

by 8

d) divided by 3

e) divided by 2

3

51. If x ? 7 divides x3 3k 3x2 13x 7 then the approximate value of k is a) 5.04 b) 4.63 c) 1.72 d) 1.34 e) 1.20

52. If x ? 1 is a factor of x2 ax 4 , then a has the value a) 4 b) 3 c) 2 d) 1 e) none of these

53. What is the sum of the real roots of the equation (x 2)(x2 3x ) 0 ? 3

a) -0.13 b) 0.13 c) 1.414 d) 3.15 e) 4.56

54. If x varies inversely as the cube root of y, and if x = 3 and y = 4, the constant of variation is a) 1.9 b) 4.8 c) 0.04 d) 192 e) 0.53

55. If x5 y8 z 3 8x4 , then x = y 8 z 3

a) 1 8

b) 1 4

c) 8

d) 8y 2 z 2

56. The sum of the roots of 3 x ? 7 x -1 + 3 = 0 is

a) 7

b) 1

c) - 7

d) -1

e) 3

3

3

7

e) 8y16z 6

Mrs. Poyner/Ms. Eisen

Final Review

page 5

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download