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Home > SparkNotes > Math Study Guides > Review >

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sparknotes

Review of Algebra II

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Review Test

3

+ x

= ?

(A)

(B)

(C)

(D)

= ?

(A)

(B)

(C)

(D)

The reduced row echelon form of

is

(A)

(B)

(C)

(D)

Which of the following is the multiplicative inverse of

?

(A)

(B)

(C)

(D)

Which of the following is a solution to

(A) (-3, 1, 2)

(B) (3, -1, -2)

(C) (6, -2, -4)

(D) (7, -5, -2)

Which of the following is equal to x , if

(A)

(B)

(C)

(D)

det

How many different values of (x, y, z) satisfy the following system of equations?

(A) 0

(B) 1

(C) 2

(D) Infinitely many.

Which of the following is a graph of 3x - y≥3 ?

Figure %: 3x - y≥3

(A) A

(B) B

(C) C

(D) D

Which of the following graphs represents the solution to the system of inequalities

Figure %: System of inequalities

(A) A

(B) B

(C) C

(D) D

Factor 15x ² - x - 6 .

(A) 15(x - 3)(x + 2)

(B) (3x + 2)(5x - 3)

(C) (3x - 2)(5x + 3)

(D) (5x - 6)(3x + 1)

Factor 8x ³ - y ³ .

(A) (2x - y)(2x ² + xy + y ²)

(B) (2x - y)(4x ² +2xy + y ²)

(C) (2x + y)(4x ² -2xy + y ²)

(D) (2x + y)(4x ² -2xy - y ²)

Factor 2x ³ +5x ² - 18x - 45 .

(A) (x + 3)(x - 3)(2x + 5)

(B) (x - 9)(2x ² + 5)

(C) (x ² + 9)(2x - 5)

(D) (x + 3)(x - 3)(2x - 5)

How many real roots does f (x) = 4x ² - 8x - 16 have?

(A) 0

(B) 1

(C) 2

(D) Infinitely many.

+ - = ?

(A)

(B)

(C)

(D)

× = ?

(A)

(B)

(C)

(D) (2x + 3)²(x + 1)²

÷ = ?

(A)

(B)

(C)

(D) 1

What is the solution set of + = ?

(A)

(B)

(C)

(D)

y is a function of x in all the following relations EXCEPT:

(A) (x, y) = {(2, 1),(3, -1),(- 2, -1),(6, 5)}

(B) (x, y) = {(2, 7),(1, 7),(- 1, 7)}

(C) (x, y) = {(4, 2),(2, 4),(0, 0),(- 4, -2),(- 2, -4)}

(D) (x, y) = {(1, 6),(0, 4),(- 2, 5),(1, 3)}

What is the domain of f (x) = ?

(A) x:x≠-1, 0

(B) x:x≠-3, 2

(C) x:x≠0, 2,-3

(D) x:x≠-3,-1, 0, 2

What is the range of f (x) = x ² - 4 ?

(A) f (x):f (x)≥4

(B) f (x):f (x)≥-4

(C) f (x):f (x)≥2

(D) f (x):-2≤f (x)≤2

If f (x) = 2x + 1 and g(x) = x ² - 6x , what is 3f (x) + 2g(x) ?

(A) x ² + 3

(B) 2x ² + 3

(C) 2x ² - 6x + 3

(D) 2x ² + 6x + 3

If f (x) = 2x - 4 and g(x) = 5x + 3 , what is fg(x) ?

(A) 10x ² - 26x - 12

(B) 10x ² - 14x - 12

(C) 10x + 2

(D) 10x - 17

If f (x) = 3x - 7 and g(x) = x ² - 1 , what is g o f (x) ?

(A) 3x ² - 10

(B) 3x ² - 7x - 1

(C) 9x ² - 42x + 48

(D) 3x ³ -7x ² - 3x + 7

What is the inverse of f (x) = + 5 ?

(A) f ^-1 =

- 5

(B) f ^-1 =

+ 4

(C) f ^-1 =

(D) f ^-1 =

If g(x) is shifted up 3 units and right 4 units from f (x) , what is g(x) ?

(A) g(x) = f (x + 4) + 3

(B) g(x) = f (x - 4) + 3

(C) g(x) = f (x - 4) - 3

(D) g(x) = f (x + 4) + 3

If g(x) is stretched horizontally by a factor of 2 and shifted down 3 units from f (x) , what is g(x) ?

(A) g(x) = 2f (x) - 3

(B) g(x) = f (2x) - 3

(C) g(x) = f (2x - 3)

(D) g(x) = f (

x) - 3

If g(x) is a reflection of f (x) = x ³ + x ² - 4 over the y -axis, what is g(x) ?

(A) g(x) = - x ³ - x ² + 4

(B) g(x) = x ³ - x ² + 4

(C) g(x) = - x ³ + x ² - 4

(D) g(x) = - x ³ - x ² - 4

Which of the following graph is symmetric with respect to the origin?

Figure %: Graphs

(A) A

(B) B

(C) C

(D) D

Name all the vertical asymptotes and holes in the graph of f (x) = ?

(A) Asymptotes: x = 2
Holes: x = -

, - 1

(B) Asymptotes: x = -

, - 1
Holes: x = 2

(C) Asymptotes: x = -

, - 1, 2
Holes: x = 3

(D) Asymptotes: x = -

, - 1
Holes: x = 3

Which equation could describe the following graph?

Figure %: Graph

(A) f (x) =

(B) f (x) =

(C) f (x) =

(D) (x) =

If 7 athletes are running a race, in how many different ways can they finish in first place, second place, and third place?

(A) 7!

(B) P(7, 3)

(C) C(7, 3)

(D) 7^3

Which of the following is equivalent to C(15, 10) ?

(A) C(15, 5)

(B) P(15, 10)

(C) C(10, 15)

(D) P(15, 5)

A function is defined recursively by

What is f (4) ?

(A) 5

(B) 7

(C) 33

(D) 47

What are the next two number in the sequence 1, 1, 2, 3, 5, 8, 13, __, __ ?

(A) 18, 23

(B) 18, 31

(C) 21, 29

(D) 21, 34

What is ()^- ?

(A) -

(B) -

(C) 16

(D) 512

If = 1 - 2x , what are all the possible values of x ?

(A) x = - 3

(B) x = - 1

(C) x = - 1, 3

(D) x = 3

Which equation could describe the following graph?

Figure %: Graph

(A) f (x) = 2^x-2

(B) f (x) = 2^x - 4

(C) f (x) = 2^x - 3

(D) f (x) = log₂ x - 4

log₃ = ?

(A) -2

(B) -

(C)

(D) 2

Simplify 3 log₂ x + 2 log₂(x - 2) - log₂(x - 3) .

(A) log₂(x ³ + x ² - 5x + 7)

(B) log₂

(C) log₂

(D) log₂

Solve for x : log₂(x ² -1) - log₂(x + 1) = 3 .

(A) x = - 1, 2

(B) x = 7

(C) x = 9

(D) x = 10

Solve for x : 6^x36^x-1 = 216 .

(A) x =

(B) x =

(C) x = 2

(D) x = 3

If $700 is put into a bank account with an interest rate of 5%, compounded yearly, how much money is in the account after 6 years?

(A) $944.90

(B) $1349.86

(C) $3995.16

(D) $14059.88

Simplify .

(A) 4

i

(B) -4

i

(C) 2

i

(D) -2

i

(2 - 3i)(5 + 7i) = ?

(A) -11 + i

(B) -11 - i

(C) 31 - i

(D) 31 + i

(4 + 3i)÷(5 + 3i) = ?

(A)

(B)

(C)

(D)

Which of the following is a factor of x ⁴ -22x ² + 31x - 28 ?

(A) x + 4

(B) x + 3

(C) x - 3

(D) x - 4

What is the remainder when P(x) = 2x ⁵ -2x ⁴ -6x ³ +12x ² + 4x + 16 is divided by x + 2 ?

(A) -2

(B) 8

(C) 16

(D) 56

Factor completely: 2x ⁴ +11x ³ +10x ² - 11x - 12 .

(A) (2x + 3)(x + 4)(x + 1)(x - 1)

(B) (2x - 3)(x - 4)(x + 1)(x - 1)

(C) (2x + 3)(x + 4)(x ² + 1)

(D) (x +

)(x + 4)(x + 1)(x - 1)

If 2 - i is a zero of P(x) = x ³ -3x ² + x + 5 , factor P(x) completely.

(A) (x + 2 + i)(x + 2 - i)(x + 1)

(B) (x - 2 + i)(x + 2 - i)(x + 1)

(C) (x - 2 + i)(x - 2 - i)(x + 1)

(D) (x - 2 + i)(x - 2 - i)(x - 1)

(x - 5y)⁴ = ?

(A) x ⁴ -20x ³ y - 30x ² y ² -20xy ³ -5y ⁴

(B) x ⁴ -20x ³ y + 30x ² y ² -20xy ³ +5y ⁴

(C) x ⁴ +20x ³ y + 150x ² y ² +500xy ³ + 625y

(D) x ⁴ -20x ³ y + 150x ² y ² -500xy ³ + 625y

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