Algebra

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If $10,000 is invested at 8%, compounded monthly, how is the investment worth after 5 years? Choose the closest answer.

$15,000

Solve the system: 3x - 2y = 10, 5x + 3y = 23

(4, 1)

A particular right triangle has an acute angle of π/6 radians, and the side opposite this angle has measure 8. What is the hypotenuse of this triangle?

16

The x-intercept of y = 4x - 8 is?

2,0

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

2x - 7

What is the period of y = sin 3x?

2π/3

The graph of f(x) = x3 -6x2 + 4x +1 hits the x-axis how many times?

3

The half-life of carbon 14 is 5,730 years. How old is a bone that has 70% of its original carbon 14? Choose the closest answer.

3,000 years

What is the amplitude of y = 4 sin (2x - π/4)?

4

The solutions of x2 -8x + 17 = 0 are?

4 + i and 4 - i

If f(x) = 2x + 3, and g(x) = x2 + x, what is g ○ f?

4x2 + 14x + 12

In radian measure, what is 210 degrees?

7π/6 radians

What kind of system is 2x + y = 3, -6x - 3y = -9?

Dependent

A frog jumps and takes 2 seconds to land. The path of the frog's flight is best modeled by the graph of f(x) = -x2 + 2x. What is the maximum height of the jump?

The correct answer is: 1

f(x) = √(x + 5) + 2, what is the domain of f-1?

[2, ∞)

f(x) = 3x - 5, what is the inverse of f?

x/3 + 5/3

What is the equation of a line through (-1, 4) and (-2,7)?

y = -3x + 1

Solve the system: y = x2 - 5, y = 2x - 2

(-1, -4) and (3, 4)

Solve the system: y = |x|, y = 2x + 3

(-1, 1)

Solve the system: y = e3x , and y = e2x-1

(-1, e-3)

What is the vertex of f(x) = x2 + 3x + 2?

(-3/2, -1/4)

What is the solution to 3x - y = 4, x + 6y = -5?

(1, -1)

Solve the system: y = x2 + 4x - 5, y = 0

(1, 0) and (-5, 0)

Solve the system: x + y + z = 6, 2x - y + z = 3, x + y - z = 0

(1, 2, 3)

Solve the system: 2x + y = 6, -2x + 3y = 5

(13/8, 11/4)

What is the point (3, 3sqrt(3)) in polar coordinates?

(6, π/3)

What are the x-intercepts of f(x) = x2 - 6?

(√6, 0) and (-√6, 0)

Solve for x: (1/2) = 2x + 3

-4

From the formula for sin (2t + t) find sin 3t in terms of sin t

-4 sin3 (t) + 3sin (t)

Let f(x) = x2 - 4, x < 0. What is f-1?

-√(x + 4), x >-4

Solve for x: e2x + 1 = 10.

0.6

What is the exact value of sin (-11π/2)?

1

What is the exact value of the cot (-3π/4)?

1

What, approximately, is log2 12? Choose the closest answer.

4

What type of system is 3x - y = 4, and -6x + 2y = 5?

Inconsistent

What kind of system is y = 3x - 5, 2x + y = 8?

Independent

Solve the system (domain is all real numbers): y = x2 + 5, y = x - 4

No solution

Solve the system: y = x2 - 4, y = 3x - 6

None of these

Use DeMoivre's theorem to find z4, if z is 1 + 1i. Express your answer in complex form.

None of these

If A = (-2, 5) and B = [4,7], A ᴗ B?

The correct answer is: (-2,7]

If f(x) = 2x +1, what is the domain?

The correct answer is: (-∞,∞)

Solve the system: x + y + z = 4, 3x - y + z = 2, y - z = -2

The correct answer is: (0, 1, 3)

Solve the system: x + y + z = 3, 2x - y + 3z = 3, x - 2y + 3z = 0

The correct answer is: (2, 1, 0)

If f (t)=t2 + t, find [ f(t + h) -f (t)]/h.

The correct answer is: 2t + h + 1

What is the domain of f(x) = √(x - 5) / √x ( √ means "the square root of")?

The correct answer is: [5, ∞)

If f(x) = 3x +2 and g(x) = x -4, (f/g)(4) is:

The correct answer is: undefined

What is i^73?

i

What the equation of the line passing through (1,4) and parallel to y = 2x + 1?

y = 2x + 2

In radian measure, what is arcsin (1/2)?

π/6

As x goes to infinity, the graph of f(x) = 5x4 - 173x3 -16x2 -7x -15 goes to (points in) what direction?


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