Q: If you invest $$15,000 at an annual interest rate of 9\% compounded monthly for 30 years, which formula should you use to find the final amount A$?

$$A = 15000\left(1 + \frac{0.09}{12}\$$right)^{12 \times 30}$$

Q: If you invest $$15,000 at 9$$\% interest compounded continuously for 30 years, what is the formula for the final amount $$A$$?

$$A = 15000e$$^{0.09 \times 30}$$

Question 1

Which of the following is the correct solution to the quadratic equation $$x^2 - 20x = -99$ using the quadratic formula?

Accepted Answer

$$x = 10 \pm \sqrt{201}$$

Question 2

Given the quadratic function $$f(x) = x^2$ + 6x - 2$$, what is the vertex of the parabola?

Accepted Answer

$$(-3, -11)$$

Question 3

For the function $$f(x) = 2x(3x-1)^2$(x+6)^3(-x+5$$)$, which zero has the graph crossing the x-axis with a flattening effect (i.e., the graph crosses but flattens out at the zero)?

Accepted Answer

$$x = -6$$

Question 4

What is the degree and leading term of the polynomial $$f(x) = 2x(3x-1)^2$(x+6)^3(-x+5$$)$?

Accepted Answer

Degree: 7, Leading term: $$2x^7$$

Question 5

If you invest $$15,000 at an annual interest rate of 9\% compounded monthly for 30 years, which formula should you use to find the final amount A$?

Accepted Answer

$$A = 15000\left(1 + \frac{0.09}{12}\$$right)^{12 	imes 30}$$

Question 6

Which of the following is the correct logarithmic form of the exponential equation $$64 = 4^x$$?

Accepted Answer

$$x = \log_4$ 64$$

Question 7

Solve for $$x$$: $$3 = \log_x 125$$

Accepted Answer

$$x = 5$$

Question 8

Express $$\log\left(\frac{1000x^3$y^4$$}{$$wz^2$$}\right)$ as a sum and/or difference of logarithms with no exponents.

Accepted Answer

$$3 + 3\log x + 4\log y - \log w - 2\log z$$

Question 9

Given $$f(x) = x^3$ + 1$$ and $$g(x) = \sqrt[3]{x-1}$$, which of the following statements is true?

Accepted Answer

$$f(g(x)) = x$$

Question 10

Solve for $$t in $$the equation $$e^{3t} = 9$.

Accepted Answer

$$t = \frac{1}{3}\ln 9$$

Question 11

Which of the following is the correct solution to $$2x^2 - 2x + 3 = 0$?

Accepted Answer

Question 12

Which of the following is the correct solution to $$x^2 - 144 = 0$?

Accepted Answer

$$x = \pm 12$$

Question 13

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

Accepted Answer

$$-36$$

Question 14

Solve for $$x$$: $$2x - 2 = 16x$$

Accepted Answer

$$x = -1$$

Question 15

Which of the following is the correct logarithmic form of the exponential equation $$3^{-2}$$ = \frac{1}{9}$$?

Accepted Answer

$$-2 = \log_3$ \frac{1}{9}$$

Question 16

Solve for $$x in $$the equation $$0 = \ln(x).$$

Accepted Answer

$$x = 1$$

Question 17

Express $$\log_3$\left(\sqrt{27x^4$y^3$$}/5\right)$ as a sum and/or difference of logarithms with no exponents.

Accepted Answer

$$\frac{1}{2}\log_3$ 27 + 2\log_3$ x + \frac{3}{2}\log_3$ y - \log_3$ 5$$

Question 18

Solve the logarithmic equation: $$2\ln(\sqrt{x}) - \ln(6x - 1) = 0.$$

Accepted Answer

Question 19

If $$f(x) = x^2$ - 4x + 8$$, what is the axis of symmetry of the parabola?

Accepted Answer

$$x = 2$$

Question 20

If you invest $$15,000 at 9$$\% interest compounded continuously for 30 years, what is the formula for the final amount $$A$$?

Accepted Answer

$$A = 15000e$$^{0.09 	imes 30}$$

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