Q: A ball is thrown upward with initial velocity $$v_0$$ from height $$h_0. $$Its height after $$t$$ seconds is $$h(t) = h_0$ + v_0$ t - \frac{1}{2} g t^2$. If h_0$ = 2 m$$, $$v_0 = 10$ m/s, g = 9.8$ m/s^2$, and t = 1$ s, what is h(1$$)$$?

$$h(1) = 2 + 10 \times 1 - \frac{1}{2} \times 9.8 \times 1^2$ = 7.1 m$$

Question 1

Which of the following equations represents the area $$A of a $$rectangle with length $$l$$ and width $$b$$?

Accepted Answer

$$A = l b$$

Question 2

Given the function $$f(x) = 2x^4$ - 3$$, what is $$f(-1)$$?

Accepted Answer

Question 3

A straight line passes through the points $$(0, 1)$$ and $$(2, 5). $$What is the equation of the line in slope-intercept form?

Accepted Answer

$$y = 2x + 1$$

Question 4

If $$y = x^2$ + 3x + 2$$, what is the value of $$y$$ when $$x = -1$$?

Accepted Answer

$$y = 0$$

Question 5

Which of the following best describes the graph of $$y = x^2$?

Accepted Answer

A parabola opening upwards

Question 6

Given the function $$f(x) = x^2$ - 4x + 3$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 7

A chemical reaction's rate $$R is $$modeled by $$R = kC$$, where $$k is a $$constant and $$C is $$the concentration. If $$k = 0.5$$ and $$C = 8$$, what is $$R$$?

Accepted Answer

$$R = 4$$

Question 8

If the volume $$V of a $$cylinder is given by $$V = \pi r^2$ h$$, what is the volume when $$r = 3$$ and $$h = 5$$?

Accepted Answer

$$V = 45\pi$$

Question 9

A population grows according to $$P(t) = P_0$ e$$^{kt}$$. If P_0$ = 100$$, $$k = 0.02$$, and $$t = 5$$, what is $$P(5)$$?

Accepted Answer

$$P(5) = 100 e$$^{0.1}$$

Question 10

Which of the following is the correct formula for the slope $$m of a $$line passing through points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$m = \frac{y_2$ - y_1$}{x_2$ - x_1$}$$

Question 11

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

Accepted Answer

$$(f \circ g)(2) = f(g(2)) = f(5) = 25$$

Question 12

A medical dosage is calculated by $$D = \frac{mg}{kg} 	imes W$$, where $$W is $$the patient's weight in kg. If the dosage is $$5 \frac{mg}{kg}$$ and the patient weighs $$70 kg$$, what is the total dosage?

Accepted Answer

$$D = 350 mg$$

Question 13

Which of the following is the vertex of the parabola $$y = x^2$ - 6x + 8$$?

Accepted Answer

$$(3, -1)$$

Question 14

If $$y = mx + b is $$the equation of a straight line, what does $$b$$ represent?

Accepted Answer

The $$y-$$intercept

Question 15

A car travels at a constant speed $$v$$ for time $$t. $$Which formula gives the distance $$d$$ traveled?

Accepted Answer

$$d = v t$$

Question 16

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

Accepted Answer

$$f(g(3)) = f(5) = 25 - 4 = 21$$

Question 17

Which of the following is the correct quadratic formula for solving $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 18

A ball is thrown upward with initial velocity $$v_0$$ from height $$h_0. $$Its height after $$t$$ seconds is $$h(t) = h_0$ + v_0$ t - \frac{1}{2} g t^2$. If h_0$ = 2 m$$, $$v_0 = 10$ m/s, g = 9.8$ m/s^2$, and t = 1$ s, what is h(1$$)$$?

Accepted Answer

$$h(1) = 2 + 10 	imes 1 - \frac{1}{2} 	imes 9.8 	imes 1^2$ = 7.1 m$$

Question 19

Which of the following is the correct expression for the difference quotient of $$f(x)$$?

Accepted Answer

$$\frac{f(x+h) - f(x)}{h}$$

Precalculus Study Notes: Functions, Graphs, and Rates of Change

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