$$\frac{\text{opposite}}{\text{adjacent}}$$

$$\lim_{h \to 0} \frac{f(a+h) - f(a)}{h}$$

Question 1

Which of the following is the correct equation of a line with slope 7 and y-intercept -3?

Accepted Answer

$$y = 7x - 3$$

Question 2

Given the line $$5x + 6y = 30$$, what is the slope of any line parallel to it?

Accepted Answer

$$-\frac{5}{6}$$

Question 3

If the lines $$-4x + 5y = -10$$ and $$5x + ky = 12$$ are perpendicular, what is the value of $$k$$?

Accepted Answer

$$4$$

Question 4

Find the midpoint $$M$$ and the length $$L of $$the segment joining $$(3, -2)$$ and $$(4, -1). $$Which is correct?

Accepted Answer

$$M = \left(\frac{7}{2}, -\frac{3}{2}\right),\ L = \sqrt{2}$$

Question 5

Which of the following is the equation of a horizontal line passing through $$(-6, -1)$$?

Accepted Answer

$$y = -1$$

Question 6

Factor $$2x^2 + 11x + 15$.

Accepted Answer

$$(2x+5)(x+3)$$

Question 7

The expression $$x^2 - 10kx + R$ is a perfect square. What is R$?

Accepted Answer

$$25k^2$$

Question 8

Solve $$3x^2 - 5x - 1 = 0$ using the quadratic formula.

Accepted Answer

$$\frac{5 \pm \sqrt{37}}{6}$$

Question 9

Which of the following triangles is a right triangle based on side lengths?

Accepted Answer

I and IV only

Question 10

A triangle $$ABC$$ has a right angle at $$B. If$$ $$AB = 3$$ and $$BC = 4$$, what is $$\cos A$$?

Accepted Answer

$$\frac{3}{5}$$

Question 11

What is the value of $$\sin \frac{2\pi}{3}$$?

Accepted Answer

$$\frac{\sqrt{3}}{2}$$

Question 12

What is the value of $$\log_2$ 64$$?

Accepted Answer

$$6$$

Question 13

Expand $$\log \frac{AB}{C}.$$

Accepted Answer

$$\log A + \log B - \log C$$

Question 14

Which of the following is the tangent of an angle in a right triangle?

Accepted Answer

$$\frac{	ext{opposite}}{	ext{adjacent}}$$

Question 15

Which of the following is the correct equation for a circle centered at $$(4, -5)$$ with radius $$16$$?

Accepted Answer

$$(x - 4)^2$ + (y + 5)^2$ = 256$$

Question 16

Which of the following best describes the function $$f(x) = e^x$$?

Accepted Answer

It is an exponential function with base $$e.$$

Question 17

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

Accepted Answer

$$(x + 1)^2$

Question 18

Which of the following is the correct definition of the derivative of a function $$f at$$ $$x = a$$?

Accepted Answer

$$\lim_{h 	o 0} \frac{f(a+h) - f(a)}{h}$$

Question 19

Which of the following is a real-world application of related rates?

Accepted Answer

Calculating how fast the water level rises in a tank as water is poured in.

MATH 203: Differential & Integral Calculus I – Course Syllabus and Preparation Guide

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