Question 1

Express $$3,680,000,000 in $$scientific notation.

Accepted Answer

$$3.68 	imes 10$$^{9}$$

Question 2

Convert $$4.571 	imes 10$$^{9}$$ to decimal form.

Accepted Answer

$$4,571,000,000$$

Question 3

Find the distance between the points $$(-4, 3)$$ and $$(5, 1).$$

Accepted Answer

$$\sqrt{85}$$

Question 4

What is the equation of a circle with center $$(5, -3)$$ and radius $$4 in $$standard form?

Accepted Answer

$$(x - 5)^2$ + (y + 3)^2$ = 16$$

Question 5

A circle has center $$(-2, 1)$$ and is tangent to the $$x-$$axis. What is its equation in standard form?

Accepted Answer

$$(x + 2)^2$ + (y - 1)^2$ = 1$$

Question 6

Write the equation of a line in point-slope form that passes through $$(2, -3)$$ and is parallel to $$2x + 5y = 3.$$

Accepted Answer

$$y + 3 = -\frac{2}{5}(x - 2)$$

Question 7

Which of the following is the equation of a line passing through $$(2, -3)$$ and perpendicular to $$2x + 5y = 3$$?

Accepted Answer

$$y + 3 = \frac{5}{2}(x - 2)$$

Question 8

Simplify the following expression:

$$\left(\frac{4a^3$b}{a^2$b^3$$}\right)\left(\frac{$$3b^2$$}{$$2a^2b^4$}\right)$$

Accepted Answer

$$\frac{6}{a^1$b^4$$}$

Question 9

Solve for $$x in $$the equation $$3x^2 + 4x - 1 = 0$ using the quadratic formula.

Accepted Answer

$$x = \frac{-4 \pm \sqrt{4^2$ - 4 \cdot 3 \cdot (-1)}}{2 \cdot 3}$$

Question 10

Solve the system of equations:

$$3x - y = 1$$

$$x + 2y = 5$$

Accepted Answer

$$x = 1, y = 2$$

Question 11

Solve the inequality $$|2x - 5| \u003c 7$$ and express the solution in interval notation.

Accepted Answer

$$(-1, 6)$$

Question 12

Which of the following is the solution to $$x^2 = 3x$?

Accepted Answer

$$x = 0 or$$ $$x = 3$$

Question 13

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P(x) = -9x^2$ + 12x - 4$$, where $$x is $$the number of units sold (in thousands). For which values of $$x is $$the profit non-positive?

Accepted Answer

$$x \leq \frac{2}{3} or$$ $$x \geq 2$$

Question 14

Solve the inequality $$x^2 - 6x + 9$$ \u003c 0$$.

Accepted Answer

No solution

Question 15

A chemist needs to mix two solutions to obtain $$5$$ liters of a $$20\%$$ acid solution. If one solution is $$10\%$$ acid and the other is $$30\%$$ acid, how many liters of the $$10\%$$ solution should be used?

Accepted Answer

$$2.5$$ liters

Question 16

Solve for $$x in $$the equation $$2x^2 - 3x - 1 = 0$ by completing the square.

Accepted Answer

$$x = 1, x = -\frac{1}{2}$$

Question 17

Solve the absolute value inequality $$\left|\frac{x + 7}{5}\right| \u003e 2.$$

Accepted Answer

$$x  3$$

Question 18

Given the complex numbers $$z_1 = 1 - i$$\sqrt{3}$$ and z_2$ = 2 - i$$, compute $$\frac{z_1$ z_2$}{1 - 2i}.$$

Accepted Answer

$$\frac{(1 - i\sqrt{3})(2 - i)}{1 - 2i}$$

Question 19

Find the midpoint of the segment joining $$(-4, 3)$$ and $$(5, 1).$$

Accepted Answer

$$(0.5, 2)$$

AP Precalculus Unit 0 Review – Step-by-Step Study Guidance

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