Precalculus - Semester 1 Exam - Review

Vocabulary

100

The term for ONE constant, variable, or product of numbers and variables.

Monomial

200

The highest exponent of a polynomial is called the ___.

Degree

300

The term for TWO constants, variables, or products of numbers and variables.

Binomial

400

A letter of the alphabet or symbol that stands for an unknown number.

Variable

500

1, 4, 9, 16, 25, 36, and 49 are all examples of ___.

Perfect squares

600

What is the symbol we use to represent an imaginary number?

i

Two-Step Inequalities

100

Solve for a:
a - 3 > -2a + 6

a > 3

200

Solve for h:
6h - 7 < 17

h < 4

300

Solve for w:

w/11 - 2 > 3

w > 55

400

Solve for c:

c/5 > -2

c > -10

500

Solve for d:
-10d - 3 < 37

d > -4

600

Solve for q:

(2q) - 4 > 12

q > 8

Absolute Value Equations (1)

100

Solve for all values of y in its simplest form:

abs(y-2)-1=2

{5,-1}

200

Solve for all values of r in its simplest form:

5+abs(6-5r)=14

{-3/5,3}

300

Solve for all values of j in its simplest form:

5+abs(j-2)=7

{4,0}

400

Solve for all values of v in its simplest form:

2+abs(5+4v)=11

{1,-7/2}

500

Solve for all values of p in its simplest form:

-3abs(8-5p)-10=-40

{-2/5,18/5}

600

Solve for all values of x in its simplest form:

4abs(8-2x)+8=36

{1/2,15/2}

Simplifying Algebraic Expressions

100

Simplify the following expression and write your answer in Standard Form:
a² - 3a² + a - 1

-2a² + a - 1

200

Simplify the following expression and write your answer in Standard Form:
9k + 4k - 2k + k - k²

-k² + 12k

300

Simplify the following expression and write your answer in Standard Form:
9j + 4j³ - 2j³ + j² - j²

2j³ + 9j

400

Simplify the following expression and write your answer in Standard Form:
-b + 2b - 2b + b - b²

-b²

500

Simplify the following expression and write your answer in Standard Form:
c + 40c - 21c + c - c² + 9

-c² + 21c + 9

600

Simplify the following expression and write your answer in Standard Form:
-m - m - 2m² + m³ - 3m²

m³ - 5m² - 2m

Absolute Value

100

|3| = ?

3

200

|-21| = ?

21

300

-|2| = ?

-2

400

-|1| = ?

-1

500

-|-44| = ?

-44

600

|-199| = ?

199

Absolute Value Equations (2)

100

Solve for y (and remember to test for rejections):

abs(2y-9)=y

{9,3}

200

Solve for m (and remember to test for rejections):

abs(4m+7)=3m

{ } 

300

Solve for x (and remember to test for rejections):

abs(2x+4)-5=x

{1,-3}

400

Solve for h (and remember to test for rejections):

abs(5h-8)=3h

{4,1}

500

Solve for p (and remember to test for rejections):

abs(4p-9)=5p

{1}

600

Solve for z (and remember to test for rejections):

abs(5z-9)-3=z

{3,1}

Terms and Degrees

100

Identify the number of terms:
3x + 4 - x²

3 terms

200

Identify the number of terms:
-4x² + 7

2 terms

300

Identify the number of terms:
3x + 4 - x² - x² + 3x³

4 terms

400

Identify the number of degrees in the following polynomial:
3x + 4 - x²

2nd degree

500

Identify the number of degrees in the following polynomial:
6x⁴ + 3x + 4x - x²

4th degree

600

Identify the number of degrees in the following polynomial:
13x - 5x⁴ - x²

4th degree

Multiplying Imaginary Numbers

100

i² = ?

-1

200

i³ = ?

-i

300

i = ?

sqrt-1

400

i⁴ = ?

1

500

(i) (i + 3)

-1 + 3i

600

(2 + 2i) (9i)

18i - 18
or
-18 + 18i

Multiplying Polynomials

100

(y + 1) (y - 9) = ?

y² - 8y - 9

200

(x - 1)² = ?

x² - 2x + 1

300

(a) (a²) (a³) = ?

a⁶

400

(g) (g + 1) = ?

g² + g

500

(b) (b - 9) (b) = ?

b³ - 9b²

600

(h + 3)³ = ?

h³ + 9h² + 27h + 27

Factoring

100

Factor the following:
x² + 6x + 9

(x + 3) (x + 3)

200

Factor the following:
a² - 3a + 2

(a - 1) (a - 2)

300

Factor the following:
g² - 1

(g + 1) (g - 1)

400

Factor the following:
k² - 4k + 4

(k - 2) (k - 2)

500

Factor the following:
x³ + 2x

(x) (x² + 2)

600

Factor the following:
f² - f - 12

(f - 4) (f + 3)