PERT Math Review: Developmental Math

PERT Lesson: Developmental Math

Comparing Integers

The absolute value of an integer is the distance from that integer to zero on the number line. Distance is always a positive measure, so the absolute value of any integer is positive.

When comparing two integers on a number line, the integer that is farther to the right is greater. The integer that is farther to the left is less.

Multiple Choice

Place the following numbers in order from least to greatest:

- 5, 2, - 8, 0, 5

• -5, -8, 0, 2, 5

• 5, 2, 0, - 5, - 8

• - 8, - 5, 0, 2, 5

• 0, - 8, - 5, 5, 2

Multiple Choice

Place the following numbers in order from least to greatest:

–1.5, –1.05, –1.052

• –1.5, –1.052, –1.05

• –1.05, –1.052, –1.5

• –1.05, –1.5, –1.052

• –1.5, –1.05, –1.052

Order the fractions from Least to Greatest

• 3/10, 9/10, 7/10

• 1/4, 1/8, 1/3

• 1, 3/6, 5/6

Multiple Choice

Place the following numbers in order from least to greatest:

3/5, 1/2, 3/4

• 1/2, 3/4, 3/5

• 3/4, 1/2, 3/5

• 1/2, 3/5, 3/4

Order of Operations: PEMDAS

• P: Parenthesis ( ) Any grouping symbol

• E: Exponents

• M/D: Multiplication OR Division (Work Left to Right)

• A/S: Addition OR Subtraction (Work Left to Right)

Multiple Choice

17 - 5 · 3

• 2

• 36

• 3

• 35

Multiple Choice

18 + (6 – 2) × 2

• 26

• 29

• 44

• 40

Multiple Choice

15 + 7 × 2 – 11 + 35=

• 38
• 251
• 53
• 50

Multiple Choice

Simplify:

[25-(13+4)+4] ÷ 3

• 6

• 2

• 3

• 4

Multiple Choice

What does 3² mean?

• 3 x 2

• 3 x 3

• 2 x 2 x 2

Multiple Choice

40 - 2⁴ + 8

• 40

• 32

• 24

• 42

Multiple Choice

8² +(7-4)²

• 74

• 72

• 70

• 73

Multiple Choice

Solve the following:

(2 + 7 - 1) ÷ 2²

• 16

• 2

• 72.25

• 8.75

Multiple Choice

Simplify:

5 + (–3) – (–6)

• - 4

• 2

• 8

• 23

Multiple Choice

 $\frac{8\ +3\left(-4\right)}{-2}$  

• 2

• -2

• 11

• 14

Combining Like Terms

Term : a number, a variable or a product or quotient of numbers or variables that is added or subtracted in an algebraic expression.

The following equation has 4 terms
 $2x-4y+7z+3$  

Variable

• a symbol (usually a letter) used to represent a quantity that can change.

  
  

• Examples: x, y, z, a, m, f, ....

Coefficient

• a number that is multiplied by a variable.

  
  

• In the term 2x, 2 is the coefficient. This means, 2 times the quantity x.

• In the term x, the coefficient is understood to be 1, even though the number is not written.

  
  

Constant

• a term in an algebraic expression that does not change; it does not contain variables. 

• In the expression x + 2, 2 is the constant.

• 
  

Like Terms

• a term that has the same variable (letter) raised to the same power.

•  $2x+7x+3-2$  

•  $2x-4y+7z+3$  

Multiple Choice

 $-6x^2-3x+7x^2-5x$  

•  $-7x^2$  

•  $x^2-2x$  

•  $x^2-8x$  

•  $13x^2+2x$  

Multiple Choice

 $5x^3+7xy-2x^2-xy+x^3$  

•  $4x^3+2x^2+7$  

•  $6x^3-2x^2+7$  

•  $5x^6-2x^2+8xy$  

•  $6x^3-2x^2+6xy$  

Multiple Choice

Simplify the Expression:

3a + 7 - 2a

• 8a

• 12a

• a + 7

• 5a + 7

Multiple Choice

Simplify the Expression:

3m - 15 + 2m - 4

• 5m - 19

• m + 19

• 5m - 15

• 24m

Multiple Choice

Simplify the Expression:

7x² - 3a +20 - 4x² + 2a

• 11x² - a + 20

• 3x² - a + 20

• 2a + 20

• 3x² - a

Multiple Choice

Simplify the Expression:

3x²y + 4x - 6y + 4x²y -2y

• 11x²y - 8y

• 3y

• 7x²y - 4y

• 7x²y + 4x - 8y

Multiple Choice

Simplify the expression:

3x² - x + 7 + 5x + 2 - 2x²

• x² + 4x + 9

• 5x² + 9

• 15

• 15x

Distributive Property

• Multiplying the number immediately outside parentheses with those inside

•  $a\left(b+c\right)=ab+ac$  

•  $Ex:\ 4\left(x+3\right)$  

•  $Ex:\ 4\left(x-3\right)$  

•  $Ex:\ -4\left(x+3\right)$  

•  $Ex:\ -4\left(x-3\right)$  

Multiple Choice

 $-3\left(x-5\right)$  

• -3x - 5

• -3x-15

• -3x+15

• -3x-8

Multiple Choice

5(a + 6)

• 5a + 6

• a + 30

• 5a + 30

• 5a - 30

Multiple Choice

8(x + 5)

• 8x + 13
• 8x + 5
• 8x + 40
• 13x

Multiple Choice

3(2c - 5)

• 6c - 15

• 6c + 15

• 6c + 15

• -6c - 15

Multiple Choice

What is the simplified version of this expression? $-4(8r+3)$  

•  $-32r-12$  

•  $32r-12$  

•  $-32r+12$  

•  $32r+12$  

Multiple Choice

What is the simplified version of this expression?  $7\left(5x-1\right)$  

•  $35x+7$  

•  $35x-1$  

•  $35x-7$  

•  $-35x-7$  

Multiple Choice

What is the simplified version of this expression?  $9\left(-5x+8\right)$  

•  $45x-72$  

•  $45x+72$  

•  $-45x-72$  

•  $-45x+72$  

Multiple Choice

7a(3b - 2c + 4)

• 10ab + 5ac + 11a
• 10ab + 5ac + 28a
• 21ab + 14ac + 28a
• 21ab - 14ac + 28a

Multiple Choice

-7(w - 4) + 3w - 27

• 4w + 15
• -4w + 1

Multiple Choice

6(x + 1) - 5(x + 2)

• 2x + 8
• x - 4

Multiple Choice

8(x + 5) - 4(x + 4)

• 4x + 24
• 4x + 16

Multiple Choice

(x - 9)² is the same as...

• (x - 9)(x + 9)

• (x - 9)

• (x - 9) (x - 9)

Multiple Choice

(x + 3)²

• x² +6x+9

• x² +9

• x² +9x+6

• x² +6

Multiple Choice

(x + 9)²

• x² +18x+81

• x² +81

• x² +18x

• x² +16x+81

Multiple Choice

(x−6)²

• x² +12x+36

• x² − 36

• x² −12x+36

• x² +36

Multiple Choice

 Multiply:     (r + 7)(r − 7) 

• r ² − 49 
• r ² + 14
• r ² − 7r + 49 

Multiple Choice

Multiply:
(3x – 1)(x + 5) 

• 3x² + 4x + 5
• 3x² + 4x - 5
• 3x² + 14x + 5
• 3x² + 14x - 5

Multiple Choice

Find the product:

(3x + 2)(2x + 4)

• 6x² + 16x + 8

• 5x² +11x + 6

• 5x² + 16x + 6

• 6x² + 11x + 8

Evaluate the expression when

x=3 and z=2

6z+4x=?

Multiple Choice

Evaluate the following expression:

-3x² - 5x + 7 when x = -2

• 5

• 10

• 12

• 7

Multiple Choice

Evaluate the following expression:

-x - 6x + 10 when x = 5

• -20

• -25

• 25

• 20

Multiple Choice

Evaluate the following expression:

25x(x - 4) when x = -1

• 100

• 115

• 125

• 130

Multiple Choice

Evaluate the following expression:

x² + 5 - x when x = 5

• 25

• 33

• 20

• 35

Multiple Choice

Evaluate the following expression:
t² - t + 1 when t = 5

• 25
• 22
• 23
• 21

Multiple Choice

What is the value of x + y if x = 3 and y = 5?

• 8
• 5
• 3
• 2

Multiple Choice

What is the value of x + y if x = 3 and y = 5?

• 8

• 5

• 3

• 2

Multiple Choice

If a = 5 and b = 6, what is the value of ab - b?

• 10

• 12

• 20

• 24

Multiple Choice

Evaluate the expression.   Let g = 3    h = 9 
4h + 2g + 4

• 42
• 46
• 34
• 58

Solving One-Step Equations

• x + 12 = 20

• x - 5 = 10

• 2x = 16

•  $\frac{x}{4}=3$  

Multiple Choice

Solve the equation: 
x + 7 = 12

• x = 5
• x = 19
• x = -5
• x = 84

Multiple Choice

Solve the equation:
x - 4 = -3

• x = -7
• x = 1
• x = 12
• x = -12

Multiple Choice

Solve the equation:
x - 3 = -12

• x = 9 
• x = -15
• x = -9
• x = 15

Multiple Choice

 $\frac{x}{12}=-2$  

• 6

• - 6

• 24

• - 24

Multiple Choice

Solve for the variable. 3x=-27

• x=9
• x=-30
• x=-9
• x=-24

Solving Multi-Step Equations

• To solve a two step equation: 1. Locate the variable in the equation 2. Use the inverse (opposite) operation on both sides of the equation FIRST use addition or subtraction to isolate the variable part SECOND use multiplication or division to isolate the variable 3. Show your answer 

Examples

•  $2x-7=15$  

•  $4x+10=34$  

•  $\frac{x}{7}+19=24$  

•  $4=\frac{x}{5}-9$  

Multiple Choice

4x + 7 = 23

• x = 16

• x = 4

• x = 9

• x = 12

Multiple Choice

20 = 2 - a

• a= 18

• a= -18

• a= -10

• a= 12

Multiple Choice

-4x+1=21

• x=120

• x=5

• x=30

• x=-5

Multiple Choice

3c + 5 = 23

• c = 3

• c = 6

• c = 7

• c = 18

Multiple Choice

7 + ^a⁄₃ = 5

• a= -2

• a= -6

• a= 3

• a= 15