Alg A: Capstone 2 Review

Alg A: Capstone 2 Review Day 1 + 2

Topic 1: Solving Equations

• See jamboard with examples.

• Slide 1

Multiple Choice

The objective when solving an equation is to....

• isolate the variable.
• check the solution.
• guess and check.
• Combine Like Terms.

Multiple Choice

Solve for x:

• x = 20

• x = 7

• x = 10

• x = 3

Solving Equations continued

• slide 2

• 
  

Multiple Choice

4x + 7 = 23

• x = 16
• x = 4
• x = 9
• x = 12

Multiple Choice

Solve for x:

 $28=5x-2$  

•  $\frac{5}{6}$  

•  $16$  

•  $6$  

•  $5$  

Multiple Choice

Solve for p:

 $\frac{1}{2}p+2\ =\ 10$  

•  $16$  

•  $4$  

•  $-4$  

•  $\frac{1}{16}$  

Multiple Choice

Solve for m:

 $\frac{m}{4}+9=21$  

•  $\frac{1}{5}$  

•  $5$  

•  $\frac{1}{3}$  

•  $3$  

Multiple Choice

20 = 2 - a

• a= 18
• a= -18
• a= -10
• a= 12

Multiple Choice

 $\frac{\left(x-4\right)}{2}=-8$  

• -12

• -20

• -16

• 2

Solving Equations

• combining like terms and variables on both sides

• slide 3

Multiple Choice

Solve the equation for x:
2x + 3x + 4 = 44

• x = 8
• x = 9
• x = 10
• x = 11

Multiple Choice

Solve for x.

4(2x+8)-3x = 47

• 13

• 2

• 3

• 7.8

Multiple Choice

Solve for f:
f - 4 = 6f + 26

• f = -5
• f = 5
• f = 6
• f = -6

Multiple Choice

Solve for x:
5x - 14 = 8x + 4

• x = 6
• x = -6
• x = -18/13
• x = 10/3

Multiple Choice

Solve for X

4(1-x)+3x = -2x-2

• x= -6

• x= 3

• x= 6

• x= -3

Multiple Choice

Solve for x:

-18-6x=6(1+3x)

• x=1

• x= -1

• No solution

• Infinite solutions

Topic 2: Absolute Value Equations

• Two answers: the positive and negative case

• see slide 4

Multiple Choice

What's a way to define absolute value?

• The value of a number

• The opposite of a number

• The distance of a number from zero

• The multiplicative inverse of a number

Multiple Choice

| x + 6 | = 11

• x = -6 and x = 11
• No Solution
• x = 5 and x = -17
• x = -5 and x = 17

Multiple Choice

Solve for a

|2a - 10| = 6

• a = 8, a = 5

• a = 8

• a = 8, a=-2

• a = 8, a = 2

Topic 3: Solving and Graphing Inequalities

• Slide 5

• 
  

Multiple Choice

Match the graph with its inequality.

• b > –2
• b < –2
• b ≥ –2
• b ≤ –2

Multiple Choice

-4x + 14 ≤ 54

• x ≥ - 10
• x ≤ -10
• x ≥ 10
• x ≤ 10

Multiple Choice

Solve and graph

• a

• b

• c

• d

Multiple Choice

-2 < x - 9 < 3

• x < 12

• 7 < x

• 7 < x < 12

Multiple Choice

Solve and graph:

• A
• B
• C
• D

Linear Equations

• Standard Form

• Slide 7

Multiple Choice

_{What is the y-intercept of the line?}

_{(Remember that the y-intercept is the point at which the line crosses the y-axis. It will always have an x-value of 0.)}

• (0,¹/₂)

• (0,1)

• (0, ^-1/2)

• (0, -1)

Multiple Choice

^{What is the x- intercept of the line?}

^{(Remember that the x-intercept is the point at which the line crosses the x-axis. It will always have a y-value of 0.)}

• (1, 0)

• (2, 0)

• ( -1, 0)

• (-2, 0)

Multiple Choice

What is the x and y intercept for the following equation ?

4x - 10y = 20

• x - int = (4, 0)

  y-int = (0, -10)

• x-int = (5, 0)

  y-int = (0, 2)

• x - int = (5, 0)

  y int = (0, -2)

• x -int = (-4, 0)

  y -int = (0, -10)

Slope-Intercept form

• graphing an equation in slope-intercept form

• writing an equation in slope intercept form

Multiple Choice

What is the equation of a line with a slope of 4 and a y-intercept of 2?

• y = -4x + 2

• y = -2x + 4

• y = 4x + 2

• y = 2x + 4

Multiple Choice

Write the equation of the line.

• y = -1/3x - 2
• y = 1/3x - 2
• y = 3x - 2
• y = -3x - 2

Multiple Choice

What is the equation of this line?

• y = 2x +2
• y = 2x -2
• y = -x + 2
• Cannot be Determined

Using Point-Slope Form

• slide 9

Multiple Choice

What is the equation of the line that has a slope of 5 and goes through the point (2,7)?

• y = 5x + 3
• y = 1/5x - 3
• y = 1/5x + 3
• y = 5x - 3

Parallel and Perpendicular Lines

• Slide 10

Multiple Choice

Write an equation for a line parallel to the line
y = 1/3x - 4 through (-3, 2)

• y = 2/3x +3
• y = -1/3x + 3
• y = 1/3x + 3
• y = -5/3x + 3

Multiple Choice

Which of the following lines goes through the point (-3, 4) and is perpendicular to
 y = 3/2x + 6?

• y = 3/2x - 6
• y = 2/3x + 3
• y = -2/3x - 2
• y = -2/3x + 2

Systems of Equations

• Graphing

• Substitution

• Elimination

• Slide 11 (if time)

Multiple Choice

Parallel Lines never intersect because...

• they have the same slopes. 
• they have the same y-intercept.
• they have different slopes.
• they have different y-intercepts. 

Multiple Choice

How many solutions will this system have?

• No Solution
• Infinitely Many Solutions
• No Clue
• One solution

Multiple Choice

^{What is the solution?} 

• 1
• -2
• (1, 2)
• (1, -1)

Multiple Choice

Solve the system by elimination.

−6x + 6y = 0

9x − 8y = 4

• (4, −9)

• Infinite number of solutions

• (−9, 4)

• (4, 4)

Multiple Choice

Solve by elimination:
-x+2y=17

2x+2y=-10

• ARN
• (-9,4)
• (-9,-4)
• (9,-4)

Multiple Choice

Solve by elimination:
4x+9y=28
-4x-y=-28

• (-7,0)
• (6,0)
• (-6,0)
• (7,0)

Multiple Choice

Solve the system of equations.

• (-6, 1)

• (-12, -12)

• (1, -6)

• No solution

• Infinite solutions

Multiple Choice

Solve the system of equations.

• (-6, 30)

• (-2, 10)

• (44, 39)

• No solution

• Infinite solutions

Multiple Choice

Solve the system of equations.

• (10, 3)

• (6, 3)

• (15, 3)

• No solution

• Infinite Solution