Combined Algebra I SOL Review

4

Solve for x: 1/2x + 8 = 10

(5,0)

What is the x-intercept of 3x + 6y = 15

0.65x + 1.75 ≤ 10 At most 12 miles

A local taxi service charges $1.75 flat rate in addition to $0.65 per mile. Kylie has no more than $10 to spend on a ride. How many miles can Kylie travel without exceeding her limit? Write an inequality that represents this situation.

130˚

A rotation of 230˚ clockwise, is the same as a rotation of ____________ counterclockwise.

291˚

A rotation of 69˚ counterclockwise, is the same as a rotation of ___________ clockwise.

-4

Determine the y-intercept of the equation y=2x -4

y = 5x is what kind of an equation?

Direct Variation

x + 2x + 2x - 5 = 80 The sum of 17, 34, and 29 is 80.

Divide $80 among three people so that the second will have twice as much as the first, and the third will have $5 less than the second.

32

Evaluate if y = 4 8y

2

Evaluate if y = 8 y/4

5

Evaluate if y = 9 y-4

7

Evaluate is y = 4 3+y

15

Evaluate is y = 7 y +8

59

Evaluate when f = 6 2f + 47

4

Evaluate when m = 2, k = 8 (8m - k)/2

6

Evaluate when m = 3, k = 10 20m / k

60

Evaluate when m = 3, k = 10 2mk

18

Evaluate when m = 3, k = 10 3k - 4m

31

Evaluate when m = 3, k = 10 7m + k

30

Evaluate when m = 3, k = 10 m * k

70

Evaluate when p = 7 5p + 35

64

Evaluate when x = 56 x/7 + x

33

Evaluate when x = 6 y = 8 and z = 3 2x + 3y -z

51

Evaluate when x =6 y = 8 and z =3 xy + z

500 - 50w ≥ 200 At most 6 weeks

Evan has $500 in a savings account at the beginning of the summer. He wants to have at least $200 in the account by the end of the summer. He withdraws $50 each week for food, clothes, and movie tickets. How many weeks can Evan keep withdrawing money from his account? Write an inequality and a sentence that represents this situation.

1. Substitute the numbers for the variables 2. Follow the Order of Operations (PEMDAS)

HOW TO EVALUATE EXPRESSIONS?

Slope = -2

Identify the slope of the line by counting the rise/run

Slope = -1/2

Identify the slope of the line by counting the rise/run - (find where the line crosses in the corner of the box)

counterclockwise

If the direction of rotation is not given, you always rotate...

71+84+79+81+x/5 ≥ 80 At least an 85%

In a math class at a community college, five chapter exams are given and an 80% must be achieved in order to take the state exit exam. Matt has completed the first four exams with scores of 71, 84, 79, and 81. What is the minimal score Matt can make on the fifth exam in order to take the state exit exam? Write an inequality and a sentence that represents this situation.

(x, y) --> (-x, -y)

In order to rotate a figure 180˚ about the origin, the rule is...

(x, y) --> (-y, -x)

In order to rotate a figure 270˚ CCW about the origin, the rule is...

(x, y) --> (x, y)

In order to rotate a figure 360˚ about the origin, the rule is...

(x, y) --> (-y, x)

In order to rotate a figure 90˚ CCW about the origin, the rule is...

5x+4≤19 At most $3.

Isaac spent $19 on a magazine and five composition books. The magazine cost $4. At most, what was the cost of each composition book? Write an inequality and a sentence that represents the situation.

1. D 2. A 3. C 4. B

Match the equations with the correct graphs shown 1. y = -2x - 4 2. y = -2x + 4 3. y = 1/2x + 2 4. y = 2x - 4

Linear - Function

Tell whether the graph is Linear or Nonlinear AND Function or Not a function

Nonlinear - Function

Tell whether the graph is Linear or Nonlinear AND Function or Not a function

Nonlinear - not a function

Tell whether the graphs in the second column are Linear or Nonlinear AND Function or Not a function

x + x + 1 = 37 The two numbers are 18 and 19

The sum of two consecutive numbers is 37. What are they?

2x + 1 + 2x + 3 = 52 x = 12, so 2 x 12 + 1 = 25, & the next one is 27. Their sum is 52.

The sum of two consecutive odd numbers is 52. What are the two odd numbers?

x + x + 12 = 84 x = 36, x + 12 = 48

The sum of two numbers is 84, and one of them is 12 more than the other. What are the two numbers?

n + n + 17 = 99 n = 41, n + 17 = 58

The sum of two numbers is 99, and one of them is 17 more than the other. What are the two numbers?

(x, y) --> (-y, -x)

To reflect something about the line y= -x, the rule is...

(x, y) --> (y, x)

To reflect something about the line y=x, the rule is...

(x, y) --> (x, -y)

To reflect something about the x-axis, the rule is...

(x, y) --> (-x, y)

To reflect something about the y-axis, the rule is...

3x - 7 = 35 x = $14

Trina spent $35 at the market. This was seven dollars less than three times what she spent at the bookstore; how much did she spend there?

parenthesis

What comes first when solving order of operations?

Standard Form

What form is this equation in?

100˚

What is AOB if AOC is 153˚ and BOC is 53˚

179˚

What is AOC if AOB = 4x - 1, BOC = 15x - 10 and AOC = 18x - 1

(0, 5)

What is they y-intercept of x + 3y = 15

Direct Variation

What kind of graph is this?

Negative Slope

What kind of slope is shown?

Positive Slope

What kind of slope is shown?

Undefined Slope

What kind of slope is shown?

Zero Slope

What kind of slope is shown?

slope

rise/run

To write the equation of a line, you need to find these two things......

slope (m) and y-intercept (b)

The m in the y=mx+b is the

slope of the line

= 348

(3a)² + cd -4b a = 6, b = 4, c = 8, and d = 5

315

(3x)²+wz - 6x w = 3, x = 6 and z = 9

(x, y)

coordinate point

= 72

efg e =6, f = 4, g = 3

11

evaluate when x = 6 y = 8 and z = 3 3z + (y - x)

16

evaluate when x = 6 y = 8 and z = 3 5x - (y + 2z)

= 28

f² +4g f = 4, g = 3

Solve and graph the inequalities -3x < 10 - x

x > -5

57

xy + wz w = 3, x = 6, y = 5, and z = 9

Write an equation in slope-intercept form using the point-slope formula m = -1/3 (-3,8)

y = -1/3x + 7

Write an equation in slope-intercept form using the point-slope formula m = -4 (1,5)

y = -4x + 9

Rearrange the equation into slope-intercept form 2x - 3y = 9

y = 2/3x - 3

Rearrange the equation into slope-intercept form 4x = 2y - 8

y = 2x + 4

Write the equation if b = -2 and m = 3

y = 3x - 2

The b in y=mx+b is the

y-intercept (where the line crosses the y-axis)

Write the equation if b = 3 and m = -2

y= -2x+3

Slope-intercept form for equation of a line.

y=mx+b

-20

y² -5z y = 5, and z = 9

113

z²+4(w+5) w = 3 and z = 9

54

3(5x - 2y + 4z) for x = -2, y = 2, and z = 8

= -49

3(x - 2y) - 4(2x + 3y) for x = -1 and y = 3

x=4

3x + 2 = 14

28

4(2 + 5) - 3(1 - 1) =

-6

4(2 - 5) + 3(1 + 1) =

x = - 4

4(x+2) - 5 = x - 9

-15

4x + 17w - 10z w = 3, x = 6, and z = 9

30

5p - 3q + 2r for p = 5, q = -3, and r = -2

-29

5x - 2y for x = -7 and y = - 3

40

8(d-4) d = 9

= 27

9k − h² for h = 3 and k = 4

= 33

9w + x w = 3, x = 6

Graph the equation f(x) = 3x + 4 if the domain is -3, -2, 0, 1

Steps: *make an input/output table *remember that f(x) is the same thing as y *make ordered pairs after making the chart *graph ordered pairs Your ordered pairs should be: (-3, -5), (-2, -2), (0, 4), (1, 7)

0.25x+1≤5 At most 16

You need to buy some pencils and an eraser. You can spend no more than $5. The eraser costs $1 and the pencils cost $0.25 each. At most, how many pencils can you buy? Write an inequality and a sentence that represents the situation.

= 50

a² + b² + c² for a = 3, b = 4, c =5

= 8

a² - a + 2 for a = 3

= -3

a²- (b³ - 5d) a = 6, b = 4, and d = 5

= 400

(p + q)² for p = 8 and q = 12

Solve the absolute value equation l x - 3 l - 6 = 2

-5, 11

Find the 18th term of the arithmetic sequence if A1 = -2 and d = -3

-53

= -17

-6m + 2n - p for m = 2, n = -3, and p = -1

Solve the absolute value equation l 2x - 4 l = 22

-9, 13

-150

10(x-2y) x = 3 y = 9

Find the 21st term in the arithmetic sequence 3, 8, 13, 18....

103

83

13y + wx w = 3, x = 6, y = 5

2x + 8 = 50 x = $21

Adam has $50, which is eight dollars more than twice what Doug has. How much has John?

Solve 6 - 2x - 1 = 4x + 8 - 6x - 3

All Real Numbers

20+35x≤150 At most 3 hours.

Comfy Canoes rents canoes for $20 plus $35 per hour. Alex does not want to spend more than $150. For how many hours can he afford to rent the canoe? Write an inequality and a sentence that represents the situation.

Identify the domain and range X Y -2 3 4 5 -1 6 2 3 1 3 4 7 -3 0

D: { -2, 4, -1, 2, 1, -3} R: { 3, 5, 6, 7, 0} Notice that you do NOT write any values more than once!

Identify the domain and range X Y -1 1 -2 1 -3 1 -4 1 -5 1 -6 1 --7 1

D: {-1.-2,-3,-4,-5,-6,-7} R: {1} Notice that you do NOT write any values more than once!

8

Find x if AB = 2x + 3, BC = 4x - 4 and AC = 5x +7

12

Find x if AB = 3x, BC = 12x - 144 and AC = 6x-36

175+3x≥490 $105 every week

Jason is saving up to buy a digital camera that costs $490. So far, he saved $175. He would like to buy the camera 3 weeks from now. How much he must save every week to have enough money to purchase the camera? Write an inequality and a sentence that represents this situation.

2x - 14 = 42 blouse cost $28

Kacey spent $42 for shoes. This was $14 less than twice what she spent for a blouse. How much was the blouse?

45,000 + 0.07x > 56,900 At least $170,000.

Melissa is a saleswoman. She receives a salary of $45,000 per year. In addition, she receives 7% of her sales amount for the year. What are the sales amounts that will allow her to earn more than $56,900 per year? Write an inequality and a sentence that represents this situation.

5x - 10 = 100 x = $55

Mona spent $100 on book. This was $10 dollars less than five times what she spent on lunch. How much did she spend on lunch?

Is this relation a function? Why? X Y -2 3 4 5 -1 6 2 3 1 3 4 7 -3 0

No - because 4 is repeated in the x values

Solve 8x + 6 - 9x = 2 - x - 15

No solution

2x + 3(x + 10) = 55 The smaller number is 5, the larger number is 15.

One number is 10 more than another. The sum of twice the smaller plus three times the larger, is 55. What are the two numbers?

10+5x≥75 At least 13 weeks.

Scott has an allowance of $10 each week. He earns an extra $5 for each hour he mows his neighbor's lawn. How many weeks will he need to save in order to have at least $75? Write an inequality and a sentence that represents the situation.

Reflection

This is an example of a _______________________.

Rotation

This is an example of a __________________________.

Translation

This is an example of a ______________________________.

Slope formula

This is the ____________________________.

midpoint formula

This is the ____________________________.

Angle Addition Postulate

This is the ______________________________.

distance formula

This is the ______________________________.

Segment Addition Postulate

This is the ________________________________.

Point-Slope Form

This is the _________________________________.

Slope-intercept Form

This is the ____________________________________.

Opposite reciprical

To find the slope of a perpendicular line, you need to know the _________________________________________.

Is it a function? X Y -1 1 -2 1 -3 1 -4 1 -5 1 -6 1 -7 1

Yes - because no x values are repeated

Find the slope of the line that passes through these 2 points (-3,-4) (2, -6)

m = -2/5

Find the slope of the line that passes through these 2 points (-1,3) (5,3)

m = 0 Because 0/6 is not simplified

Find the slope of the line that passes through these 2 points (-6,2) (-6-9)

m = undefined Because -11/0 is not simplified

26

p² + m for m = 1, and p = 5

Solve and graph the inequalities -4(3 - x) > 5(x + 1)

x < -17

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

x = - 1/2

Find the x and y intercepts and graph -5y + 2x = -10

x = -5 y = 2 (-5,0) (0,2)

Solve 4x + 12 = 2x - 6

x = -9

Find the x and y intercepts and graph 6x + 3y = 12

x = 2 y = 4 (2,0) (0,4)