Free Printable TOPICs 1 and 2

Worksheets

TOPICs 1 and 2 - REVIEW

Total questions: 66

Worksheet time: 17hrs 30mins

Name

Class

Date

When you graph an inequality, you used a closed dot when you use which symbols?

≤, ≥

<, >

When graphing an inequality, you use an open dot when you use which symbol?

<, >

≤, ≥

What inequality is graphed?

x > 2 and x ≤ -3

x > 2 and x < -3

x > 2 or x ≤ -3

x > 2 or x < -3

What inequality is graphed?

x > 2 and x < 4

2 ≤ x ≤ 4

x > 2 or x < 4

x ≥ 2 or x ≤ 4

Write an inequality for Graph 3.

x ≤ -2 AND x > 5

x ≤ -2 OR x > 5

x ≥ -2 OR x < 5

-2 ≤ x < 5

-2 < x - 9 < 3

x < 12

7 < x

7 < x < 12

0 < x + 7 < 9

-7< x <2

-7< x or x<2

2 < x < -7

-7>x or x>2

Solve: -3 ≤ 2x - 1 ≤ 5

-1 ≤ x ≤ 3

-1 < x < 3

1 < x < 3

1 ≤ x ≤ 3

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

10.

What is the reason that absolute value is always written as a positive?

Absolute value is talking about numbers so it must be positive.

Absolute value does not always have to be positive.

Absolute value is like a clock it has only positive numbers.

Absolute value is talking about distance, distance is always measured by positive numbers.

11.

What is the absolute value of |-26|.

-26

-20

12.

Evaluate each expression.
| x + 9 | = -5

-14

-4

{-14, -4}

no solution

13.

| x – 3 |= 0

-3

{-3, 3}

no solution

14.

∣ 2x + 9 ∣ = 15

x = 3

x = 3
x = -6

x = 3
x = -12

x = 6
x = -12

15.

|v + 8| − 5 = 2

{-1,-15}

{-1,-5}

{-15,15}

No Solution

16.

Solve for x
l 5x l = 40

x = 8 and x =-8

x = 35 and x = -35

Only x = 8

No Solution

17.

Solve for x
l x−6 l + 4= 10

x = 12 and x = 0

x = 3 and x = -3

x = -12 and x = 0

No Solution

18.

Solve for x
2 lx−4l+8=18

x = 9 and x =-1

x = 1 and x = -9

x= 4 and x = -2

No Solution

19.

3x - 2 > 13

x > 3.6

x ≥ 5

x > 5

x> 15

20.

2x + 3 ≤ 15

x ≤ 6

x ≥ -6

x ≤ 9

x≤ -9

21.

2x + 7 < -11

x < 2.5

x < - 2.5

x ≤ -9

x<-9

22.

Solve:
3x-2>10

x>4

x<6

x≥4

x>3.5

23.

Solve for x:
6(2x + 1) = 18

17/12

24.

Solve for x:
2 - 4x = 3x - 12

-14

-2

25.

Solve for x:
4x + 1 = 7x - 5

-1

6/11

26.

x - 8 = -5

-13

-3

27.

x - 62 = 123
How should you show your work to isolate the variable and solve the equation?

Add 62 to each side.

Subtract 62 from each side.

Multiply each side by 62.

Add 123 to each side.

28.

What is the inverse operation of division?

Division

Multiplication

Addition

Subtraction

29.

The variable, k, is being divided by 11. How should you show your work to isolate the variable?

Divide both sides by 11

Multiply both sides by 11.

Add 11 to both sides.

Subtract 11 to both sides.

30.

What is the inverse operation of subtraction?

Subtraction

Multiplication

Division

Addition

31.

Level 3

Solve for a

a= -2

a= -6

a= 3

a= 15

32.

Level 3

Identify the steps to solve for b

Add 6 to both sides and divide both sides by 5

Add 6 to both sides and multiply both sides by 5

Subtract 6 from both sides then multiply both sides by 5

Subtract 6 from both sides then divide both sides by 5

33.

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

isolate the variable.

check the solution.

guess and check.

Combine Like Terms.

34.

-15 = 5a +12- 2a + 6

-11

-3

35.

2x + 3(5x - 7) = 47

x = 1

x = 2

x = 3

x = 4

36.

Peppy Pets charges a flat fee of $15 plus $3 per hour to keep a dog during the day. Happy Hounds charges a flat fee of $21 plus $1 per hour. For how many hours is the total fee charged by the companies the same?

2 hours

3 hours

4 hours

5 hours

37.

Pick the correct inequality.

38.

When graphing b< 6 would you use an open or closed circle?

Open

closed

39.

10 ≥ x - 3

x ≤ 13

x ≥ 13

x ≤ 7

x ≥ 7

40.

When do you "flip the inequalities sign"?

When you add or subtract a negative

When it's a 1-step problem

When you multiply or divide a negative

When it's a 2-step problem

41.

Ms. Senff wants to adopt more cats. The shelter charges an adoption fee of $25, and it charges $40 per cat. If Ms. Senff has $185, how many cats can she adopt?

5.8 cats

5 cats

20 cats

4 cats

42.

One plane at an altitude (height) of 400 ft is rising at a rate of 30 feet per minute. Another plane is at an altitude of 1600 ft, but it is descending at a rate of 50 ft per minute. How long will it take for them to be at the same altitude?

10 minutes

15 minutes

25 minutes

60 minutes

43.

F = (GMm) / r²
(solve for G)

G = (Fr²) / (Mm)

G = FMmr²

Fr²= GMm

Fr²M²= G

44.

Solve:
y = mx + b , for b

y - mx = b

y + mx = b

^y/_mx = b

y + mx = -b

45.

Ms. Hernandez is taking her children and their friends to the movies. She will pay $10 for her adult ticket and $7 for each child ticket. Ms. Hernandez does not want to spend more than $40. Which inequality can be used to find c, the number of child tickets Ms. Hernandez can purchase?

7 + 10x > 40

10x - 7 ≤ 40

10 + 7x > 40

10 + 7x ≤ 40

46.

If x = -3, then which inequality is true?

-5x + 2 ≤ 12

3x - 7 ≥ -16

14 + 2x < 5

1/2x + 6 > 11

47.

Which situation best represents the equation below?

26 = 179 - 9k

A pool of water has 26 gallons of water in it. It is filled at a rate of 9 gallons per minute, until there are 179 gallons.

A dairy farm has 179 cows in it. All of the cows are placed in groups of nine. There are 26 groups of cows.

There were 26 boxes for delivery at the post office one morning. By the end of the day, 179 boxes had been added to the delivery pile. The boxes will be delivered in groups of k.

A school assembly has 179 students in it. Nine teachers escort k number of students out of the assembly, until there are 26 students remaining.

48.

Solve.

|x + 4| < 5

x < -9 or x > 1

-9 < x < 1

x < 9 or x > -1

-1 < x < 9

49.

Solve.
|y - 4| ≥ 8

y ≤ -4 or y ≥ 12

-4 ≤ y ≤ -12

y ≤ 4 or y ≥ -12

-12 ≤ x ≤ 4

50.

Solve.

|d + ⅔| + ¾ < 0

no solution

d > -9 and d < ½

d > -¾ and d < 9

d < -1/12 and d > -7/12

51.

Solve.

3|2d + 9| + 13 > 10

d > 5 or d < -1

d < -4 or d > 5

No Solution

All real numbers

52.

Solve.

|-3f| ≥ 6.3

-18.9 ≤ f ≤ 18.9

no solution

f ≤ -2.1 or f ≥ 2.1

-2.1 ≤ f ≤ 2.1

53.

Solve.
|4m + 9| ≥ 21

-7.5 ≤ m ≤ 3

m ≤ -7.5 or m ≥ 3

-3 ≤ m ≤ 7.5

m ≤ -3 or m ≥ 7.5

54.

The rules for an essay contest say that entries can have 500 words with an absolute deviation of at most 30 words. Which inequality represents represents the acceptable number of words?

|x - 30| < 500

|x - 30| ≤ 500

|x - 500| < 30

|x - 500| ≤ 30

55.

Find the slope

-5/3

-3/5

5/3

3/5

56.

Find the slope:

3/4

4/3

-3/4

-4/3

57.

The slopes of parallel lines are...

the same

opposite

always different

58.

Slope is know as rise/

run

fall

none

rise

59.

Find the slope of the line that passes through:
(6,7) and (4,2)

2/5

-5/2

5/2

-1/2

60.

Find the slope of the line that passes through:
(10, 1) and (5, 2)

1/5

-1/5

-5

61.

Give the slope and y-intercept
6x - 3y = -9

slope is 6
y-intercept is 9

m=2
b=3

slope is 2
y-intercept is -3

m = 3
b = 2

62.

Which of the following are written in standard form?

y=3x-5

3x+16=5y

2/3 x + 9/13 y = 21

5x+7y=-12

63.

Write the equation of a line in point slope form that goes through the points (4,7) and (5,1).

y-7=-6(x-4)

y+1=-6(x+5)

y-7=-1/6(x-4)

y-1=-1/6(x-5)

64.

Use the equations given to determine if the following lines are parallel, perpendicular, neither or both.
y=2x-3
y=-1/2x+3

parallel

perpendicular

neither parallel nor perpendicular

both parallel and perpendicular

65.

Use the equations given to determine if the following lines are parallel, perpendicular, neither or both.
y=4x-2
y-3=-1/4(x-8)

parallel

perpendicular

neither parallel nor perpendicular

both parallel and perpendicular

66.

Write the equation in Standard Form:
y - 5 = 1/3(x + 8)

-x + 3y = 23

y = 1/3x + 23/3

x - 3y = -13

x - 3y = - 23

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TOPICs 1 and 2 - REVIEW

Total questions: 66

Worksheet time: 17hrs 30mins

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