Algebra 1 Midterm Review Packet - Canyon Crest Academy ...teachers.sduhsd.net/dmartin/Algebra1/Documents/... · Algebra 1 Midterm Review Packet 1 Name: _____ Notes #42: Review of

Algebra 1 Midterm Review Packet

1

Name: ____________________ Notes #42: Review of Chapters 1-3 Convert to an algebraic expression 1.) the product of 9 and 3 less than p

2.) three times the sum of 11 and a number

3.) the quotient of 3 and the sum of x and 5

Convert to a word expression 4.) x2 + 5 5.) -4(n – 3)

6.) 7

4

w

Real Numbers Rational Numbers Integers Whole Numbers Natural Numbers Name the set(s) of numbers to which each number belongs 7.) 3.6 8.) 0 9.) -7

Evaluate each expression: 10.) 8 5 3 9 11.)

14(2 3 ) (6 )

2f g g f

12.) 5 + 42 × 8 – 23 ÷ 22

Name the property that each equation illustrates: 13.) 83 + 6 = 6 + 83 14.) (1)(4y) = 4y 15.) 15x + 15y = 15(x + y)

16.) (8 · 7) · 6 = 8 · (7 · 6) 17.) (8 · 7) · 6 = (7 · 8) · 6 18.) 0 + (-5m) = -5m

19.) 0 = 0 · 18 20.) -2xy + 2xy = 0 21.)

21.5 1

3


2

Solve each equation: 22.) 24 – 2(2m +1) = -6

23.) 4(3 + 5y) – 4 = 3 + 2(y – 2) 24.) 10 8a 2(5 4a)

25.) 6m 5 7m 7 m 26.)

3

w 6

5

w 4 27.)

3 1 11 2

4 2 4d d d

Write equations and solve each word problem: 28.) The perimeter of a rectangle is 150 cm. The length is 15 cm greater than the width. Find the dimensions.

29.) The sum of three consecutive integers is 126. What are the integers?

30.) Two cars leave town at the same time heading in the same direction. One car travels at 60mph and the other travels at 40mph. After how many hours will they be 50 miles apart? Distance Rate Time Slow Car

Fast Car


3

31.) Two cars leave town at the same time going in opposite directions. One of them travels 60mph and the other travels at 30mph. In how many hours will they be 150 miles apart? Distance Rate Time Slow Car

Fast Car

32.) Raisins cost $2 per pound and nuts cost $5 per pound. How many pounds of each should you use to make a 30-lb mixture that costs $4 per pound? Raisins

Nuts

Mixture

33.) A chemist has a 10% acid solution and a 60% acid solution. How many liters of each solution does the chemist need to make 200 L of a solution that is 50% acid? Solution 1

Solution 2

Final Solution


4

Solve and graph each solution: 34.) -8z – 6 < 3z + 12 35.)

5 12( 3) 1

6 9y y

36.) -3 < 2x – 1 13 37.) 4v + 3 < -1 or -2v + 7 < 1

Solve each absolute value equality: 38.) 2 5 11p 39.) 3 5 6r

Solve and graph each absolute value inequality: 40.) 5 14d 41.) 3 8k


5

Homework #42: 1-30 all Convert as directed: 1.) Convert to a fraction in simplest form: 2.16

2.) Convert to a decimal: 3

38

Add/subtract/multiply/divide the fractions; leave in simplest form.

3.) 3 5

2 58 6

4.) 3 5

7 210 6

5.) 2 1

3 53 2

6.) 2 1

4 25 2

Write an expression for each phrase: 7.) the quotient of m and the difference of w and 2

8.) the sum of three times j and twice b

Write a phrase for each expression: 9.) 3k – 6

10.) 5

4 p

Evaluate each expression for a = -1, b = 2, c = -3: 11.) 2b ÷ a + 3c

12.) 22

1

a b

c


6

Name the set(s) of numbers to which each number belongs: 13.) a) 4.12

b.) 0

Which property does each equation illustrate? 14.) a) 3z + 0 = 3z

b) 3a + (2b + c) = (3a + 2b) + c

c) 3 3

02 2

d) 3 2

12 3

e.) (2x + 3y)(4z) = (4z)(2x + 3y) f.) -3(2m – n) = -6m + 3n

Distribute and simplify: 15.) a) 5x + 2y – (3x – 5y + z) b) 2(3a – 4b) – 5(2b – 3a) Solve each equation. Please show all of your steps/work.

16.) a) 3

95

d b.) 6 12 33y c.) 4 3(2 1) 3x x

17.) 5( 3) 9 6 3( 2)y y 18.) 4 3 3

15 4 10

x x x


7

19.) 4h +7 = 4h - 3 20.) 5 – (8f + 10) = -8f – 5

21.) 5

8 6

x x

Solve each word problem. 22.) The width of a rectangle is 6cm less than the length. The perimeter of the rectangle is 72cm. Write and solve an equation to find the dimensions of the rectangle. 23.) The sum of three consecutive integers is 582. Find the integers. 24.) Mr. Anthony and Mrs. Spragg leave CCA at the same time going in opposite directions. Mr. Anthony travels 50mph and Mrs. Spragg travels at 40mph. How long will it take for them to be 45 miles apart? Distance Rate Time Mr. Anthony

Mrs. Spragg


8

25.) Luke Skywalker and Han Solo leave the Rebel Base at same time heading in the same direction on their speeder bikes. Luke travels at 80mph and Han travels at 120mph. After how many hours will they be 100 miles apart? Distance Rate Time Luke Skywalker

Han Solo

26.) A lab technician has one solution that is 30% chlorinated and another that is 80% chlorinated. How much of each solution is needed to make a 100L solution that is 50% chlorine? volume % Amt of chlorine Solution 1

Solution 2

Final Solution

27.) Write an inequality to model each situation a) The high temperature will be at least 72°F today. b) The airplane can contain at most 100 passengers.

28.) Write an inequality for each graph: a) b)

29.) Solve for the variable and graph: 3 2 1 17n

30.) Solve for the variable and graph: 4 1 13b or 6 6 48b

**This is the end of Homework #42**


9

Notes #43: Review of Chapters 4-6, and section 7.1 Find the domain and range of each relation. Is the relation a function? 1.) {(3, 2), (7, 0), (2, 1), (3, 4)} 2.) {(3, 1), (4, 1), (5, 1), (6, 1)}

3.) Sketch a graph of a relation that is a function 4.) Sketch a graph of a relation that is not a function

5.) Find the range of each function for the domain {-2, 0, 3} h(x) = -x2 + 3x – 1

6.) Write a function for each: the value v(d) of a pile of d dimes a worker’s earnings e(h) for h hours of work at $9.50 per hour the distance d(t) traveled at 55 miles per hour in t hours

7.) Write a function rule for the table: x f(x) 1 -4 2 -3 3 -2 4 -1

Zero Exponents Negative Exponents 8.) Simplify each expression: a) 0(3.5) b) (-4)-2 c) -5-2

9.) Simplify each expression:

a) 0

2

3x

y b) 2 3 0

1

3

5

x y

z


10

10.) Evaluate each expression for r = -2 and s = 3

a) 4s-2 b) 2

2

r

s

c) (-r2)(-s2)

11.) Find the slope of the line passing through the pair of points: a) (-4, 7) and (2, 9) b) (3, 8) and (3, -1)

Slope-Intercept Form Standard Form Intercepts 12.) Write the equation in slope-intercept form. State the slope (m) and y-intercept (b)

12

3x y

13.) Write the equation in standard form and find the x and y intercepts.

36

4y x

14.) Write the equation of the line with slope of 2

7 and y-intercept 4 in standard form.

15.) Graph the line by finding the slope and y-intercept. 4 2 6x y

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9-8

-7

-6

-5

-4

-3-2

-1

12

3

45

6

7

89

10

y

16.) Graph the line by finding the x and y intercepts.

2 3x y

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9-8

-7

-6

-5

-4

-3-2

-1

12

3

45

6

7

89

10

y


11

17.) Write the equation of the line with slope -4 and passing through the point (6, -1) in standard form.

18.) Write the equation of the line passing through the points (-3, 2) and (1, 4) in slope-intercept form

19.) Write the equation of the line parallel to y = -2x + 3 and passing through the point (4, -1) in standard form.

20.) Write the equation of the line perpendicular to 3x – y = 2 and passing through the point (-1, -2) in standard form.

21.) Solve for a and b using the substitution method

2 4

3 4 15

a b

a b

22.) Solve for x and y by using the addition/elimination method: 2 5 3

3 6 9

x y

x y


12

23.) Graph the linear inequality: 5 2 9x y

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9-8

-7

-6

-5

-4

-3-2

-1

12

3

45

6

7

89

10

y

24.) Graph the set of linear inequalities and shade the solution region.

2 1

4 3

y x

x y

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9-8

-7

-6

-5

-4

-3-2

-1

12

3

45

6

7

89

10

y

Write a system of equations to model each problem and solve. 25.) You have 32 coins that are only nickels and quarters. The coins total $5.00. How many of each coin do you have? a) write let statements to define your variables b) write two equations c) solve 26.) Kim bought 2 popsicles and 3 cokes for her friends for $5.50. Rick bought 3 popsicles and 2 cokes for $5.75. Find the cost of a popsicle and a drink. a) write let statements to define your variables b) write two equations c) solve


13

27.) The sum of two numbers is 105. The difference of the two numbers is 59. Find the numbers. a) write let statements to define your variables b) write two equations c) solve 28.) Susan and Katie each have a savings account. Susan started with $140 and is saving $5 a week. Katie started with $200 and is withdrawing $10 per week. After how many weeks will they have the same amount of money in their accounts? a) write let statements to define your variables b) write two equations c) solve


14

Homework #43: 31-60 all 31.) Solve and graph: 7 3(4 6) 4 1x x

32.) Solve and graph:

2 7m

33.) Solve and graph:

2 1 7p

34.) Solve:

a) 7 1 20x b) 3 2 11x

35.) Name the coordinates of each point and the quadrant in which it is found: a.) A b.) B c.) C

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9-8

-7

-6-5

-4

-3-2

-1

12

3

45

6

7

8

9

10y

36.) Find the domain and range of each relation. Is each relation a function? a)

x y 0 0 2 6 0 -3

b.) {(-3, 2), (0, 5), (4, 2)}

37.) Find the range of each function for the domain {-3, 2, 5} g(x) = -2x2


15

38.) Model the table with a function rule

x f(x) 1 -2 2 -4 3 -6 4 -8

39.) Simplify each expression: a) (-3a2b)0 b) 4a0b-3

40.) Simplify each expression: a) -4-2 b) (-3)-3

41.) Simplify each expression:

a) 1 3

2

5 x

y

b) 2 5 3

2

2

5

x y

z

42.) Evaluate each expression for x = -2 and y = 3

a) -3x2y-1 b) 2

02

x

y

43.) Find the slope of the line passing through the given points: (-3, 1) and (1, -5)

44.) State whether the point is a solution of the given line. (-3, 2) 2x + y = 8

45.) Write each equation in slope-intercept form. State the slope (m) and y-intercept (b)

23

5x y

______________

m = ______, b = _______

46.) Write the equation in standard form and find the x and y intercepts.

48

5y x

47.) Write the equation of the graphed line in slope-intercept form.

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9-8

-7

-6

-5

-4

-3

-2

-1

12

3

4

5

6

7

89

10

y


16

48.) Graph the line by finding the slope and y-intercept. 4 3 9x y

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9-8

-7

-6

-5

-4

-3-2

-1

12

3

45

6

7

89

10

y

49.) Graph the line by finding the x and y intercepts. 4 8x y

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9-8

-7

-6

-5

-4

-3-2

-1

12

3

45

6

7

89

10

y

50.) Find the equation of the line with slope -5 and passing through the point (9, 2) in standard form.

51.) Find the equation of the line passing through the points (-6, 2) and (1, 5) in slope-intercept form.

52.) Find the equation of the line parallel to y = 5x – 1 and passing through the point (3, -2) in standard form.

53.) Find the equation of the line perpendicular to 2

13

y x and passing through the point (3, -2) in

standard form.


17

54.) Solve for x and y by graphing. 2 6

6

x y

y x

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9-8

-7

-6

-5

-4

-3-2

-1

12

3

45

6

7

89

10

y

55.) Without solving, state whether each system of linear equations will have one solution, no solution, or infinitely many solutions.

a) 3

2 6 2

x y

x y

b) 2

13

3 2 5

y x

y x

c) 4 2 6

1

x y

x y

56.) Solve for a and b using the substitution method

3 5

2 4 0

b a

a b

57.) Solve for x and y by using the addition/elimination method:

a) 3 2

4 3 7

x y

x y

b) 3 5 15

2 4 12

x y

x y


18

58.) Graph each linear inequality: a) 2 3 9x y

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9-8

-7

-6

-5

-4

-3-2

-1

12

3

45

6

7

89

10

y

b) 2 4x y

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9-8

-7

-6

-5

-4

-3-2

-1

12

3

45

6

7

89

10

y

59.) Graph the set of linear inequalities and shade the solution region.

3 5

2 3

y x

x y

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9-8

-7

-6

-5

-4

-3-2

-1

12

3

45

6

7

89

10

y

60.) Two sandwiches and three drinks cost $20. At the same café, three sandwiches and two drinks cost $25. What is the cost of one sandwich?

**This is the end of Homework #43**


19

Notes #44: Midterm Review For #1-3, solve and graph each inequality. Please show all work. 1.) 3 2( 3) 4 5x x

2.) 2 1 5x

3.) 4 3 2x

4.) Solve and show checks but do not graph. 3 2 7x

For #5-9, Find the domain and range of each relation. Then state whether it is a function. 5.) {(1, -3), (-7, 2), (4, 1), (6, -3)} 6.) {(-3, 5), (-3, 8)} 7.)

8.)

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9-8

-7

-6-5

-4

-3-2

-1

12

3

45

6

7

8

9

10y

9.)

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9-8

-7

-6-5

-4

-3-2

-1

12

3

45

6

7

8

9

10y


20

For #10-15, solve for the variables:

10.) 4 3(2 1) 3x x 11.) 4 3 3

15 4 10

x x x 12.) 2 3

9 14

d

d

13.) 4 7

5 10x

14.) -7 < 5x – 2 13

15.) Simplify: a) 3-2 b) -32 c) x-5

16.) At a supermarket salad bar, the price of a salad depends on its weight. Salad costs $0.25 per oz. a) write a rule to describe the function

b) How much would a 9-ounce salad cost?

c.) How much salad could you buy with $5.00?

17.) Find the slope and y-intercept of the line:

5 2( 1)y x

18.) Simplify:

a) 3

5

8

2

m

m b) 7

0

12

18

x

x c)

3

8

27

6

z

z

19.) Write the equation, in slope-intercept form, of the line with slope of 3 and passing through the point (-1, 5).

20.) Find the x-intercept and y-intercept and use these points to graph the line. 3x – 2y = -6 x-intercept: (____, _____) y-intercept: (____, _____)

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

89

10y


21

21.) Write the equation, in standard form, of the line passing through the points (-2, 1) and (3, 5).

22.) Find the equation of the line parallel to: 2x + 3y = 6 and passing through the point (-3, 1). Leave in slope-intercept form.

23.) State whether the lines are parallel, perpendicular, or neither:

1

32

2 5

y x

x y

24.) Find the equation of the line perpendicular to y = 4x – 7 and passing through the point (-2, 3). Leave in slope-intercept form.

25.) Graph: 2 3 6x y

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9-8

-7

-6-5

-4

-3-2

-1

12

3

45

6

7

89

10y

26.) Solve by addition/elimination: 4 9 61

10 3 25

x y

x y

27.) Write let statements and two equations. Do not solve. Three apples and two bananas cost $3.06. Five apples and three bananas cost $4.95. Find the cost of an apple and a banana.

28.) Write let statements and two equations. Do not solve. Bob’s Taxi service charges a flat rate $7.00 plus $1.75 per mile. Sue’s Taxi service charges a flat rate of $4.00 plus $1.80 per mile. For what mileage is the cost the same?

**End of Notes #44**


22

Homework #44: 61-85 all Correct Online 61.) Solve by graphing:

7

3 2 6

x y

x y

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

y

62.) Solve by graphing: 2

4

x y

x y

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

y

63.) Simplify: a) 8m2n0 if m = -2 and n = 3 b) x-2 if x = 5

c) 2( 2 5 )

3

m n

n

for m = -3 and n = -1

64.) You have 25 coins that are only nickels and dimes. The coins total $2.15. How many of each coin do you have? a) write let statements to define your variables b) write two equations c) solve


13

22 5

y x

x y



23

67.) Find the equation of the line parallel to: 2x + 5y = 6 and passing through the point (-5, 1). Convert to standard form.

68.) Find the slope and y-intercept of the line and graph using these values. x – 2y = 8 slope = ______ y-int_____

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

y

69.) Find the slope and y-intercept of the line. Use these values to graph the line.

4 3( 1)y x slope = ____, y-int = _____

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10x

-10

-9-8

-7

-6-5

-4

-3-2

-1

12

3

45

6

7

89

10y


1

32

2 5

y x

x y

71.) Write the equation, in standard form, of the line passing through the points (-2, 1) and (5, 5).

72.) Find the equation of the line parallel to: 4x + 3y = 6 and passing through the point (-2, 1). Leave in slope-intercept form.


24


74.) Solve: 5 2(3 1) 1x x

75.) 1 3 5

12 4 12

y y 76.) 6 4 8k

77.) Solve and check: 3 1 8x 78.) Solve and graph: 2 3 5x

79.) Solve and graph: 4 1 7x 80.) (5 6) (2 3) 3 9x x x

81.) 2(2 1) (3 4) 9x x x 82.) Identify each property: a) 4mn(1) = 4mn b) 3x + 2y = 2y + 3x


25

83.) Define a variable, write an equation, and solve: A+ Taxi service charges $8.00 plus $2.50 per mile. If you only have $73 to spend, how far can you drive in the taxi?

84.) Simplify: 3(x + 5) – 2(2 – 7x)

85.) Evaluate: 14 – 3(5 – 42 + 5)

Midterm Schedule: Thursday 4/15

Period 1 8:15 – 10:15 Period 2 10:40 – 12:40 Friday 4/16

Period 3 8:15 – 10:15 Period 4 10:40 – 12:40

Please bring the following to class for your midterm:

Notes #42-44 and HW #42-44 (this completed, corrected packet)

Completed late homework assignments with a signed pass

Bathroom passes Extra credit points Something quiet to do in case you finish your

midterm early.