advanced algebra 1 midterm exam review. chapter 1 equations

Advanced Algebra 1Midterm Exam Review

Chapter 1Equations

Give two ways to write each algebraicexpression in words.

1. j – 3

2. 4p

3. Mark is 5 years older than Juan, who is y years old. Write an expression for Mark’s age.

The difference of j and 3; 3 less than j.

4 times p; The product of 4 and p.

y + 5

Lesson Quiz: Part I

Evaluate each expression for c = 6, d = 5, and e = 10.

4. 5. c + d

Shemika practices basketball for 2 hours each day.

de

12

11

2d

10 hours; 24 hours; 40 hours

Lesson Quiz: Part II

6. Write an expression for the number of hours she practices in d days.

7. Find the number of hours she practices in 5, 12, and 20 days.

Lesson Quiz

Solve each equation.

1. r – 4 = –8 2. 3. m + 13 = 584. 0.75 = n + 0.65. –5 + c = 226. This year a high school had 578 sophomores enrolled. This is 89 less than the number enrolled last year. Write and solve an equation to find the number of sophomores enrolled last year.

–4

450.15

27

s – 89 = 578; s = 667

Lesson Quiz: Part 1


1.

2.

3. 8y = 4

4. 126 = 9q

5.

6.

21

2.8

–14

40

Lesson Quiz: Part 2

7. A person's weight on Venus is about his or her weight on Earth. Write and solve an equation to find how much a person weighs on Earth if he or she weighs 108 pounds on Venus.

910

Lesson Quiz: Part 1


1. 4y + 8 = 2

2.

3. 2y + 29 – 8y = 5

4. 3(x – 9) = 30

5. x – (12 – x) = 38

6.

–8

4

19

25

9

Lesson Quiz: Part 2

7. If 3b – (6 – b) = –22, find the value of 7b.8. Josie bought 4 cases of sports drinks for an upcoming meet. After talking to her coach, she bought 3 more cases and spent an additional $6.95 on other items. Her receipts totaled $74.15. Write and solve an equation to find how much each case of sports drinks cost.

–28

4c + 3c + 6.95 = 74.15; $9.60

Lesson Quiz


1. 7x + 2 = 5x + 8 2. 4(2x – 5) = 5x + 4

3. 6 – 7(a + 1) = –3(2 – a)

4. 4(3x + 1) – 7x = 6 + 5x – 2

5.6. A painting company charges $250 base plus $16 per hour. Another painting company charges $210 base plus $18 per hour. How long is a job for which the two companies costs are the same?

38

all real numbers1

20 hours

Lesson Quiz: Part 1

Solve for the indicated variable.

1.

2.

3. 2x + 7y = 14 for y

4.

P = R – C for C C = R – P

for m m = x(k – 6 )

5. for C C = Rt + S

for h

Lesson Quiz: Part 2

Euler’s formula, V – E + F = 2, relates the number of vertices V, the number of edges E, and the number of faces F of a polyhedron.

6. Solve Euler’s formula for F.

7. How many faces does a polyhedron with 8 vertices and 12 edges have?

F = 2 – V + E

6

Lesson Quiz


1. 15 = |x| 2. 2|x – 7| = 14

3. |x + 1|– 9 = –9 4. |5 + x| – 3 = –2

5. 7 + |x – 8| = 6

–15, 15 0, 14

–1 –6, –4

no solution

6. Inline skates typically have wheels with a diameter of 74 mm. The wheels are manufactured so that the diameters vary from this value by at most 0.1 mm. Write and solve an absolute-value equation to find the minimum and maximum diameters of the wheels. |x – 74| = 0.1; 73.9 mm; 74.1 mm

Lesson Quiz: Part 1

1. In a school, the ratio of boys to girls is 4:3. There are 216 boys. How many girls are there?162

Find each unit rate. Round to the nearest hundredth if necessary.

2. Nuts cost $10.75 for 3 pounds. $3.58/lb

3. Sue washes 25 cars in 5 hours. 5 cars/h

4. A car travels 180 miles in 4 hours. What is the car’s speed in feet per minute? 3960 ft/min

Lesson Quiz: Part 2

Solve each proportion.

5.

6.

7. A scale model of a car is 9 inches long. The scale is 1:18. How many inches long is the car it represents?

6

16

162 in.

Lesson Quiz: Part 1

Solve for the indicated variable.

1.

2.

3. 2x + 7y = 14 for y

4.

P = R – C for C C = R – P

for m m = x(k – 6 )

5. for C C = Rt + S

for h

Lesson Quiz: Part 2

Euler’s formula, V – E + F = 2, relates the number of vertices V, the number of edges E, and the number of faces F of a polyhedron.

6. Solve Euler’s formula for F.

7. How many faces does a polyhedron with 8 vertices and 12 edges have?

F = 2 – V + E

6

Chapter 2Inequalities

Lesson Quiz: Part I1. Describe the solutions of 7 < x + 4.

all real numbers greater than 3

2. Graph h ≥ –4.75

–5 –4.75 –4.5

Write the inequality shown by each graph.

3. x ≥ 3

4. x < –5.5


5. A cell phone plan offers free minutes for no more than 250 minutes per month. Define a variable and write an inequality for the possible number of free minutes. Graph the solution.

0 ≤ m ≤ 250

0 250

Let m = number of minutes

Lesson Quiz: Part I

Solve each inequality and graph the solutions.

1. 13 < x + 7

x > 6

2. –6 + h ≥ 15h ≥ 21

3. 6.7 + y ≤ –2.1

y ≤ –8.8


4. A certain restaurant has room for 120 customers. On one night, there are 72 customers dining. Write and solve an inequality to show how many more people can eat at the restaurant. x + 72 ≤ 120; x ≤ 48, where x is a natural number

Lesson QuizSolve each inequality and graph the solutions.

1. 8x < –24 x < –3 2. –5x ≥ 30 x ≤ –6

3. x > 20 4. x ≥ 6

5. A soccer coach plans to order more shirts for her team. Each shirt costs $9.85. She has $77 left in her uniform budget. What are the possible number of shirts she can buy?0, 1, 2, 3, 4, 5, 6, or 7 shirts

Lesson Quiz: Part ISolve each inequality and graph the solutions.

1. 13 – 2x ≥ 21 x ≤ –4

2. –11 + 2 < 3p p > –3

3. 23 < –2(3 – t) t > 7

4.


5. A video store has two movie rental plans. Plan A includes a $25 membership fee plus $1.25 for each movie rental. Plan B costs $40 for unlimited movie rentals. For what number of movie rentals is plan B less than plan A?

more than 12 movies

Lesson Quiz: Part I

Solve each inequality and graph the solutions.

1. t < 5t + 24 t > –6

2. 5x – 9 ≤ 4.1x – 81 x ≤ –80

b < 133. 4b + 4(1 – b) > b – 9


4. Rick bought a photo printer and supplies for $186.90, which will allow him to print photos for $0.29 each. A photo store charges $0.55 to print each photo. How many photos must Rick print before his total cost is less than getting prints made at the photo store?

Rick must print more than 718 photos.

Lesson Quiz: Part III

Solve each inequality.

5. 2y – 2 ≥ 2(y + 7)

no solutions

6. 2(–6r – 5) < –3(4r + 2)

all real numbers

Lesson Quiz: Part I

1. The target heart rate during exercise for a 15 year-old is between 154 and 174 beats per minute inclusive. Write a compound inequality to show the heart rates that are within the target range. Graph the solutions.

154 ≤ h ≤ 174


Solve each compound inequality and graph the solutions.

2. 2 ≤ 2w + 4 ≤ 12

–1 ≤ w ≤ 4

3. 3 + r > −2 OR 3 + r < −7

r > –5 OR r < –10


Write the compound inequality shown by each graph.

4.

x < −7 OR x ≥ 0

5.

−2 ≤ a < 4

Chapter 3Functions

Lesson Quiz: Part I

1. Write a possible situation for the given graph.

Possible Situation: The level of water in a bucket stays constant. A steady rain raises the level. The rain slows down. Someone dumps the bucket.

2. A pet store is selling puppies for $50 each. It has 8 puppies to sell. Sketch a graph for this situation.


Lesson Quiz: Part I

1. Express the relation {(–2, 5), (–1, 4), (1, 3), (2, 4)} as a table, as a graph, and as a

mapping diagram.


2. Give the domain and range of the relation.

D: –3 ≤ x ≤ 2: R: –2 ≤ y ≤ 4

3. Give the domain and range of the relation. Tell whether the relation is a function. Explain.


D: {5, 10, 15}; R: {2, 4, 6, 8};The relation is not a function since 5 is paired with 2 and 4.

Lesson Quiz: Part I

Identify the independent and dependent variables. Write a rule in function notation for each situation.

1. A buffet charges $8.95 per person.

independent: number of peopledependent: costf(p) = 8.95p

2. A moving company charges $130 for weekly truck rental plus $1.50 per mile.independent: milesdependent: costf(m) = 130 + 1.50m


Evaluate each function for the given input values.

4. For f(x) = 6x – 1, find f(x) when x = 3.5 and when x = –5.

f(3.5) = 20f(–5) = –31

3. For g(t) = , find g(t) when t = 20 and

when t = –12.g(20) = 2g(–12) = –6


Write a function to describe the situation. Find a reasonable domain and range for the function.

5. A theater can be rented for exactly 2, 3, or 4 hours. The cost is a $100 deposit plus $200 per hour.

f(h) = 200h + 100Domain: {2, 3, 4}Range: {$500, $700, $900}

Lesson Quiz: Part I

1. Graph the function for the given domain.

3x + y = 4D: {–1, 0, 1, 2}

2. Graph the function y = |x + 3|.


3. The function y = 3x describes the distance (in inches) a giant tortoise walks in x seconds. Graph the function. Use the graph to estimate how many inches the tortoise will walk in 5.5 seconds.

About 16.5 in.

Lesson Quiz: Part IFor Items 1 and 2, identify the correlation you would expect to see between each pair of data sets. Explain.

1. The outside temperature in the summer and the cost of the electric billPositive correlation; as the outside temperature increases, the electric bill increases because of the use of the air conditioner.

2. The price of a car and the number of passengers it seatsNo correlation; a very expensive car could seat only 2 passengers.


3. The scatter plot shows the number of orders placed for flowers before Valentine’s Day at one shop. Based on this relationship, predict the number of flower orders placed on February 12.

about 45

Lesson Quiz: Part I

Determine whether each sequence appears to be an arithmetic sequence. If so, find the common difference and the next three terms in the sequence.

1. 3, 9, 27, 81,… not arithmetic

2. 5, 6.5, 8, 9.5,… arithmetic; 1.5; 11, 12.5, 14

Lesson Quiz: Part IIFind the indicated term of each arithmetic sequence.

3. 23rd term: –4, –7, –10, –13, …

4. 40th term: 2, 7, 12, 17, …

5. 7th term: a1 = –12, d = 2

6. 34th term: a1 = 3.2, d = 2.6

7. Zelle has knitted 61 rows of a scarf. Each day she adds 17 more rows. How many rows total has Zelle knitted 16 days later?

–70

197

0

89

333 rows

Chapter 4Linear Functions

Lesson Quiz: Part I

Tell whether each set of ordered pairs satisfies a linear function. Explain.

1. {(–3, 10), (–1, 9), (1, 7), (3, 4), (5, 0)}

No; a constant change of +2 in x corresponds to different changes in y.

2. {(3, 4), (5, 7), (7, 10), (9, 13), (11, 16)}

Yes; a constant change of +2 in x corresponds to a constant change of +3 in y.


Tell whether each function is linear. If so, graph the function.

3. y = 3 – 2x

4. 3y = 12

no

yes


5. The cost of a can of iced-tea mix at Save More Grocery is $4.75. The function f(x) = 4.75x gives the cost of x cans of iced-tea mix. Graph this function and give its domain and range.

D: {0, 1, 2, 3, …}R: {0, 4.75, 9.50, 14.25,…}

Lesson Quiz: Part I1. An amateur filmmaker has $6000 to make a film

that costs $75/h to produce. The function f(x) = 6000 – 75x gives the amount of money left to make the film after x hours of production. Graph this function and find the intercepts. What does each intercept represent?

x-int.: 80; number of hours it takes to spend all the money

y-int.: 6000; the initial amount of money available.

Lesson Quiz: Part II2. Use intercepts to graph the line described by

Lesson Quiz: Part IName each of the following.

1. The table shows the number of bikes made by a company for certain years. Find the rate of change for each time period. During which time period did the number of bikes increase at the fastest rate?

1 to 2: 3; 2 to 5: 4; 5 to 7: 0; 7 to 11: 3.5; from years 2 to 5


Find the slope of each line.

undefined

2. 3.

Lesson Quiz

1. Find the slope of the line that contains (5, 3)

and (–1, 4).

2. Find the slope of the line. Then tell what the slope represents.

50; speed of bus is 50 mi/h

3. Find the slope of the line described by x + 2y = 8.

Lesson Quiz: Part ITell whether each equation represents a direct variation. If so, identify the constant of variation.

1. 2y = 6x yes; 3

2. 3x = 4y – 7 no

Tell whether each relationship is a direct variation. Explain.

3. 4.


5. The value of y varies directly with x, and y = –8 when x = 20. Find y when x = –4. 1.6

6. Apples cost $0.80 per pound. The equation y = 0.8x describes the cost y of x pounds of apples. Graph this direct variation.

2

4

6

Lesson Quiz: Part IWrite the equation that describes each line in the slope-intercept form.

1. slope = 3, y-intercept = –2

y = 3x – 2

2. slope = 0, y-intercept =

y =

3. slope = , (2, 7) is on the line

y = x + 4


Write each equation in slope-intercept form. Then graph the line described by the equation.

4. 6x + 2y = 10

y = –3x + 5

5. x – y = 6

y = x – 6

Lesson Quiz: Part IWrite an equation in slope-intercept form for the line with the given slope that contains the given point.

1. Slope = –1; (0, 9) y = –x + 9

2. Slope = ; (3, –6) y = x – 5

Write an equation in slope-intercept form for the line through the two points.

3. (–1, 7) and (2, 1)

4. (0, 4) and (–7, 2)

y = –2x + 5

y = x + 4


5. The cost to take a taxi from the airport is a linear function of the distance driven. The cost for 5, 10, and 20 miles are shown in the table. Write an equation in slope-intercept form that represents the function.

y = 1.6x + 6

Lesson Quiz: Part I

Write an equation is slope-intercept form for the line described.

1. contains the point (8, –12) and is parallel to

2. contains the point (4, –3) and is perpendicular

to y = 4x + 5


3. Show that WXYZ is a rectangle.

The product of the slopes of adjacent sides is –1. Therefore, all angles are right angles, and WXYZ is a rectangle.

slope of = XY

slope of YZ = 4

slope of = WZ

slope of XW = 4

Lesson Quiz: Part I

Describe the transformation from the graph of f(x) to the graph of g(x).1. f(x) = 4x, g(x) = x

2.

3.

4.

rotated about (0, 0) (less steep)

translated 7 units up

reflected across the y-axis, rot. about (0, 0)

f(x) = x – 1, g(x) = x + 6

f(x) = x, g(x) = 2x

rotated about (0, 0) (steeper)f(x) = 5x, g(x) = –5x


5. f(x) = x, g(x) = x – 4

6.translated 4 units down

f(x) = –3x, g(x) = –x + 1

rotated about (0, 0) (less steep), translated 1 unit up

7. A cashier gets a $50 bonus for working on a holiday plus $9/h. The total holiday salary is given by the function f(x) = 9x + 50. How will the graph change if the bonus is raised to $75? if the hourly rate is raised to $12/h?

translate 25 units up; rotated about (0, 50) (steeper)

Chapter 5System of Equations and Inequalities

Lesson Quiz: Part I

Tell whether the ordered pair is a solution of the given system.

1. (–3, 1);

2. (2, –4);

yes

no


Solve the system by graphing.

3.

4. Joy has 5 collectable stamps and will buy 2 more each month. Ronald has 25 collectable stamps and will sell 3 each month. After how many months will they have the same number of stamps? How many will that be?

(2, 5)

4 months

y + 2x = 9

y = 4x – 3

13 stamps

Lesson Quiz: Part I

Solve each system by substitution.

1.

2.

3.

(1, 2)

(–2, –4)y = 2x

x = 6y – 11

3x – 2y = –1

–3x + y = –1

x – y = 4


4. Plumber A charges $60 an hour. Plumber B charges $40 to visit your home plus $55 for each hour. For how many hours will the total cost for each plumber be the same? How much will that cost be? If a customer thinks they will need a plumber for 5 hours, which plumber should the customer hire? Explain.

8 hours; $480; plumber A: plumber A is cheaper for less than 8 hours.

Lesson QuizSolve each system by elimination.

1.

2.

3.

(2, –3)

(11, 3)

(–3, –7)

2x + y = 253y = 2x – 13

x = –2y – 4–3x + 4y = –18

–2x + 3y = –153x + 2y = –23

4. Harlan has $44 to buy 7 pairs of socks. Athletic socks cost $5 per pair. Dress socks cost $8 per pair. How many pairs of each can Harlan buy?4 pairs of athletic socks and 3 pairs of dress socks

Lesson Quiz: Part I

Solve and classify each system.

1.

2.

3.

infinitely many solutions; consistent, dependent

no solutions; inconsistent

y = 5x – 15x – y – 1 = 0

y = 4 + x

–x + y = 1

y = 3(x + 1)y = x – 2

consistent, independent


4. If the pattern in the table continues, when will the sales for Hats Off equal sales for Tops?

never

Lesson Quiz: Part I

1. You can spend at most $12.00 for drinks at a picnic. Iced tea costs $1.50 a gallon, and lemonade costs $2.00 per gallon. Write an inequality to describe the situation. Graph the solutions, describe reasonable solutions, and then give two possible combinations of drinks you could buy.

1.50x + 2.00y ≤ 12.00

Lesson Quiz: Part I

1.50x + 2.00y ≤ 12.00

Only whole number solutions are reasonable. Possible answer: (2 gal tea, 3 gal lemonade) and (4 gal tea, 1 gal lemonde)


2. Write an inequality to represent the graph.

Lesson Quiz: Part Iy < x + 2 5x + 2y ≥ 10

1. Graph .

Give two ordered pairs that are solutions and two that are not solutions.

Possible answer: solutions: (4, 4), (8, 6); not solutions: (0, 0), (–2, 3)


2. Dee has at most $150 to spend on restocking dolls and trains at her toy store. Dolls cost $7.50 and trains cost $5.00. Dee needs no more than 10 trains and she needs at least 8 dolls. Show and describe all possible combinations of dolls and trains that Dee can buy. List two possible combinations.

Solutions

Lesson Quiz: Part II Continued

Reasonable answers must be whole numbers. Possible answer: (12 dolls, 6 trains) and (16 dolls, 4 trains)

advanced algebra 1 midterm exam review. chapter 1 equations

Documents

hours lesson quiz

h slide

number of hours

number enrolled

number of edges e

number of sophomores

absolutevalue equation

midterm exam review