Algebra I
Unit 1 Review for Test 2
Name: ____________________________
Unit 1: Relationships Between Quantities and Expressions
Key Terms: variable, term, coefficient, constant, algebraic expression, evaluate, order of operations, like terms, simplest
form, percent of change, unit rate, conversion factor, radical expression, radicand, rational numbers, irrational numbers,
terminating decimal, repeating decimal, like terms, distributive property
Lesson 10.3 – Working with Radicals – Simplify, Add, Subtract, and Multiply Radicals
Use the Product Property of Square Roots and the rules of working with radicals to simplify – show all work. If the radical
cannot be simplified, explain why not:
1.
7√125
2.
4.
5√3 ∙ 2√21
5. −4√3 ∙ 7√10
6. 2√8 ∙ 10√18
8. −2√45 + 9√5 − 3√20
9. 2√7 + 7√2
7. 6√6 − 4√6 + 16√6
4√34
3. √3 ∙ √15
10. Gardens are being constructed based on the shaded regions in the diagram below.
Part A) If the side measure of the large square is √18 𝑢𝑛𝑖𝑡𝑠 , show on the diagram
how this could also be represented as 3√2 𝑢𝑛𝑖𝑡𝑠.
√𝟏𝟖
Part B) Calculate the garden area (all shaded regions).
√𝟏𝟖
Lesson Classifying Rational and Irrational Numbers – Move between representations of numbers and classify numbers
Write each of these rational numbers as a fraction.
11. 153
12. 0.153
13. 0. ̅̅̅̅̅
153
Classify each number as rational or irrational, if possible. Explain your reasoning by writing rational numbers as a ratio of
two integers and irrational numbers based on decimal behavior.
14.
√45
3
15. (6 + √2)(6 − √2)
16. 1.53 …
17. Explain why the sum or product of −12 and 3√5 is an irrational number. Give evidence of your reasoning.
Lesson Polynomial Arithmetic – Add, Subtract, and Multiply Polynomials
Use the appropriate method to simplify each expression:
18. −4(6 − 5𝑛) − 5𝑛
19. (8 − 3𝑘 4 + 5𝑘 2 ) + (3𝑘 4 − 𝑘 2 − 1)
20. (6𝑥 2 + 5 − 𝑥) + (3𝑥 2 + 6𝑥 − 4)
21. (2 − 7𝑛2 + 2𝑛3 ) − (4𝑛 + 3 + 3𝑛2 )
22. (6 − 𝑥 2 − 2𝑥 4 ) − (2𝑥 2 + 5𝑥 4 + 7)
23. (5 + 6𝑚 − 3𝑚2 ) − (5 + 10𝑚 − 3𝑚2 )
24. 6(3𝑝2 + 5𝑝 − 1)
25. 4𝑚(2𝑚2 − 7𝑚 + 2)
26. −3(−5𝑥 2 − 4𝑥 − 6)
27. 8𝑎(−2𝑎2 − 2𝑎 − 2)
28. (5𝑥 − 4)(𝑥 + 4)
29. (7𝑝 − 2)(7𝑝 − 3)
30. (8𝑥 + 8)(2𝑥 + 1)
31. (3𝑛 + 4)(7𝑛 − 6)
32. Part A) Write the dimensions for the rectangle below.
Part B) Write an expression that represents the area of the rectangle.
Part C) Evaluate the area if x = 6 inches.
Unit 1 – Cumulative Review (additional practice available in the Unit 1 Test 1 Review Packet)
Lesson 1.1 – Variables and Expressions – Write Expressions and Identify Parts of Expressions
Identify each term, coefficient, and constant for the expressions below:
33. −12 + 3𝑥 + 25 − 18𝑥
34. −4(6𝑥 − 2) + 6𝑥
35. Tom wrote the verbal expression: eleven plus x times three for the algebraic expression 11𝑥 + 3
Part A) Identify Tom’s mistake:
Part B) Write the correct verbal expression for 11𝑥 + 3 :
36. A car rental company charges $28 per day and an additional $0.15 per mile driven for miles over 120.
Part A) Write an expression to represent the total cost of renting a car for d, days and m, miles
Part B) Evaluate the expression if a car was rented for 4 days and driven 260 miles.
37. Allie purchased 6 shirts from an online store and received a 15% discount. Shipping cost was $3.50.
Part A) Let x represent the price of each shirt.
Write an algebraic expression to describe the total bill, including shipping.
Part B) Identify any constants in the context of the problem:
Part C) Evaluate the expression, if the shirts cost $25 each:
Lesson 1.2 – Order of Operations – Evaluate Expressions Using Order of Operations
38. Evaluate the expression, using the given values 3𝑥 2 − 10𝑦 − 𝑧; 𝑢𝑠𝑒 𝑥 = 4, 𝑦 = 2, 𝑎𝑛𝑑 𝑧 = 5
Lesson 1.4 – Distributive Property – Use the Distributive Property to Simplify and Evaluate Expressions
39. The Parks and Recreation Department is planning to build fencing around the new Dog Park that is being constructed
on a rectangular plot of land. Write and then simplify the expression representing the amount of fencing that will be
needed to go around the perimeter of the Dog Park if the length of the lot is 4m – 1 feet and the width is m + 6 feet.
Lesson - Interpreting Complicated Expressions – Interpret the impact of changes
Use your understanding of algebraic expressions and the order of operations to answer the following:
40. Is the expression 6(2 − 1) + 3𝑥 − 1 equal to the expression 3𝑥 + 6? Explain your answer.
41. The product of 4, x, and y is represented by 4xy. If the value of x is negative, what can be said about the value of y in
order for the product to be positive. Give an example to illustrate your reasoning.
Lesson 2.7 – Percent of Change – Calculate Percent of Change and Use Percent to Evaluate Purchasing Problems
Determine whether each percent of change is a percent of increase or a percent of decrease. Then find the percent of
change to the nearest whole percent.
42. Original: 36
43. Original: 40
New: 52
New: 24
44. A jacket is on sale at 40% off. If the original price is $65, find the discounted price.
45. Hector is planning to purchase a shirt that is $36 and will need to pay tax at 6.5%. Hector only has $40 with him, will he
be able to purchase the shirt?
Lesson – Unit Conversions – Create and solve equations that model real-world situations
Use conversion factors to convert the unit rates:
46. A rectangle has a length of 60 inches and a width of 2 feet. What is the perimeter of the rectangle in feet?
47. A dripping faucet wastes 2.5 cups of water every 12 hours. How much water is wasted in a week?
CHALLENGE PROBLEMS:
PROBLEM 1)
Part A) Five gallons of milk weighs 43 pounds. Find the unit rate in pounds per gallon.
Part B) Determine the cargo weight of a milk tanker truck when it is full (9,000 gallon capacity).
Part C) After the tanker’s first delivery, its cargo weight was down to 67,725 pounds. How many gallons were delivered?
Part D) How many more deliveries will the tanker make if each stop receives the same amount of milk?
PROBLEM 2) This rectangle shows the floor plan of a dance studio. The shaded part of the plan is the reception and office
area that is getting new flooring installed.
Part A) Write an algebraic expression that represents the area of the dance studio
that is getting new flooring.
Part B) The entire studio is also getting new wood trim along the outer edge of the
rectangular space. Write an algebraic expression that represents the
perimeter of the dance studio.