algebra i topic ii: algebraic expressions & equations...

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ALGEBRA I TOPIC II: Algebraic Expressions & Equations Curriculum and Instruction Page 1 of 10 Division of Mathematics, Science, and Advanced Academics Good Luck to: ______________________________________________________________ Period: ________________ Date ________________________________ DIRECTIONS: Show all work in the space provided. Use the following for problems 1 – 4. Kathy is six years older than her cat. Next year she will be twice as old as her cat will be. How old is her cat now? 1. Write an equation to determine the cat’s age, c , in years. Equation: ______________________ 2. Solve the equation to determine the cat’s age, c , in years. 3. How old is Kathy? 4. How did you determine her age? __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ __________________________________________________________________________ 5. Identify the property used: a + (b + c) = (a + b) + c A. Associative Property of Addition B. Commutative Property of Addition C. Identity Property of Addition D. Identity Property of Multiplication

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Page 1: ALGEBRA I TOPIC II: Algebraic Expressions & Equations …adamerritt.dadeschools.net/documents/2011-2012/TOPIC ASSESSMEN… · ALGEBRA I TOPIC II: Algebraic Expressions & Equations

ALGEBRA I TOPIC II: Algebraic Expressions & Equations

Curriculum and Instruction Page 1 of 10 Division of Mathematics, Science, and Advanced Academics

Good Luck to: ______________________________________________________________

Period: ________________ Date ________________________________

DIRECTIONS: Show all work in the space provided.

Use the following for problems 1 – 4. Kathy is six years older than her cat. Next year she will be twice as old as her cat will be. How old is her cat now?

1. Write an equation to determine the cat’s age, c , in years.

Equation: ______________________

2. Solve the equation to determine the cat’s age, c , in years.

3. How old is Kathy?

4. How did you determine her age?

__________________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________

__________________________________________________________________________

5. Identify the property used:

a + (b + c) = (a + b)+ c A. Associative Property of Addition

B. Commutative Property of Addition

C. Identity Property of Addition

D. Identity Property of Multiplication

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ALGEBRA I TOPIC II: Algebraic Expressions & Equations

Curriculum and Instruction Page 2 of 10 Division of Mathematics, Science, and Advanced Academics

6. Create an equation that demonstrates the use of the commutative property. Equation: ______________________

7. Solve the following equation for y :

(Round to the nearest tenth):

1.7y = 20

8. Solve the following equation for r :

72 = 17 + r A. 89

B. 55

C. 4.24

D. 0.24

Use the following for problems 9 – 10. Two college friends rent an apartment. They have to pay the landlord two months of rent and $500 security deposit when they sign the lease. The total amount they pay the landlord is $1,750.

9. Write an equation for the total cost, c , in dollars. Equation: ______________________

10. What is the rent for one month?

Rent for one month: ______________

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ALGEBRA I TOPIC II: Algebraic Expressions & Equations

Curriculum and Instruction Page 3 of 10 Division of Mathematics, Science, and Advanced Academics

11. Solve the following equation for x : 2.7x + 5.1= 24

A. 7

B. 5

C. 4

D. 2

12. Solve the equation below for x . Show all work and show final check of answer through

substitution. x =________________

13. Simplify the following expression:

3k(k + 4) A. 3k + 7

B. 3k2 +12k

C. 3k2 + 7k

D. 3k2 + 4

14. Simplify the following expression: (2x + 5y)+ (3x − 2y) A. 5x + 3y

B. −x + 3y

C. −x + 7y

D. 5x + 7y

2x + 5 = 4x − 3

Page 4: ALGEBRA I TOPIC II: Algebraic Expressions & Equations …adamerritt.dadeschools.net/documents/2011-2012/TOPIC ASSESSMEN… · ALGEBRA I TOPIC II: Algebraic Expressions & Equations

ALGEBRA I TOPIC II: Algebraic Expressions & Equations

Curriculum and Instruction Page 4 of 10 Division of Mathematics, Science, and Advanced Academics

15. Simplify the following expression: (2x + 5y)− (3x − 2y) A. 5x + 7y

B. 5x + 3y

C. −x + 7y

D. −x + 3y

16. Simplify the following expression:

3(x + 2y)− 2(7x − y) Simplified expression: _________________

17. How many terms are in the simplified expression of:

2r + 3s − 5t − r − 3s A. 5

B. 4

C. 3

D. 2

18. Find the difference of the polynomials, then determine the coefficient of the third degree of a :

(2a3 + 6b2 + 2b)− 3(a3 − 3b)

19. What is the degree of the following polynomial:

14u4 + u3 − 5u2 + 8u

Page 5: ALGEBRA I TOPIC II: Algebraic Expressions & Equations …adamerritt.dadeschools.net/documents/2011-2012/TOPIC ASSESSMEN… · ALGEBRA I TOPIC II: Algebraic Expressions & Equations

ALGEBRA I TOPIC II: Algebraic Expressions & Equations

Curriculum and Instruction Page 5 of 10 Division of Mathematics, Science, and Advanced Academics

20. The formula for the area of a parallelogram is A = bh where A is the area, b is the length of the base, and h is the height of the parallelogram. Solve the equation for b , the length of the base. b = ___________

Use the following for problems 21 – 22. The formula P = 2l + 2w gives the perimeter, P , of a rectangle in terms of l , the length of the base, and w , the length of the height.

21. Express l in terms of P and w . l = ________________

22. How long is the width, w , if the height is 12 inches and the perimeter is 56 inches?

w = ___________

Use the following for problems 23 – 24.

You can use the formula a = hn

to find the batting average a of a batter who has h hits in n

times at bat.

23. Solve the formula for h . h =________________

24. If a batter has a batting average of 0.290 and has been at bat 300 times, how many hits does the batter have? Number of hits: _______

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ALGEBRA I TOPIC II: Algebraic Expressions & Equations

Curriculum and Instruction Page 6 of 10 Division of Mathematics, Science, and Advanced Academics

25. Solve for p . (Simplify Completely):

2m + 13p = n

p = ___________

26. Solve for d . (Simplify Completely): 3d − 7e = 9 f d = ___________

   

Page 7: ALGEBRA I TOPIC II: Algebraic Expressions & Equations …adamerritt.dadeschools.net/documents/2011-2012/TOPIC ASSESSMEN… · ALGEBRA I TOPIC II: Algebraic Expressions & Equations

ALGEBRA I TOPIC II: Algebraic Expressions & Equations

Curriculum and Instruction Page 7 of 10 Division of Mathematics, Science, and Advanced Academics

Use the following for problems 27 – 33. Stephanie had to solve the equation below. Her teacher wanted her to justify each step used to solve the equation. Choose the correct property used for each step.

= G= Step 1= Step 2= Step 3= Step 4= Step 5= Step 6= Step 7= Step 8*= Step 9

= Step 10

= Step 11*

= Step 12

= Step 13*

= Step 14

4 −10x = 5x + 2(3x − 5)4 −10x = 5x + 6x −104 −10x = 11x −10

4 −10x +10x = 11x −10 +10x4 −10x +10x = 11x +10x −10

4 + 0 = 11x +10x −104 = 21x −10

4 +10 = 21x −10 +104 +10 = 21x + 0*14 = 21x1421

= 2121x

1421

= 1x*

1421

= x

14 ÷ 721÷ 7

= x*

23= x

=Given

27. Which choice best represents the property that Stephanie used to get from the Given equation to Step 1?

4 −10x = 5x + 2(3x − 5)4 −10x = 5x + 6x −10

Given

Step 1 A. Addition Property of Equality

B. Distributive Property

C. Multiplication Property of Equality

D. Simplify by Combining Like Terms

Page 8: ALGEBRA I TOPIC II: Algebraic Expressions & Equations …adamerritt.dadeschools.net/documents/2011-2012/TOPIC ASSESSMEN… · ALGEBRA I TOPIC II: Algebraic Expressions & Equations

ALGEBRA I TOPIC II: Algebraic Expressions & Equations

Curriculum and Instruction Page 8 of 10 Division of Mathematics, Science, and Advanced Academics

28. Which choice best represents the property that Stephanie used to get from Step 2 to Step 3?

4 −10x = 11x −104 −10x +10x = 11x −10 +10x

Step 2

Step 3 A. Addition Property of Equality

B. Closure Property of Addition

C. Distributive Property

D. Multiplication Property of Equality

29. Which choice best represents the property that Stephanie used to get from Step 3 to Step 4?

4 −10x +10x = 11x −10 +10x4 −10x +10x = 11x +10x −10

Step 3

Step 4 A. Associative Property of Addition

B. Commutative Property of Addition

C. Identity Property of Addition

D. Inverse Property of Addition

30. Which choice best represents the property that Stephanie used to get from Step 4 to Step 5?

4 −10x +10x = 11x +10x −104 + 0 = 11x +10x −10

Step 4 Step 5

A. Closure Property of Addition

B. Distributive Property

C. Inverse Property of Addition

D. Inverse Property of Multiplication

31. Which choice best represents the property that Stephanie used to get from Step 6 to Step 7?

4 = 21x −104 +10 = 21x −10 +10

Step 6

Step 7 A. Addition Property of Equality

B. Closure Property of Addition

C. Distributive Property

D. Multiplication Property of Equality

Page 9: ALGEBRA I TOPIC II: Algebraic Expressions & Equations …adamerritt.dadeschools.net/documents/2011-2012/TOPIC ASSESSMEN… · ALGEBRA I TOPIC II: Algebraic Expressions & Equations

ALGEBRA I TOPIC II: Algebraic Expressions & Equations

Curriculum and Instruction Page 9 of 10 Division of Mathematics, Science, and Advanced Academics

32. Which choice best represents the property that Stephanie used to get from Step 7 to Step 8?

4 +10 = 21x −10 +104 +10 = 21x + 0

Step 7

Step 8 A. Closure Property of Addition

B. Distributive Property

C. Inverse Property of Addition

D. Inverse Property of Multiplication

33. Which choice best represents the property that Stephanie used to get from Step 9 to Step 10?

14 = 21x1421

= 2121x

Step 9

Step 10

A. Distributive Property

B. Division Property of Equality

C. Identity Property of Multiplication

D. Inverse Property of Addition

Use the following for problems 34 – 38.

Prove: For all real numbers a and b (a + b)+ (−a) = b

Steps Justification Step 1 a and b are real numbers Given Step 2 −a is a real number Property of Additive Inverse Step 3 (a + b)+ (−a) = (b + a)+ (−a) 34. ? Step 4 = b + a + (−a)[ ] 35. ? Step 5 = b + 0 36. ? Step 6 = b 37. ? Step 7 Therefore, (a + b)+ (−a) = b 38. ?

34. Which property justifies Step 3? A. Associative Property of Addition

B. Commutative Property of Addition

C. Identity Property of Addition

D. Inverse Property of Addition

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ALGEBRA I TOPIC II: Algebraic Expressions & Equations

Curriculum and Instruction Page 10 of 10 Division of Mathematics, Science, and Advanced Academics

35. Which property justifies Step 4?

A. Associative Property of Addition

B. Commutative Property of Addition

C. Identity Property of Addition

D. Inverse Property of Addition

36. Which property justifies Step 5? A. Closure Property of Addition

B. Distributive Property

C. Inverse Property of Addition

D. Inverse Property of Multiplication

37. Which property justifies Step 6? A. Closure Property of Addition

B. Distributive Property

C. Identity Property of Addition

D. Identity Property of Multiplication

38. Which property justifies Step 7? A. Identity Property of Addition

B. Reflexive Property of Equality

C. Symmetric Property of Equality

D. Transitive Property of Equality

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ALGEBRA I TOPIC II: Algebraic Expressions & Equations

Curriculum and Instruction Answer Key Page 1 of 3 Division of Mathematics, Science, and Advanced Academics

ANSWER KEY

Solution NGSSS

1. Note: k = Kathy 's age now & c = Kathy 's cat 's age now & k = 6 + c

Answers may vary. One possible equation is . MA.912.A.3.1

2.

MA.912.A.3.1

3.

MA.912.A.3.1

4. Answers may vary. One possible way to determine Kathy’s age is to first find her cat’s age then add 6 to find Kathy’s age. MA.912.A.3.1

5. A. Associative Property of Addition MA.912.A.3.1

6. Answers may vary. One possible equation is 2 + (x + 3) = 2 + (3+ x) . MA.912.A.3.2

7.

MA.912.A.3.1

8. B. 55 MA.912.A.3.1

9. The equation of the scenario would be2x + 500 = 1750 . MA.912.A.3.1

10. The cost for one month would be $625. MA.912.A.3.1

11. A. 7 MA.912.A.3.1

12.

Answers may vary. One possible explanation of work is: 2x + 5 = 4x - 32x + 8 = 4x

8 = 2xx = 4

The solution is x = 4 . Check: (4)+ 5 = 4(4)− 3

13= 13

MA.912.A.3.1

13. B. 3k2 +12k MA.912.A.3.2

14. A. 5x + 3y MA.912.A.4.2

15. C. −x + 7y MA.912.A.4.2

16. −11x + 8y MA.912.A.4.2

17. D. 2 MA.912.A.4.2

6 + (c +1) = 2(c +1)

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ALGEBRA I TOPIC II: Algebraic Expressions & Equations

Curriculum and Instruction Answer Key Page 2 of 3 Division of Mathematics, Science, and Advanced Academics

18. The difference is: −a3 + 6b2 +11b so the coefficient of a3 is:

MA.912.A.4.2

19.

MA.912.A.4.2

20. b = Ah

MA.912.A.3.3

21. l = P − 2w2

MA.912.A.3.3

22. w = 16 inches MA.912.A.3.3

23. h = an MA.912.A.3.3

24. Number of hits: 87 MA.912.A.3.3

25. p = 3(n − 2m) or p = 3n − 6m MA.912.A.3.3

26. d = 3 f + 73e or d =

139 f + 7( ) MA.912.A.3.3

27. B. Distributive Property MA.912.A.3.2

28. A. Addition Property of Equality MA.912.A.3.2

29. B. Commutative Property of Addition MA.912.A.3.2

30. C. Inverse Property of Addition MA.912.A.3.2

31. A. Addition Property of Equality MA.912.A.3.2

32. C. Inverse Property of Addition MA.912.A.3.2

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ALGEBRA I TOPIC II: Algebraic Expressions & Equations

Curriculum and Instruction Answer Key Page 3 of 3 Division of Mathematics, Science, and Advanced Academics

33. B. Division Property of Equality MA.912.A.3.2

34. B. Commutative Property of Addition MA.912.A.3.2

35. A. Associatative Property of Addition MA.912.A.3.2

36. C. Inverse Property of Addition MA.912.A.3.2

37. C. Identity Property of Addition MA.912.A.3.2

38. D. Transitive Property of Equality MA.912.A.3.2