Name



Common Core Algebra

Introduction to Algebra

Ms. Moorer

[pic]

Name_____________________

Day 1 - Evaluating Algebraic Expressions

When evaluating algebraic expressions, simply “______________________________________”

1) Evaluate [pic] when [pic] 2) Evaluate [pic] when [pic]

3) Evaluate [pic] when a)[pic] b)[pic]

4) When [pic]and [pic], evaluate

a)[pic] b)[pic] c) [pic]

5) Evaluate [pic] when [pic] and [pic]

6) Evaluate [pic] when [pic]

7) Evaluate [pic] when [pic]

Evaluate the following algebraic expressions using:

[pic]

1) [pic] 2) [pic] 3) [pic]

4) [pic] 5) [pic] 6) [pic]

7) [pic] 8) [pic] 9) [pic]

10) [pic] 11) [pic] 12) [pic]

13) [pic] 14) [pic] 15) [pic]

Homework

| |If [pic], then [pic] equals |

| |(1) -36 (3) 6 |

| |(2) -6 (4) 18 |

| |What is the value of the expression [pic] when [pic] and [pic] |

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| |If x = –4 and y = 3, what is the value of [pic]? |

| |(1) –13 (3) –31 |

| |(2) –23 (4) –85 |

| |If a = 3 and b = -1, what is the value of [pic] |

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| |If [pic] and [pic] what is the value of [pic] |

| |(1) -20 (3) 8 |

| |(2) -2 (4) 16 |

| | |

| |If x = 4 and y = -2, the value of [pic] is |

| |(1) 32 (3) -4 |

| |(2) 8 (4) -8 |

| |What is the value of [pic], if x = 4 and y = –3? |

| |(1) –2 (3) 10 |

| |(2) 2 (4) 14 |

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| |Brett was given the problem: “Evaluate [pic] when x = 3.” Brett wrote that the answer was 41. Was Brett correct? |

| |Explain your answer. |

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Day 2 - Real Number Properties

|Property |Meaning |Examples |

|Additive Identity Property or identity element |When zero is added to or subtracted from |a + 0 = a |

|of addition property |any number, the number remains unchanged. |18 – 0 = 18 |

| | |0 +10 = 10 |

| | |12 – 0 = 12 |

|Multiplicative Identity Property or identity |Any number multiplied by 1 remains |a [pic] 1 = a |

|element of multiplication property |unchanged |1 [pic] 5 = 5 |

| | |-2 [pic] 1 = -2 |

| | |[pic][pic] 1 = [pic] |

|Additive Inverse Property |The sum of a number and its additive |a + -a = 0 |

| |inverse (also called its opposite) is |-2 + 2 = 0 |

| |zero. |[pic] + -[pic] = 0 |

|Multiplicative Inverse Property |The product of any number and its |a [pic] [pic] = 1 |

| |multiplicative inverse (or its reciprocal)|[pic] [pic] 2 = 1 |

| |is 1. | |

|Multiplicative Property of Zero |The product of zero and any number is |a [pic] 0 = 0 |

| |always zero. |0 [pic] 2 = 0 |

| | |-3(0) = 0 |

|Reflexive Property |Any quantity is equal to itself |a = a |

| | |5 = 5 |

| | |4 + 2 = 4 + 2 |

|Symmetric Property |If one quantity equals a second quantity, |If a = b, then b = a |

| |then the second quantity equals the first.|If 9 = 6 + 3, then 6 + 3 = 9 |

|Transitive Property |If one quantity equals a second quantity |If a = b, b = c, then a = c. |

| |and the second quantity equals a third |If 5 + 7 = 8 + 4, |

| |quantity, then the first quantity equals |8 + 4 = 12, then |

| |the third quantity. |5 + 7 = 12 |

|Substitution Property |A quantity may be subsitut4ed for its |If a = b, then a maybe replaced by b in any |

| |equal in any expression. |expression. |

| | |If n = 15, then 3n = 3 [pic] 15 |

|Distributive Property |Multiplication can be distributed over |A(b + c) = a(b) + a(c) |

| |addition or subtraction. |2(3 + 5) = 2(3) + 2(5) |

| | |2(5 – 1) = 2(5) – 2(1)[pic] |

|Commutative Property of |The order of the numbers does not affect |a + b = b + a |

|addition or multiplication |the sum or the product. |2 + 3 = 3 + 2 |

| | |3(11) = 11(3) |

| | |4[pic]6 = 6[pic]4 |

|Associative Property of addition or |The way the numbers are paired does NOT |(a + b) + c = a + (b + c) |

|multiplication |affect the sum or the product. |(2 + 3) + 4 = 2 + (3 + 4) |

| | |(2 [pic] 3)4 = 2(3[pic]4) |

Number Properties

Which property is displayed by the given equation?

1) [pic] 2) [pic]

3) [pic] 4) [pic]

5) [pic] 6) [pic]

What is the additive inverse (opposite) and multiplicative inverse (reciprocal) of each number?

7) 14 AI: MI:

8) [pic] AI: MI:

9) [pic] AI: MI:

10) 2.5 AI: MI:

Replace the ? with the proper number to make the sentence true, and Name the property illustrated.

11) 8 + 6 = 6 + ? 12) [pic]

13) [pic] 14) [pic]

15) [pic] 16) [pic]

17) [pic] 18) [pic]

19) [pic] 20) [pic]

Homework

Give an example of the property named.

1. additive identity: 2. substitution property:

3. symmetric property: 4. multiplicative identity property:

5. reflexive property: 6. transitive property:

7. multiplicative property of zero: 8. additive inverse property:

9. multiplicative inverse property: 10. zero product property:

Name the property illustrated by each statement.

1. 5 · 1 = 5 2. If a + b = 9, then 9 = a + b 3. (3 + 5) + 4 = 8 + 4

4. 6 · 0 = 0 5. a + 0 = a 6. 2 · ½ = 1

7. 5x = 5x 8. If xy = 0, then x = 0 and/or y = 0 9. 7 + (-7) = 0

11. 5( 2 + 4) = 5(6) 12. 2x + 7 = 2x + 7 13. abc = 1abc

14. If 8 = x, then x = 8 15. 9 + 0 = 9 16. ¾ · 0 = 0

17. If 10 = 6 + 4 and 6+ 4 = 12 – 2, then 10 = 12 – 2

Evaluate the expression and name the property used for each step.

18. 9(8 + 2) – 45 · 2 19. 12 + 3(42 – 16)

Day 3 - Verbal Phrases into Symbols

Steps:

I) Think of a similar problem in arthimetic

II) Write an expression for the arithmetic problem, using numbers.

III) Write a similar expression for the problem, using letters or variables.

Represent each phrase by an algebraic expression:

1) a distance that is 20 meters shorter than x meters

2) a bill for n baseball caps, each costing d dollars

3) a weight that is 40 pounds heavier than p pounds

4) an amount of money that is twice d dollars

5) the number of baseball cards, if b cards are added to a collection of 100 cards

6) Hector’s height, if he was h inches tall before he grew 2 inches

7) the total cost of n envelops that cost $0.39 each

8) the cost of one pen, if 12 pens cost d dollars

9) Mark paycheck, if he gets paid n dollars a day for 4 days plus a $30 bonus

Create an algebraic expression to help solve the following word problems:

10) Brianna paid 17 dollars for batteries and film for her camera. If the batteries cost x dollars, express the cost of the film in terms of x.

11) The cost of a mountain bike is 5 times the cost of a skateboard. If the skateboard costs c dollars, represent the cost of the mountain bike.

12) The number of kilometers traveled by a bus is represented by k. If a train traveled 200 kilometers farther than the bus, represent the number of kilometers traveled by the train.

13) The length of a rectangle is represented by L. If the width is one-half of its length, represent its width.

14) A ballpoint pen sells for 27 cents. Represent the cost of p pens, in dollars.

15) A man bought a stock for c dollars and sold it for a profit of 25 dollars. Represent the amount for which he sold it at.

16) If a car travels for 5 hours at an average rate of k kilometers per hour, represent the distance traveled.

17) Represent the cost of t feet of lumber that sells for g cents a foot.

18) If a car traveled 550 miles in h hours, represent how many miles the car traveled per hour.

19) a) Represent the total number of days in w weeks and 5 days

b) Represent the total number of days in w weeks and d days

20) A theater has m rows of seats with c seats in each row. If a show at the theater sells out 5 performances, represent the number of people to see the show.

Homework: Variables and Expressions

I. Indicate with math symbols what operations are being described by the given word(s). Use [pic]

1. sum _____ 2. product _______ 3. decreased by ______

4. quotient _______ 5. increased by _____ 6. difference _________

7. more than ______ 8. less than _______

9. twice something ______

II. Write a verbal expression for the algebraic expression.

10. ab 11. x + 7

12. 2x 13. m3

14. x – 6 15. 8y2

16. [pic] 17. ½ (x + y)

18. 3x – 4 19. 5(a – b)

III. Write an algebraic expression to the given verbal expression.

20. eight less than a number 21. a number increased by seven

22. the quotient of m and n 23. a number squared

24. nine times a number 25. a number decreased by three

26. seven more than the cube of a number 27. one-half the product of x and y

28. the product of twice a and b 29. twice the product of a and b

Day 4 - Solving Equations

To solve an equation means to isolate the variable on one side of the equation. You can do this by using the addition/subtraction property of equality.

Solve and check each equation.

1. w + 14 = -8 2. y + (-10) = 6 3. -11 = a + 8

4. -13 + h = -5 5. -2.3 = x + (-1.1) 6. -7 = -16 - k

7. m - (-13) = 37 8. 6x + 7 = 8x – 13

9. [pic] 10. 7b – 6.5 = -2.3b + 8.3

11. [pic] 12. -7(x – 3) = -4

13. 28 – 2.2y = 11.6y + 262.6 14. 7 – 3x = x – 4(2 + x)

Extra Practice

Directions: Solve each equation for the given variable

1. 4m – 10 = 38 2. 2a – 8 – 5a – 2 = -70

3. -4(t – 9) = 4 4. 6h + 3 = h – 32

5. -5 + 3x = -5x + 11 6. [pic]

7 What is the additive inverse of [pic]?

|1) |[pic] |

|2) |[pic] |

|3) |[pic] |

|4) |[pic] |

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8 What is the additive inverse of the expression [pic]?

|1) |[pic] |

|2) |[pic] |

|3) |[pic] |

9 Which property is illustrated by the equation [pic]?

|1) |commutative property of addition |

|2) |distributive property |

|3) |additive inverse property |

|4) |additive identity property |

10 Which property is represented by the statement [pic]?

|1) |commutative |

|2) |distributive |

|3) |associative |

|4) |identity |

| | |

11. A method for solving [pic] is shown below. Identify the property used to obtain each of the two indicated steps.

[pic]

12. The value of the expression [pic] when [pic] and [pic] is

|1) |[pic] |

|2) |10 |

|3) |[pic] |

|4) |4 |

13. If [pic] and [pic], what is the value of [pic]?

[pic][pic]

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