Introduction to Variables and Algebraic...

Mini-Lecture 2.1 Introduction to Variables and Algebraic Expressions

Learning Objectives:

1. Evaluate algebraic expressions given replacement values. 2. Translate phrases into variable expressions.

Addition (+) Subtraction (-) Multiplication (•) Division (÷) Sum, plus, added to, more than, increased by, total

Difference, minus, subtract, less than, decreased by, less

Product, times, multiply, multiply by, of, double, triple

Quotient, divide, shared equally among, divided by, divided into

3. Key Vocabulary: variable, algebra, algebraic expression, expression, evaluating the expression.

Examples:

1. Evaluate each expression for x = 12 , y = 4 , and z = 3

a) x y z− + b) ( )x y z− + c) ( )5 3 7x + d) 2 3xy z−

e) 2 4x y− f) g) 3 2y − x 34 3x yz

− h) 32

2y z x−⎛ ⎞

⎜ ⎟⎝ ⎠

2. Write each phrase as a variable expression. Use x to represent “a number.”

a) The sum of a number and eleven b) Fifteen added to a number c) The difference between a number and three hundred d) A number subtracted from forty-two e) The product of sixteen and a number f) A number times thirteen g) The quotient of thirty and a number h) Seven divided by a number i) The quotient of eighteen and a number, decreased by two

Teaching Notes:

• Remind students that order of operations apply with variables. • Many students will have difficulty translating a phrase into an algebraic expression. • Refer students to textbook for Translating Phrases into Variable Expressions Chart.

Answers: 1a) 11; 1b) 5; 1c) 215; 1d) 87; 1e) 128; 1f) 40; 1g) 5; 1h) 216; 2a) x=11; 2b) 15+x; 2c) 300-x;

2d) 42-x; 2e) 16x; 2f) 13x; 2g) 30/x; 2h) 7/x; 2i) 18 2x

−

M-10 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Mini-Lecture 2.2 Introduction to Integers


1. Represent real-life situations with integers. 2. Graph integers on a number line. 3. Compare integers. 4. Find the absolute value of a number. 5. Find the opposite of a number. 6. Read bar graphs containing integers. 7. Key Vocabulary: positive numbers, negative numbers, signed numbers, integers, is less than, is

greater than, opposite, absolute value. Examples:

1. Represent each quantity by an integer.

a) A scuba diver is swimming 25 feet below sea level. b) The record high temperature for the town is 113°F. c) The number of televisions sold reflected a 35 percent loss from the previous year.

2. Graph each integer in the list on the same number line.

a) 1, 3, 5, 6 b) 2, -2, 3, -3 c) 4, 0, -2, -5 d) 0, -1, -2, -5

3. Insert < or > between each pair of integers to make a true statement.

a) 5 ____ 10 b) 0 ____ 3− c) 42 ____ 38− − d) 22 ____ 22−

4. Simplify.

a) 2 b) 12− c) 3− d) 14−

e) 45− f) 103− − g) x− if x = -25 h) x if x = 8−

5. Find the opposite of each integer.

a) 9 b) c) 0 d) 15− 16−

6. The bar graph shows the January temperatures for four days in Boston..

a) Which day was the coldest? b) Which day was the warmest?

-10-505

10

Mon. Tues. Wed. Thurs.

Teaching Notes:

• Many students will confuse absolute value and opposite. • Encourage students to list everyday situation where negative numbers are used.

Answers: 1a) -25; 1b) +113; 1c) –35; 2a) 2b) 2c)

M-11

2d) ; 3a) <; 3b) >; 3c) <; 3d) <; 4a) 2, 4b) 12; 4c) 3; 4d) -14; 4e) -45; 4f) -103; 4g) 25; 4h)8; 5a) -9; 5b) 15; 5c) 0; 5d) 16; 6a) Wed.; 6b) Thurs.

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Mini-Lecture 2.3 Adding Integers


1. Add integers. 2. Evaluate an algebraic expression by adding. 3. Solve problems by adding integers.

Examples:

1. Add. a) b) c) 23 12+ 23 ( 17)− + − 11 ( 2)− + − d) 21 ( 13)− + − e) f) g) 6 ( 8)+ − 3 5− + 74 27− + h) 51 (24)− + i) j) k) 48 ( 13)− + − 79 97− + 6 ( 54)+ − l) 4 ( 24)− + − m) 2 n) 14 o) 3 ( 19) ( 8)+ − + − 25 ( 16)+ + − 25 ( 4) ( 2) ( 6)− + − + − + −

2. Evaluate x y+ for the given replacement values.

a) and b) 5x = − 14y = 33x = − and 27y = − c) 43x = − and 38y =

3. Solve.

a) Find the sum of and 25. b) Find the sum of 7− 52, 13, 82and− − c) During a storm in Anchorage Alaska, the temperature was 10°F at Noon. At 1 p.m., the temperature had dropped 7°. At 2 p.m., the temperature dropped another 5°; and finally, at 3 p.m., the temperature had dropped an additional 9°. Use positive and negative numbers to represent his situation. Then find the present temperature.

Teaching Notes:

• Some students need to see adding integers done on a number line first. • Many students have a better understanding if they think of depositing and withdrawing money from a

bank account. • Refer students to the rules for adding signed numbers in the textbook. Answers: 1a) 35; 1b) –40; 1c) –13; 1d) –34; 1e) –2; 1f) 2; 1g) –47; 1h) –27; 1i) –21; 1j) 18; 1k) –8; 1l –28; 1m) –4; 1n) 23; 1o) –37; 2a) 9; 2b) –60; 2c) –5; 3a) 18; 3b) –121; 3c) -11°.


Mini-Lecture 2.4 Subtracting Integers


1. Subtract integers. 2. Add and subtract integers. 3. Evaluate an algebraic expression by subtracting. 4. Solve problems by subtracting integers. 5. Key Vocabulary: additive inverse.

Examples:

1. Subtract.

a) b) c) 49 ( 2)− − − 14 ( 2)− − − ( 3)− − d) 20 20−

e) f) g) 2 5− 2 12− − 150 410− − h) 147 ( 85)− − −

2. Simplify.

a) b) c) 6 20 15+ − 1 11 12− − − 1 20 10− − + d) 16 11 18 ( 4)− + − + −

3. Evaluate x y− for the given replacement values. a) and b) 8x2x = − 8y = − = and 32y =− c) and d) 3x9x = − 9y = − = and 15y = −

4. Solve.

a) Amy has $545 in her checking account. She writes a check for $257, makes a deposit of $75, and then writes another check for $409. Find the balance in her account. (Write the amount as an integer. b) The city of Manchester has an elevation of 13,005 feet above sea level while the city of Catherine has an elevation of 17,532 feet below sea level. Find the difference in elevation between those two cities. c) The temperature on a January morning in Worcester is 5 F− ° at 2 a.m. If the temperature drops 4° by 3 a.m., rise 6° by 4 a.m., and then drops 8° by 5 a.m., find the temperature by 8 a.m.

Teaching Notes:

• Many students find subtracting signed numbers difficult at first. • Some students like to see subtracting signed numbers on a number line. • Many students make errors when evaluating x – y when y is a negative number. Encourage students

to make a direct substitution first so they do not forget to write the subtraction symbol. Answers: 1a) –7; 1b) –12; 1c) 7; 1d) 0; 1e) –3; 1f) –14; 1g) –560; 1h) –62; 2a) 11; 2b) –24; 2c) –11; 2d) –27; 3a) 6; 3b) 40; 3c) 0; 3d) 18; 4a) -$46; 4b) 4527 ft.; 4c) -11°F.

M-13Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Mini-Lecture 2.5 Multiplying and Dividing Integers


1. Multiply integers. 2. Divide integers. 3. Evaluate an algebraic expression by multiplying or dividing. 4. Solve problems by multiplying or dividing integers.

Examples:

1. Multiply.

a) b) c) 7( 6)− 4(10)− 20(13)− d) 10( 19)− − e) f) ( g) ( 4( 4)( 3)(6)− − 50)(0)( 5)(8)− − )( 5)( 4)( 3)− − − − h) ( 2)(3)( 1)( 4)(2)− − − i) j) ( k) 24− )33− 33− l) ( )28−

2. Find each quotient.

a) b) 36 c) 21 7÷ ( 6)÷ −486

− d) 170

−

3. Evaluate xy and also xy

for the given replacement values.

a) b) 8 4x and y= = − 30 10x and y= − = − − c) 0 16x and y= =

4. Solve.

a) Find the product of and . 13− 5− b) Find the quotient of 63 and . 9− c) Better Electric Co. marked $15 off the price of each microwave in stock. If there are 57 microwaves in stock, write the total reduction in price of all microwaves as an integer. d) During a cold front in Canada the temperature dropped 4°F each hour for 7 hours. Express the total drop in temperature as an integer.

Teaching Notes:

• Some students need a review of basic multiplication and division facts before they begin working with integers.

• Some students mix up the rules for addition of integers and the rules for multiplication/division of integers.

• Many students have a hard time understanding the difference between ( )223 3and− − Answers:1a) -42; 1b) -40; 1c) -260; 1d) -190; 1e) 72; 1f) 0; 1g) 240; 1h) -48; 1i) -16; 1j) -27; 1k) -27; 1l) 64; 2a) 3; 2b) -6; 2c) -8; 2d) undefined; 3a) -2; 3b) 3; 3c) 0; 4a) 65; 4b) -7; 4c) -$855; 4d) -28°F.


Mini-Lecture 2.6 Order of Operations


1. Simplify expressions by using the order of operations. 2. Evaluate an algebraic expression.

Examples:

1. Simplify.

a) b) 2 5 6− + i 2 5(5 8)− − − c) 2( 5)(7 3) 7− − − d) 80 e) f) ( 8) 15÷ − − 33 8(2− ) ( )28 2 7 2 3− − +

g) h) i) 28 2(6) 45− + ÷ 5 23( 2) (8 10)− + − ( )( )21 7 15 5⎡ ⎤÷ − ÷ −⎣ ⎦i

j) 8( 2) 4 385 5

− − +− ÷

k) [ ][ ]36 ( 4) 1

2 ( 2)− ÷ − −

− − l)

[ ]20( 1) ( 5)( 3)2 12 ( 3 3)

− − − −− ÷ − −

2. Evaluate each expression for 3, 6, 1x y and z= − = = − .

a) x y z+ + b) 2 3y z x− + c) 2x y z− +

d) 82

xy

e) 25y x− f) 3x yz+

Teaching Notes:

• Many students confuse the addition/subtraction rules with the multiplication/division rules when working with many operations in one expression.

• Encourage students to perform one operation at a time. • Refer students to Order of Operations in the textbook.

Answers: 1a) 28; 1b) 13; 1c) -47; 1d) -25; 1e) 11; 1f) 5; 1g) 61; 1h) -2; 1i) 1; 1j) 1; 1k) 2; 1l) –9’ 2a) 2; 2b) 12; 2c) 2; 2d) -2; 2e) 21; 2f) -33

M-15Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Chapter 2 PreTest – Form A Find the sum. 1. 6 ( 18)− + − 2. 21 45− + 3. 5 ( 16)+ − Find the difference. 4. 14 15− − 5. 10 ( 8)− − − 6. 16 16− − Find the product. 7. ( )5 14− − 8. 13(13)− 9. 0( 27)− Find the quotient. 10. ( )48 6− ÷ −

11. 186

12. ( )72 8÷ −

Name: ____________ Date: _____________ 1. _____________ 2. _____________ 3. _____________ 4. _____________ 5. _____________ 6. _____________ 7. _____________ 8. _____________ 9. _____________ 10. _____________ 11. _____________ 12. _____________

T-17Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Chapter 2 PreTest – Form A (cont’d) Simplify. 13. ( ) ( )2 43 7 8 8− ÷ −

14. 28 5(4) 21− + ÷3

15. [ ]

12( 1) ( 8)( 7)2 12 ( 3 3)

− − − −− ÷ − −

Evaluate. 16. Evaluate: 2 x y− + + for and 20x = − 14y =

17. Evaluate: ( )2

2

a b+

− for and 15a = 3b =

A football team had control of the ball for the first six plays in a game. The chart shows the yards gained or lost in each of those plays. Play # 1 2 3 4 5 6 Yards gained (+) or lost (-) +2 +15 -2 -3 +20 -5

18. What was the net gain or loss considering the first three plays? 19. Which play had the most loss of yards? 20. What was the total net gain or loss for all listed plays?

Name: ____________ 13. _____________ 14. _____________ 15. _____________ 16. _____________ 17. _____________ 18. _____________ 19. _____________ 20. _____________

T-18 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Chapter 2 PreTest – Form B Find the sum. 1. 5 ( 11)− + − 2. 4 9− + 3. 22 ( 5)− + − Find the difference. 4. 9 14− − 5. 15 ( 13)− − − 6. 14 14− − Find the product. 7. 12( 3)− − 8. 11(4)− 9. 14(0)− Find the quotient. 10. 45 ( 5)− ÷ −

11. 404−

12. ( )20 4÷ −

Name: ____________ Date: _____________ 1. _____________ 2. _____________ 3. _____________ 4. _____________ 5. _____________ 6. _____________ 7. _____________ 8. _____________ 9. _____________ 10. _____________ 11. _____________ 12. _____________


Chapter 2 PreTest – Form B (cont’d) Simplify. 13. ( ) (2 518 20 11 11− ÷ − ) 14. 25 2(3) 24 4− + ÷

15. ( )( )( )

14( 1) 6 52 20 5 5

− − − −

⎡ ⎤− ÷ − −⎣ ⎦

Evaluate. 16. 9 x y− + + for and 19x = − 12y =

17. ( )2

7

a b+

− for and 33a = 3b =

Play # 1 2 3 4 5 6 Yards gained (+) or lost (-) +4 +16 -7 -10 +20 -8

A football team had control of the ball for the first six plays in a game. The chart shows the yards gained or lost in each of those plays. 18. What was the net gain or loss considering the first three plays? 19. Which play had the most loss of yards? 20. What was the total net gain or loss for all listed plays?

Name: ____________ 13. _____________ 14. _____________ 15. _____________ 16. _____________ 17. _____________ 18. _____________ 19. _____________ 20. _____________


Additional Exercises 2.1 Evaluate each expression for x = 3, y = 5, and z = 2. 1. 5 2x+ 2. 8 3xy z− 3. y z x− + 4. 5 3y z− 5. 3 4y x− 6. ( )10 y z− + 7. ( )4z y x+ −

8. 3 3y zx+

9. ( )22 3x z+ 10. ( )2xy x y z+ − Write each phrase as a variable expression. Use x to represent “a number.” 11. The sum of a number and fourteen. 12. The total of twenty and a number. 13. Twenty-five decreased by a number. 14. A number less fourteen. 15. The product of three and a number.

Name: ____________ Date: _____________ 1. _____________ 2. _____________ 3. _____________ 4. _____________ 5. _____________ 6. _____________ 7. _____________ 8. _____________ 9. _____________ 10. _____________ 11. _____________ 12. _____________ 13. _____________ 14. _____________ 15. _____________

E-17Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

E-18

Additional Exercises 2.1 (con’t) 16. The product of a number and five. 17. The quotient of a number and thirty-three 18. Twenty-two divided by a number. 19. The sum of eight and a number added to the product of six and

the number. 20. The quotient of thirty and a number, decreased by eight.

Name: ____________ 16. _____________ 17._____________ 18._____________ 19. _____________ 20. _____________


Additional Exercises 2.2 Represent each quantity by an integer. 1. A scuba diver is swimming 57 feet below the surface of the

water in the Atlantic Ocean. 2. For the fourth quarter of the fiscal year, Trenchway

Corporation reported a net gain of $2.57 per share. Graph each integer in the list on the same number line. 3. 2, 4, 5, 6− − 4. 1, 1, 0, 3, 3− − Insert < or > between each pair of integers to make a true statement.. 5. 2 ____ 3− 6. 0 ____ 10− 7. 23____ 15− − 8. 8____ 8− Simplify. 9. 8 10. 20− 11. 18− − 12. 6− 13. x− if x = -7

Name: ____________ Date: _____________ 1. _____________ 2. _____________ 3. _____________ 4. _____________ 5. _____________ 6. _____________ 7. _____________ 8. _____________ 9. _____________ 10. _____________ 11. _____________ 12. _____________ 13. _____________


Additional Exercises 2.2 (con’t) Find the opposite of each integer. 14. 23 15. 103− 16. 81− 17. 100 Alicia started a business making fancy sandals. The bar graph below tracks her net income for five weeks.

-300-200-100

0100200300400500

Wk 1 Wk 2 Wk 3 Wk 4 Wk 5

18. Write the net income for Week 3 as an integer. 19. Which week did Alicia have the greatest net income. 20. Which week did Alicia lose the most amount of money?

Name: ____________ 14. _____________ 15. _____________ 16. _____________ 17. _____________ 18. _____________ 19. _____________ 20. _____________

E-20 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Additional Exercises 2.3 Add using a number line. 1. 3 ( 4)− + − Add. 2. 3 ( 19)− + − 3. 34 14+ 4. 6 2− + 5. 35 ( 18)− + − 6. 44 0− + 7. 77 ( 93)+ − 8. 10 ( 12)− + − 9. 15 ( 17)− + − 10. ( 7 5) 62− + 11. 40 40− + 12. 5 1 4 ( 24)+ + − 13. ( 13) 4 ( 3)− + + − 14. 20 5 ( 18)− + + −

Name: ____________ Date: _____________ 1. _____________ 2. _____________ 3. _____________ 4. _____________ 5. _____________ 6. _____________ 7. _____________ 8. _____________ 9. _____________ 10. _____________ 11. _____________ 12. _____________ 13. _____________ 14. _____________


Additional Exercises 2.3 (con’t) Add. 15. 22 ( 10) 13 ( 7)+ − + + − Evaluate x y+ for the given replacement values. 16. 3 5x and y=− = 17. 10 30x and y=− =− 18. 15 27x and y= =− Solve. 19. Find the sum of 38, 5, 16and− − 20. Suppose a deep-sea diver dives from the surface to 205 feet

below the surface. He then dives down another 38 feet. Use positive and negative numbers to represent this situation. Then find the diver’s present depth.

Name: ____________ 15. _____________ 16. _____________ 17. _____________ 18. _____________ 19. _____________ 20. _____________


Additional Exercises 2.4 Subtract 1. 4 9− 2. 10 13− − 3. 11 ( 6)− − − 4. 9 ( 6)− − 5. 19 19− 6. 0 4− 7. 12 12− − 8. 110 375− − Solve. 9. Subtract 16 from 22− 10. Subtract from 3− 15− Simplify. 11. 8 1 4 6− + 12. 1 1 5 3− − 13. 4 1 0 5− +

Name: ____________ Date: _____________ 1. ____________ 2. ____________ 3. ____________ 4. ____________ 5. ____________ 6. ____________ 7. ____________ 8. ____________ 9. ____________ 10. ____________ 11. ____________ 12. ____________ 13. ____________


Additional Exercises 2.4 (con’t) Simplify. 14. 2 6 18− + − 15. 4 1 ( 12) 4− + − − − Evaluate x y− for the given replacement values. 16. 2 7x and y= − = 17. 13 18x and y= =− 18. 5 5x and y=− =− Solve. 19. The temperature on a February morning is 8 F− ° at 8 a.m. If

the temperature drops 2°F by 9 a.m., rises 10°F by 10 a.m., and then drops 5°F by 11 a.m., find the temperature by 11 a.m.

20. Alicia has $289 in her checking account. She writes a check

for $56, makes a deposit for $98, and then writes another check for $248. Find the amount left in her account. (Write the amount as an integer.)

Name: ____________ 14. _____________ 15. _____________ 16. _____________ 17. _____________ 18. _____________ 19. _____________ 20. _____________


Additional Exercises 2.5 Multiply. 1. 3( 4)− − 2. –5(10) 3. 3( 16)− 4. 13(8)− 5. ( 50)(0)( 4)(8)− − 6. ( 2)(5)( 1)( 4)(2)− − − Evaluate. 7. 29− 8. ( )32− Find each quotient. 9. 42 ( 7)÷ − 10. 24 6− ÷

11. 1020

−

12. 7010−−

13. 968−

Name: ____________ Date: _____________ 1. _____________ 2. _____________ 3. _____________ 4. _____________ 5. _____________ 6. _____________ 7. _____________ 8. _____________ 9. _____________ 10. _____________ 11. _____________ 12. _____________ 13. _____________


Additional Exercises 2.5 (con’t) Evaluate ab for the given replacement values.

E-26

−

14. 12 4a and b=− =− 15. 192 12a and b= =

Evaluate xy

for the given replacement values.

16. 49 7x and y=− = − 17. 0 1x and y= =− 21 Solve. 18. Find the quotient of and 9. 72− 19. Find the product of and 16− 8− 20. During a cold front in Northern New Hampshire the

temperature dropped 4 F° each hour for five hours. Represent this drop as a product of signed numbers and find the total drop in temperature.

Name: ____________ 14. _____________ 15. _____________ 16. _____________ 17. _____________ 18. _____________ 19. _____________ 20. _____________


Additional Exercises 2.6 Simplify. 1. 43− 2. ( )25− 3. 2 4 7− + i 4. 8 2(3 6)+ − 5. 2( 4)(8 5) 14− − − 6. 70 ( 7) 18÷ − −

E-27

)

3

7. 34 7(4− 8. 27 2(19 4 ) 8− − + 9. 27 2(4) 27− + ÷ 10. 25( 4) (8 10)− + − 11. ( )42(4 8) 5 4− ÷ −

12. ( )( )18 6 6 2⎡ ⎤− ÷ − ÷ −⎣ ⎦i

13. [ ][ ]

40 ( 8) 11 ( 1)÷ − +− −

Name: ____________ Date: _____________ 1. _____________ 2. _____________ 3. _____________ 4. _____________ 5. _____________ 6. _____________ 7. _____________ 8. _____________ 9. _____________ 10. _____________ 11. _____________ 12. _____________ 13. _____________


Additional Exercises 2.6

14. [ ]

23 9( 4)

5 ( 14)

⎡ ⎤+ −⎣ ⎦+ −

15. [ ][ ]9 3( 1)11 (15)− −−

16. 8( 2) 5 645 3

− − +− ÷

17. [ ]

16( 1) ( 8)( 7)2 20 ( 5 5)

− − − −− ÷ − −

Evaluate each expression for 5, 3, 2x y and z= − = = − 18. x y z+ + 19. 2 5 4x y z− +

20. 23 5x zx−

Name: ____________ 14. _____________ 15. _____________ 16. _____________ 17. _____________ 18. _____________ 19. _____________ 20. _____________


A-3

Activity 2-A Integers and Introduction to Variables

Writing with Signed Numbers Write a word problem to accompany the given mathematical expression. Be sure to include the correct answer in your problem. Answers will vary. The first one is done for you! 1. 15 ( 12) Answer: Alicia ate 15 crackers with 12 calories in each. How many calories did Alicia eat. (180 calories) 2. $325.00 + $209.27 + (-$137.89) + (-$53.22) + ($12.00) + (-$317.16)

3. $140.72

8−

4. 8 12 4 6 9 3− ° + ° − ° − ° − ° + ° 5. 3(-$25.99) + 2(-$15.99) + 12($4.99)


Activity 2-B Integers and Introduction to Variables

How Far is it Anyways? Towns A, B, C, O, M, and N are situated on an interstate highway that is a straight line. Locations of all the towns A, B, C, M, and N are compared with respect to their distances from the Town O. The distances of towns to the right of Town O are measured by positive numbers and the distances of the towns on the left of Town O are measured by negative numbers. The distances of the different towns from Town O are as follows:

Town A: -43 miles

Town B: 45 miles

Town C: -12 miles

Town M: 29 miles

Town N: -34 miles

Town O

1. Plot each town on the line the correct distance from Town O.

2. Which town is the closest to Town O?

3. Which town is closest to Town A?

4. Which town is closest to Town M?

5. How far is it from Town C to Town M? Write an equation describing this distance.

A-4 Copyright © 2007 Pearson Education, Inc., publishing as Pearson Prentice Hall

Chapter 2 Test – Form A Fill in the blank. 1. The opposite of is ________. ( 16)− − Simplify each expression. 2. 15 ( 19)− + − 3. 14 ( 1)− − − 4. 7( 6)− −

5. 909

−−

6. 27 42− + 7. 21 ( 32)+ − 8. 18 18− − 9. ( )( )16 9− 10. 82 ( 63)+ − 11. 9 ( 9)− − 12. 14 4 6− − +

Name: ____________ Date: _____________ 1. _____________ 2. _____________ 3. _____________ 4. _____________ 5. _____________ 6. _____________ 7. _____________ 8. _____________ 9. _____________ 10. _____________ 11. _____________ 12. _____________


Chapter 2 Test – Form A (cont’d) Simplify each expression. 13. ( )( )( )( )25 0 8 2− − 14. 3 ( 8) ( 16) 11+ − − − +

15. 6( 4) 5 960 3

− − +− ÷

16. ( )

20( 1) ( 4)( 5)2 8 2 2

− − − −⎡ ⎤− ÷ − −⎣ ⎦

Evaluate.

17. xy

for and 15x = − 3y =

18. 9x y− for and 2x = 4y =− Solve. 19. In a particular card game, it is possible to have a negative

score. If Ally’s score is 19, what is her new score if she loses 24 points.

20. A plane flying at an altitude of 30,000 feet descends 1000 feet

three times before ascending 2000 feet. What is the current altitude of the plane?

Name: ____________ 13. _____________ 14. _____________ 15. _____________ 16. _____________ 17. _____________ 18. _____________ 19. _____________ 20. _____________


Chapter 2 Test – Form B Fill in the blank. 1. The opposite of is _______. ( 22)− − Simplify each expression. 2. 6 ( 22)− + − 3. 14 ( 10)− − − 4. 8( 10)− −

5. 549

−−

6. 35 8− + 7. 4 99− + 8. 17 17− − 9. 3(16)− 10. 69 ( 27)+ − 11. 8 ( 8)− − 12. 15 10 2+ −

Name: ____________ Date: _____________ 1. _____________ 2. _____________ 3. _____________ 4. _____________ 5. _____________ 6. _____________ 7. _____________ 8. _____________ 9. _____________ 10. _____________ 11. _____________ 12. _____________


Chapter 2 Test – Form B (cont’d) Simplify each expression. 13. ( 29)(0)( 2)(5)− − 14. 5 ( 20) 4 ( 1)+ − − + −

15. 8( 6) 2 9205 5

− − +− ÷

16. [ ]

20( 1) ( 8)( 5)2 8 ( 2 2)− − − −− ÷ − −

Evaluate.

17. xy


18. 5x y+ for and 7x = 5y =− Solve. 19. In a card game, it is possible to have a negative score. If

Stacey’s score is 22, what is her new score if she loses 27 points?


five times before ascending 2000 feet. What is the current altitude of the plane?

Name: ____________ 13. _____________ 14. _____________ 15. _____________ 16. _____________ 17. _____________ 18. _____________ 19. _____________ 20. _____________


Chapter 2 Test – Form C Fill in the blank. 1. The opposite of is _______. ( 20)− − Simplify each expression. 2. 13 ( 5)− + − 3. 15 ( 5)− − − 4. 9( 4)− −

5. 305

−−

6. 3 19− + 7. 65 ( 83)+ − 8. 13 13− − 9. 13(8)− 10. 99 ( 38)+ − 11. 14 ( 14)− − 12. 8 3 6− −

Name: ____________ Date: _____________ 1. _____________ 2. _____________ 3. _____________ 4. _____________ 5. _____________ 6. _____________ 7. _____________ 8. _____________ 9. _____________ 10. _____________ 11. _____________ 12. _____________


Chapter 2 Test – Form C (cont’d) Simplify each expression. 13. ( 37)(0)( 4)(10)− − 14. 1 9 ( 15) ( 6) 4+ − − − +

15. 8( 2) 4 385 5

− − +− ÷

16. [ ]

20( 1) ( 8)( 7)2 12 ( 3 3)

− − − −− ÷ − −

Evaluate.

17. xy

for and 30x =− 6y =

18. 3x y+ for and 7x = 2y= − Solve. 19. A plane flying at an altitude of 30,000 feet descends 1000 feet

five times before ascending 2000 feet. What is the current altitude of the plane?

20. In a card game, it is possible to have a negative score. If

Amy’s score is 22, what is her new score if she loses 31 points?

Name: ____________ 13. _____________ 14. _____________ 15. _____________ 16. _____________ 17. _____________ 18. _____________ 19. _____________ 20. _____________


Chapter 2 Test – Form D Fill in the blank. 1. The opposite of ( )29− − = __________. Simplify each expression. 2. 12 ( 11)− + − 3. 15 ( 21)− − − 4. 8( 6)− −

5. 729

−−

6. 45 36− + 7. 51 (30)− + 8. 10 10− − 9. 13(17)− 10. 22 ( 28)+ − 11. 3 ( 3)− − 12. 10 14 12− − −

Name: ____________ Date: _____________ 1. _____________ 2. _____________ 3. _____________ 4. _____________ 5. _____________ 6. _____________ 7. _____________ 8. _____________ 9. _____________ 10. _____________ 11. _____________ 12. _____________


Chapter 2 Test – Form D (cont’d) Simplify each expression. 13. ( 26)(0)( 7)(4)− − 14. 13 2 3 ( 4)− + − + −

15. 7( 6) 5 2135 3− − +− ÷

16. [ ]

12( 10) ( 8)( 2)2 12 ( 3 3)− − − −− ÷ − −

Evaluate.

17. xy

for and 28x = 4y = −

18. 4x y− for and 2x = − 1y = − Solve. 19. In a card game, it is possible to have a negative score. If

Amanda’s score is 20, what is her new score if she loses 25 points?


four times before ascending 2000 feet. What is the current altitude of the plane?

Name: ____________ 13. _____________ 14. _____________ 15. _____________ 16. _____________ 17. _____________ 18. _____________ 19. _____________ 20. _____________


Chapter 2 Test – Form E Name:____________ Date: _____________ 1. Fill in the blank. The opposite of ( 29)− − is _______

a) 129

− b) c) 0 d) 29 29−

Simplify each expression. 2. 22 ( 8)− + −

a) 30 b) -30 c) 14 d) -14 3. 12 ( 1)− − −

a) -11 b) 11 c) -13 d) 13 4. 7( 4)− −

a) 18 b) 21 c) 280 d) 28

5. 284

−−

a) 7 b) 24 c) 7− d) 24− 6. 17 14− +

a) b) 31 c) 31− 3− d) 3 7. 27 (63)− +

a) 36 b) c) 90 d) 36− 90− 8. 16 16− −

a) 0 b) c) 32− 16− d) 32 9. 8(20)−

a) 152 b) c) 180− 152− d) 160− 10. 4 ( 59)+ −

a) b) c) 55− 63 63− d) 55


Chapter 2 Test – Form E (cont’d) Name: _____________ 11. 7 ( 7)− −

a) 7 b) 14 c) 14− d) 0 12. 15 7 13− + −

a) b) c) 35− 9− 21− d) 5 Simplify each expression. 13. ( )( )( )( )45 0 9 7− −

a) 45 b) 1 c) 45− d) 0 14. 4 1 ( 20) 7− + − − +

a) 24 b) c) 10 d) 18− 16−

15. 8( 6) 5 4147 3− − +− ÷

a) 3 b) 1 c) 1− d) 13

16. [ ]

20( 1) ( 8)( 9)2 8 ( 2 2)− − − −− ÷ − −

a) b) c) 23 23− 13− d) undefined Evaluate.

17. xy

for and 32x = − 8y=

a) b) c) 4 d) 24 4− 24−

18. 8x y− for x = -7 and y = -5

a) 47 b) 33 c) -47 d) 3 19. In a card game it is possible to have a negative score. If Madeline’s score is 19, what is her new

score if she loses 24 points? a) -5 points b) -43 points c) 43 points d) 5 points

20. A plane flying at an altitude to 20,000 feet descends 2000 feet four times before ascending 1000 feet. What is the current altitude of the plane? a) 12,000 feet b) 11,000 feet c) 13,000 feet d) 27,000 feet


Chapter 2 Test – Form F Name:____________

Date: _____________

1. Fill in the blank. The opposite of ( 12)− − = ______.

a) 112

− b) c) 0 d) 12 12−

Simplify each expression. 2. 10 ( 23)− + −

a) 33 b) -33 c) -13 d) 13 3. 13 ( 3)− − −

a) b) 10 c) -16 d) 16 10− 4. 6( 9)− −

a) 44 b) 48 c) 540 d) 54

5. 306

−−

a) 5 b) 24 c) -5 d) -24 6. 14 28− +

a) -42 b) 42 c) 14 d) -14 7. ( )88 (44)− +

a) -44 b) 44 c) 132 d) -132 8. 13 13− −

a) 0 b) -26 c) -13 d) 26 9. 6(16)−

a) 90 b) -112 c) -90 d) -96 10. 26 ( 51)+ −

a) -25 b) 77 c) -77 d) 25


Chapter 2 Test – Form F (cont’d) Name: _____________ Simplify each expression. 11. 8 ( 8)− −

a) 8 b) 16 c) -16 d) 0 12. 10 10 9− − +

a) 9 b) -9 c) -11 d) -29 13. ( )( )( )( )44 0 4 8− −

a) 44 b) 1 c) -44 d) 0 14. 1 16 18 ( 4)− + − + −

a) -7 b) -3 c) 1 d) 29

15. 4( 2) 3 815 5

− − +− ÷

a) 5 b) 1 c) -1 d) 15

16. ( )

16( 2) ( 8)( 5)2 12 3 3

− − − −⎡ ⎤− ÷ − −⎣ ⎦

a) 14 b) -18 c) -6 d) undefined Evaluate.

17. xy


a) -5 b) -24 c) 5 d) 24 18. 7x y+ for and 1x =− 2y =−

a) -13 b) 15 c) 13 d) -15 19. In a card game, it is possible to have a negative score. If Jacob’s score is 19, what is his new

score if he loses 30 points?

a) -11 points b) -49 points c) 49 points d) 11 points 20. A plane flying at an altitude of 20,000 feet descends 2000 feet three times before ascending

1000 feet. What is the current altitude of the plane?

a) 14,000 feet b) 13,000 feet c) 15,000 feet d) 25,000 feet


Chapters 1-2 Test – Form A Name: ____________ Date: _____________ Evaluate. 1. 500 – 147 1. _______________ 2. 293 × 50 2. _______________ 3. 28,872 ÷ 72 3. _______________ 4. 3,256 × 1,000 4. _______________ 5. 42 ⋅ 52 5. _______________ 6. 17 6. _______________ 16 2 4 3− ÷ + ⋅

7. 2

36 9 2( 25 3) 4

÷ ⋅− +

7. _______________

8. Estimate the sum by rounding each number to the nearest hundred. 1642 + 2351 + 398 8. _______________ Simplify. 9. 7− 9. _______________ 10. 103− − 10. ______________ Perform each indicated operation. 11. 11. ______________ 8 2− i 12. 12. _______________ (114 6− ÷ − ) 13. . 13. _______________ 2 13− + 14. 5 1 14. _______________ 6− 15. ( )11 5− + − 15. _______________ 16. ( )10 5− − − 16. _______________


Chapters 1-2 Test – Form A (cont’d) Name: ____________ 17. Simplify: ( ) ( )15 5 3 40 5− + + ÷ −i . 17. _______________

18. A store bought 24 ten-pound bags of oranges for $168. How much did they pay per bag? 18. _______________ 19. Evaluate: x y− when and 6x = − 7y = 19. _______________ 20. A weather forecaster predicts that the temperature will drop 5 degrees each hour for the next 7 hours. If the temperature is 31 degrees before the temperature starts falling, what is the temperature after the drop? 20. _______________


Chapters 1-2 Test – Form B Name: ____________ Date: _____________

1. Evaluate: 800 – 239

a. 661 b. 561 c. 571 d. 671 2. Evaluate: 375 × 40 a. 1,500 b.16,000 c.12,800 d. 15,000 3. Evaluate: 5640 ⋅ 100 a. 564 b. 56,400 c. 5,640,000 d. 564,000 4. Evaluate: 33,279 ÷ 61 a. 545, R: 34 b. 545, R: 44 c. 535, R: 34 d. 535, R: 44 5. Evaluate: 3 15 3⋅ a. 225 b. 125 c. 375 d. 75 6. Evaluate: 7 28 7 72 9+ ÷ − ÷ a. 5 b. 7 c. 8 d. 3

7. Evaluate: 2

49 7 2( 25 3) 3

÷ ⋅− +

a. 2 b. 4 c. 1 d. 7 8. Estimate the difference by rounding each number to the nearest hundred: 7483 – 1927 a. 5000 b. 5600 c. 5500 d. 5700 9. Simplify: 20− a. 20 b. 40 c. –20 d. 0 10. Simplify: 26− −

a. 26 b. –26 c. 52 d. 0 Perform each indicated operation. 11. ( )13 18− −i

a. 252 b. 234 c. 247 d. –247 12. ( )69 3− ÷ −

a. 207 b. 13 c. –23 d. 23


Chapters 1- 2 Test – Form B (cont’d) Name:__________ Perform each indicated operation. 13. 2 ( 4)+ −

a. 6 b. 2 c. –6 d. –2 14. 2 15−

a. 13 b. 17 c. –17 d. –13 15. ( )9 5− + −

a. –4 b. 14 c. –14 d. 4 16. ( )15 9− − −

a. 6 b. 24 c. –6 d. –24 17. Simplify: ( ) ( )12 5 3 20 5− + + ÷ −i

a. –19 b. 1 c. –7 d. –5 18. A farmer wants a field 36 yards long with an area of 1008 square yards. How wide should the field be? a. 18 yards b. 26 yards c. 28 yards d. 24 yards 19. Evaluate x y− when and 6x = − 2y =

a. 8 b. 4 c. –8 d. –4 20. A weather forecaster predicts that the temperature will drop 6 degrees each hour for the next

7 hours. If the temperature is 23 degrees before the temperature starts falling, what is the temperature after the drop?

a. b. c. 42− ° 42° 19− ° d. 10 °


Introduction to Variables and Algebraic...

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