Upper Dublin High School
Algebra 292
Pre-Algebra Review Packet
2012-2013
Name ______
Teacher ______Period _____
Alg 292 Chapter 1.1 – 1.4 ______
Review Packet Day 1 [Class Notes]
1.1 Evaluate Expressions
- Variable:
ex) Evaluate the expression 13n when n = 3
- Power, Base, Exponent:
ex)
1.1 Apply Order of Operations
- PEMDAS:
ex) 7(13 – 8) 24 – (32 + 1)
2[30 – (8 + 13)] 20-1252-1
1.2 Write Expressions
Ex) 4 less than the quantity 6 times a number n
Ex) 3 times the sum of 7 and a number y
1.3 Write Equations and Inequalities
- Equation:
- Inequality:
Ex) Write an inequality for the sentence: “The sum of 3 and twice a number k is no more than 15”. Then check whether 4 is a solution of the inequality.
Alg 292 Chapter 1.1 – 1.4
Review Packet – Day 1 [Homework]
[From textbook pp53-54 #5 – 27 all, p24 #3 – 9 all]
Evaluate the expression.
1. 3+x when x = 13 2. y-2 when y = 18
3. 20k when k = 2 4. 40w when w = 0.5
5. z2 when z = 20 6. w3 when w = 0.1
7. A DVD storage sleeve has the shape of a square with an edge length of 5 inches. What is the area of the front of the sleeve?
8. You store square notepaper in a cube-shaped box with an inside edge length of 3 inches. What is the volume of the box?
Evaluate the expression.
9. 12-6+2 10. 1+2∙92 11. 3+23-6+2
12. 15-(4+32) 13. 20-1252-1 14. 50-[7+32+2]
Evaluate the expression when x = 4.
15. 15x-8 16. 3x2+4 17. 2(x-1)2
Translate the verbal phrase into an expression.
18. The sum of a number k and 7.
19. 5 less than a number z.
20. The quotient of a number k and 12.
21. 3 times the square of a number x.
22. A toll road charges trucks a toll of $3 per axle. Write an expression for the total toll for a truck.
23. You purchase some notebooks for $2.95 each and a package of pens for $2.19. Write an expression for the total amount (in dollars) that you spend.
Write an equation or an inequality.
24. The sum of 42 and a number n is equal to 51.
25. The difference of a number z and 11 is equal to 35.
26. The difference of 9 and the quotient of a number t and 6 is 5.
27. The sum of 12 and the quantity 8 times a number k is equal to 48.
28. The product of 9 and the quantity 5 more than a number t is less than 6.
29. The product of 4 and a number w is at most 51.
30. The sum of a number b and 3 is greater than 8 and less than 12.
Alg 292 Chapter 1.5: Problem Solving Using Equations ______
Review Packet – Day 2 [Class Notes]
Write an equation for each problem and solve. Label your variables. Show your work.
1. The UDHS freshman class has a total of 350 students. There are 12 more females than males. How many females and males are there?
2. Mike has twice as much money as Lisa. Lisa has $16 less than Amanda. Together they have $200. How much money does each have?
3. The width of a rectangular yard is 15 feet less than the length. The perimeter of the yard is 470 feet. Find the length and width.
Algebra 292 Chapter 1.5: Problem Solving Using Equations
Review Packet – Day 2 [Homework]
Write an equation for each problem and solve. Label your variables. Show your work.
1. Two numbers differ by 57. Their sum is 185. Find the numbers.
2. The U.S. Senate has 100 members, all Democrats or Republicans. Recently there were 12 more Democrats than Republicans. How many Senators from each political party were there at that time.
3. The ninth grade class has 17 more girls than boys. There is a total of 431 students. How many boys and girls are there?
4. Julie has one and a half times as much money as Brady. Together they have $225. How much money does each have.
5. A rectangle is 12 feet longer than it is wide. Its perimeter is 68 feet. Find its length and width.
6. Luis weighs 5 pounds more than Carla. Carla weighs 2 pounds more than Rita. Together their weights total 333 pounds. How much does each weigh?
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7. Your school’s service club is sponsoring a dance in the school gm to raise money for a local charity. The expenses will be $600. The club members will sell tickets for $10. They hope to raise enough money to cover the expenses and have enough left to donate $1000 to the charity.
a) How many tickets must they sell to cover their expenses?
b) How many tickets must they sell to cover their expenses and meet their goal?
c) The school allows no more than 200 students in the gymnasium for a dance.
Can the club members sell enough tickets to exceed their goal? What is the
greatest possible amount by which they can exceed their goal? Explain your
reasoning.
8. Each of the long sides of a rectangle has a length of x inches. Each of the
others sides is 1 inch shorter than the long sides. The perimeter of the
rectangle is 22 inches. Find the length and the width of the rectangle. Justify
your answer.
9. A stackable storage rack holds 22 DVDs and costs $21. How much would it
cost to buy enough racks to hold 127 DVDs?
10. You have saved $70 to buy a mountain board that costs $250. You plan to
save $10 each week. How many weeks will it take to save for the mountain
board?
Alg 292 1.5 – Problem Solving Using Equations ______
Review Packet – Day 3 [Class Work & Homework]
Write an equation for each problem and solve it. Label the variables and show your work.
1. There are twice as many girls as boys in the 84 member chorus. How many boys
and girls are there?
2. Amie has $3 more than twice the amount of money that Steph has. Together they have $159. How much money does each have?
3. Bill has three times as much money as Laura. Julie has $10 more than Laura. Together they have $280. How much money does each have?
4. Kirsten built a rectangular corral with a fence on three sides. A side of the barn served as a short side of the corral. She used 130 feet of fencing. The length of the corral was 20 feet longer than the width.
a) Find the dimensions of the corral.
b) If the fencing costs $5.50 per foot, how much money did she spend on
fencing?
c) How much money did she save by not having to fence one of the sides?
5. The UDHS swim team is having a car wash fundraiser. Each car costs $5 and the team spent $70 on supplies. How many cars do they need to wash to make a profit of $485?
6. The length of a rectangular yard is 5 feet less than twice the width. If the perimeter is 494 feet, find the length and width of the yard.
7. The length of a rectangular yard is 35 feet less than twice the width and the perimeter is 410 feet. If the fencing costs $6 per foot, how much money will it take to buy fencing to put all of the way around the yard?
Alg 292 Chapter 2.1 – 2.4 ______
Review Packet – Day 4 [Class Notes]
2.1 Integers and Rational Numbers
Natural Numbers:
Whole Numbers:
Integers:
Rational Numbers:
Absolute Values:
2.2 & 2.3 Add and Subtract Real Numbers
Properties of Addition
· Commutative Property
· Associative Property
· Identity Property
· Inverse Property
Alg 292 Chapter 2.1 – 2.3
Review Packet – Day 4 [Homework]
Tell whether each number in the list is a whole number, an integer, or a rational number. Then order the numbers from least to greatest.
1. 3, -5, -2.4, 1
2. 0.25, -0.5, 0.2, -2
3. -0.01, 0.1, 0, -110
4. -2.7, ½, 0.3, -7
For the given value of a, find -a and |a|
5. a=6 6. a=-18 7. a=13.4
8. a=-6.1 9. a=-119 10. a=34
Evaluate the expression when x=-0.75
11. -x 12. x-0.75 13. 2∙(-x)
14. x+|x| 15. -x+|x|
Evaluate
16. -11 + 3 17. -1 + 6 18. 13 + (-17)
19. 5 + (-10) 20. -9 + (-4) 21. -8 + (-2)
22. -2.4+3.9 23. 415+-912 24. -49+145
25. 13 – (-5) 26. -15 – 29 27. -3.6 – 22.2
28. -53-83 29. 12-56 30. -11 – (-3)
31. -13 + 5 + (-7) 32. -18 + (-12) + (-19) 33. -312+-725+-9310
Identify the property being illustrated.
34. -3 + 3 = 0 35. (-6 + 1) + 7 = -6 + (1 + 7)
36. 9 + (-1) = -1 + 9 37. -8 + 0 = -8
38. (x + 2) + 3 = x + (2 + 3) 39. y + (-4) = -4 + y
Find the change in temperature or elevation.
40. From -5°C to -13°C 41. From -300 ft to -100 ft
Evaluate the expression for the given value of x.
42. 3+x+-7; x=6 43. x+-5+5;x=-3
44. 114+x+-312; x=-825 45. 3.6-6.6-x; x=-11
Algebra 292 Chapter 2.4 – 2.6 ______
Review Packet – Day 5 [Class Notes]
2.4 Multiply Real Numbers
The Sign of a Product
· The product of two real numbers with SAME sign is ______
· The product of two real numbers with DIFFERENT signs is ______
Properties of Multiplication
· Commutative Property
· Associative Property
· Identity Property
· Property of Zero
· Property of -1
2.5 Distributive Property
Let a, b, and c be real numbers:
The product of a and (b + c):
The product of a and (b – c):
Example)
a) 4(y + 3) b) (y + 7 )y c) n(n – 9)
Terms and Coefficients
-x+2x+8
Example) 3x-4-6x+2
Terms: Like terms:
Coefficients: Constant terms:
2.6 Divide Real Numbers
Inverse Property of Multiplication
- The product of a nonzero number and its multiplicative inverse is 1.
Example)
Division Rule
- To divide a number a by a nonzero number b, multiply a by the multiplicative inverse of b.
Example)
The Sign of a Quotient
- The quotient of two real numbers with the SAME sign is ______
- The quotient of two real numbers with DIFFERENT signs is ______
- The quotient of 0 and any nonzero real number is ______
Alg 292 Chapter 2.4 – 2.6
Review Packet – Day 5 [Homework]
Find the product.
1. 10 (-9) 2. -12 (-3) 3. 2.6 (-8)
4. -12(28) 5. 45(-20) 6. -64(-3.5)
7. -23(-21) 8. 8x4.2(-5) 9. -3-5(-4x)
Identify the property illustrated.
10. 5.6∙-3.2=-3.2∙5.6 11. 0∙2.1=0 12. -1∙-1.5=1.5
Evaluate the expression when x = -3 and y = 4.1
13. x + 2y 14. y – 4x
15. xy – 10.1 16. 3x – |y|
Use the distributive property to write an equivalent expression.
17. 5x(x+3) 18. 2x(x-8) 19. -4x(x+6)
20. 10x-1(-7x) 21. 12(8x-1) 22. 25x(x2-1)
Identify the terms, like terms, coefficients, and constant terms of the expression.
23. -2x2+3x+5x-1 24. 6x2-3x+1-5x2+2
Simplify the expression.
25. 35x-1+7 26. 3x+5(x-4)
27. 10x-3(2x+8) 28. 4x-1-2+15x
29. 6-5x-3-12x 30. 20-8-x(-3)
Translate the verbal phrase into an expression. Then simplify the expression.
31. Twice the difference of 5 and x, increased by the product of 2 and x.
32. A local sports store is selling packs of 8 tennis balls for 25% off the regular price. You buy 3 packs of tennis balls. Write an equation that gives the total cost t as a
function of the regular cost r of a pack of tennis balls. Then find the total cost if a
pack of tennis balls regularly costs $20.
33. You are using solid colored fabric that costs $.06 per square and patterned fabric that costs $.10 per square to make a quilt. You need 660 squares to complete the quilt. Write an equation that gives the total cost c as a function of the number n of solid squares used. Then find the total cost if you use 200 solid colored squares.
Find the multiplicative inverse of the number.
31. -7 32. -15 33. -78
Find the quotient.
34. -32÷(-2) 35. -1÷-65
36. -34÷4 37. 17÷-218
38. -13÷15 39. -19÷-8
Simplify the expression.
40. -8x+279 41. 15x-5-5 42. 12x-20-4
43. During a 14-day period, there is the following activity on your bank account. You deposit $100, withdraw $75, deposit $85, and withdraw $150. What is the rate of change (in dollars per day) in your bank account? Round your answer to the nearest cent.
ALG 292 Chapters 1 and 2 Review ______
Review Packet – Day 6
Solve each equation.
1. 2. 3. 4.