Download chap 1 binder and hw-1 - King Philip Regional School District

Learning Goals
7th Grade Extended Class
Chapter 1: Connections to Algebra
1. To evaluate a variable expression.
2. To write a variable expression that models a real-life situation.
3. To evaluate expressions containing exponents.
4. To use exponents in real-life problems.
5. To use scientific notation to express very large or very small numbers.
6. To convert numbers from scientific notations to standard form.
7. To use the order of operations to evaluate expressions.
8. To use the order of operations to evaluate algebraic expressions.
9. To check solutions of equations.
10. To solve equations using mental math.
11. To translate verbal phrases into algebraic expressions.
12. To use a verbal model to write an algebraic expression or inequality to solve a reallife problem.
13. To use tables and graphs to organize data.
14. To identify a function.
15. To make an input-output table for a function.
16. To write an equation for a real-life function.
7th Grade Extended Class
Name: _________________________________
Chapter 1 Binder Sheet
Day
1
Class Color: _____________________________
Lessons and Homework
Due Date
Lesson 1.1 Variables in Algebra
Homework: Variables in Algebra Wksht
2
Lesson 1.2 Exponents and Powers
Homework: Exponents and Powers Wksht
3
Lesson Scientific Notation
Homework: Scientific Notation Wksht
4
Lesson 1.3 Order of Operations
Homework: Order of Operations Wksht
5
Lesson 1.3 Order of Operations
Homework: More Order of Operations Wksht
6
Quiz Lesson 1.1-1.3
7
Lesson 1.4 Equations and Inequalities
Homework: Equations and Inequalities Wksht
8
Lesson 1.5 Translating Expressions and Equations
Homework: Translating Expressions and Equations Wksht
9
Lesson 1.5 A Problem Solving Plan Using Models
Homework: Problem Solving Wksht
10
Quiz Lesson 1.4-1.5
11
Lesson 1.6 Tables and Graphs
Homework: Tables and Graphs Wksht
12
Lesson 1.7 An Introduction to Functions
Homework: An Introduction to Functions Wksht
13
Review Chapter 1
Homework: Chapter 1 Practice Test
14
Review Chapter 1
Homework: Study for Test
15
Chapter 1 Test
Homework: Review Question A
16

Review Question B
The binder sheet is subject to change.
* Worksheets have been adapted from Algebra 1 (2004) McDougall Littell Inc
Name _________________________________________________________
Variables in Algebra Worksheet
Evaluate the expression for the given value of the variable.
1.
x – 5 when x = 9
2. y + 4 when y = 19
3. w + 8 when w = 3.6
4. 7 – x when x = 2.9
5. m ÷ 3 when m = 2.7
6. h(2.5) when h = 100
7.
2
5
+ f when f =
3
6
8.
5
 t when t = 16
8
Use the following formula to calculate the simple interest earned. I = p•r•t
Simple Interest = Amount of deposit• Interest rate (as a decimal) • time (in years)
9. Deposit: $500
Interest: 4%
Time: 1 year
10. Deposit: $250
Interest: 5%
Time: 6 months
11. Deposit: $2000
Interest: 6.5%
Time: 18 months
Use the following formula to find the average rate of speed.
Rate = Distance ÷ Time
12. An airplane travels 800 miles in 120 minutes
13. A friend jogs 2 miles in ½ hour
14. A car travels 240 kilometers in 2.5 hours
15. Write an expression for the perimeter of the
triangle.
16. Find the perimeter of the triangle, in feet, if x = 10
inches.
17. Write an expression for the
4x ft
2x ft
perimeter of the figure.
x ft
18. Find the perimeter of the figure
if x = 2 ft.
Name _________________________________________________________
Exponents and Powers Worksheet
Write the expression in exponential form.
1.
Three to the fourth power
2. X cubed
3. 3 to the wth power
4. 4*4*4*4*4*4*4
5. 6a squared
6. 3x • 3x • 3x
Evaluate the power.
7. 16
8. 105
9. 93
10. 34
11. 25
12. 42
Evaluate the expression for the given variables.
13. x3 when x = 2
14. 3x when x = 5
15. (x-y)4 when x = 5 and y = 3
16. 14 – y2 when y = 3
17. a2 + b3 when a = 7 and b = 1
18. 101 – z2 when z = 10
Solve the following problems. Don’t forget your labels!
19. Jeff plans to cover the floor of his room with 1 foot square tiles. If the room
is a square that measures 10.5 feet in each side, how many tiles will he need?
20. A cubical box is constructed in order to package a gift. If the edge of the
cube is 8 inches, how much material is needed to make the box? (The surface area
of a cube is S=6s2 where s is the edge length.)
Name _________________________________________________________
Scientific Notation Worksheet
Write each number in scientific notation.
1.
0.07882
2. 118,000
3. 87,200
4. 0.0000000272338
5. 0.00002786
6. 450
7. 74171.7
8. 770
9. 0.00000085
10. 0.000000000000664
Write each number in standard form.
11. 3.443 * 10-5
12. 7.7563 * 10-7
13. 1.525 * 106
14. 6.58457 * 107
15. 5.256 * 104
16. 1.23 * 10-8
17. 5 * 10-9
18. 7 * 1011
Please answer the following questions in complete sentences.
19. How many numbers can be in front of the decimal point for scientific notation?
20. Please explain which way to move the decimal point when changing a number
from scientific notation to standard form.
21. Please explain how you know whether the exponent will be positive or negative
when changing a number from standard form to scientific notation.
22. What is the significance of the exponent in scientific notation?
Name _________________________________________________________
Order of Operations Worksheet
Evaluate each expression.
1.
20 ÷ [4 - (10 - 23)]
2. (8 + 5) • (35 ÷ 7) + 6
3.
27
3
23 4
4. 2(2 + 6 • 2 + 2 - 22)
5. 6 + 4 (3 + 2) – 12 ÷ 4
6. (5 + 62 - 1) - 33 + 7
7. 15 ÷ 3 * 2 – (6 +2) + 4
8. (6 / 3 + 12) 10 * 4 + 9
Please insert grouping symbols to make each statement true.
9. 3 + 7 • 4 – 2 = 20
10. 300 ÷ 50 ÷ 2 * 3 = 4
11. 4 – 2 * 9 – 4 = 10
12. 4 + 6 / 2 + 5 * 2 = 20
Place the following numbers in order to arrive at the answer at the end. Don’t
forget to follow the order of operations!
13.
2
4
5
6
8
11
22
_____ - _____ + _____ * _____ - _____ ÷_____ - _____ = 11
14.
2
5
6
7
9
10
36
_____ ÷ _____ + _____ ÷ _____ - _____ +_____ • _____ = 19
Name _______________________________________________________
More Order of Operations Worksheet
Evaluate the expression for the given value of the variable.
1.
3 + 2x2 when x = 3
2. 50 – 3y2 when y = 4
3. 4 • 2a3 when a = 10
4. 6 + m3 when m = ½
5. w2 ÷ 5 + 3 when w = ¼
6. 32 -
24
when p = 6
p2
Evaluate the expression.
7. 2 + 36 / 4
8. 10 ÷ 5 + 3 * 2
9. 4 – 20 ÷ 10 + 7
10. 3 • (24 + 1) – 8
11. 2 * 32 ÷ 3 + 10 – 4
12. 4(2 + 3) – 18
Two calculators were used to evaluate the expression. They gave different
results. Which calculator followed the order of operations?
13. 12 – 4 * 2 + 1
Calculator 1: 5
Calculator 2: 17
14. 5 * 3 – 4 * 2
Calculator 1: 7
Calculator 2: 22
15. 2 * 6 + 3 / 3
Calculator 1: 5
Calculator 2: 13
16. 10 – 5 * 4 ÷ 10
Calculator 1: 8
Calculator 2: 2
17. During a track meet, Katie throws a shotput 36 ft, 35 ft, and 37 ft. Write
an expression that represents the length of her average throw in feet. Evaluate
the expression.
18. You want to buy a new baseball hat. The hat costs $17 plus 6% sales tax.
Write an expression that represents how much money in dollars you need to buy
the hat. Evaluate the expression.
Name _________________________________________________________
Equations and Inequalities Worksheet
Decide whether the following is an A) expression, B) equation, or C) inequality.
1.
5x + 9 = 22
4. 5.2 = 3x – 9
2. 8x – 1
3. 4x – 2 > 12
5. 39 < 4x
6. 89 – 2a - 19
Check whether the given number is a solution of the equation.
7. 2x + 3 = 7; 4
8. 4x + 2 = 10; 1
9. 4y – 6 = 2y; 3
10. 17 - 4y = 13; 1
11. y + 3y = 2y + 4; 3
12. x2 – 6 = 30; 6
Use mental math to solve the equation. Then write a question that could be used to
solve the equation.
13. x – 3 = 5
14. 4t = 20
15. x ÷ 2 = 3
16. 4 + x = 6
Check whether the given number is a solution of the inequality.
17. X – 5 < 7; 9
18. x + 3 > 7; 4
19. 2x + 1 ≥ 10; 6
20. 5x + 1 ≥ x – 3; 4
KPMS is replacing some of the lockers. When the old lockers are removed
there is a space that is 144 inches long. Each new locker has a width of 8
inches. You want to know how many lockers can be installed. You write the
equation 8x = 144 to model the situation.
21. What do the 8, x, and 144 represent?
22. Use mental math to solve the equation.
The Statue of Liberty’s torch has 14 lamps that give off 14,000 watts of
light. You want to know how many watts are given off in one lamp if all of
the lamps are identical. You write the equation 14x = 14000 to model the
situation.
23. What do the 14, x, and 14000 represent?
24. Use mental math to solve the equation.
Name _________________________________________________________
Translating Expressions and Equations Worksheet
Write an algebraic expression for each phrase.
1. Five more than a number x
2. Triple a number h
3. Half of a number d
4. Three less than a number y
5. The product of a number w and four
6. Six more than twice a number p
7. A number r decreased by ten
number k and nine
8. Four times the sum of a
9. Two times the difference of a number f and 7
Write a phrase for each algebraic expression.
10. 3m
13. 2(b -5)
11. 6 – x
14. 2r + 3
12. f/2
15. 3(d + 3)
Write the algebraic equation or inequality for the statement.
18. Two more than a number x is ten.
19. The sum of a number y and four is thirteen.
20. Eight more than a number p is greater than or equal to nine.
21. The difference of a number a and two is seven.
22. Four less than the product of six and a number t is eight.
23. A number s divided by two is greater than five.
Name _________________________________________________________
Algebraic Geometry Worksheet
Solve each problem by drawing a picture, defining the variables, writing an
equation, and solving.
1.
The length of a rectangle is 4 inches more than the width. The perimeter is
40 inches. Find the length and the width.
2. The perimeter of a rectangle is 82 feet. The length is 5 feet more than
twice the width. Find the length and width.
3. A rectangular field has a perimeter of 174 meters. The length of the field
is 9 meters more than twice the width. Fins the dimensions of the field.
4. The perimeter of a triangle is 37 centimeters. Two sides of the triangle
are equal. Each of those sides is 5 centimeters more than the third side.
Find the length of each of the three sides.
5. Side A of a triangle is 3 inches longer than side B. Side C is one inch shorter
than twice side B. The perimeter of the triangle is 26 inches. Find the length
of each of the three sides.
6. A 33 kilometer bicycle race course is designed in the shape of a triangle.
The first leg of the race is 5 km shorter than the second, and the third leg
is twice the first. Find the distance of each leg of the race.
Name _________________________________________________________
Tables and Graphs Worksheet
1.
Who eats the most carbohydrates?
2. Which two categories consume 10% of their total calories in protein?
3. What percent of Americans diets is made up by fats?
4. Which class had the
most boys?
5. Which class has the
most total students?
6. How many more male
students were in Room
301 than female
students?
7. How many students were enrolled in the fifth grade?
8. Compare the number of females in the fifth grade to the number of males.
The table below represents the fall enrollment of students (in millions) in grades K8 for private and public schools.
Year
Public
School
Private
School
1980
27.6
1985
27.0
1990
29.9
1995
32.4
4.0
4.2
4.1
4.4
9. How many students were enrolled in public school in 1985?
10. What year had the fewest total students enrolled?
11. Construct a bar graph that displays the enrollment for both private and
public schools.
12. In which decade did the life
expectancy in Brazil increase the least?
13. In which decade did the life
expectancy increase the most?
14. Discuss what the line graph shows.
Name _________________________________________________________
An Introduction to Functions Worksheet
Does the table represent a function? Explain.
1.
2.
Input Output
2
5
4
6
6
5
8
6
3.
Input Output
5
0
4
0
3
0
2
0
4.
Input Output
1
1
1
2
2
3
2
4
5.
Input Output
3
6
4
5
5
4
6
3
6.
Input Output
4
3
13
7
9
4
4
0
Input Output
1
1
0
0
5
5
2
2
Make an input-output table for the function. Use 0, 1, 2, and 3 as the domain.
7. y = 2x + 4
8. y = 5x
9. y = 7 – x
Input
Output
10. y = x + 4
Input
Output
Input
Output
11. y = ½ + x
Input
Output
Input
Output
12. y = 11 - x
Input
Output
You join a yoga class at the local Y. The cost is $3 per class plus $10 for
the initial membership.
13. Write an equation that shows the relationship between the number of classes n
you attend and the amount you pay p.
14. Evaluate the equation for n = 1, 2, 5, 8, and 10. Organize your results in an
input-output table.
15. Draw a line graph to represent the data in the input-output table.
When the monarch butterfly is migrating to the south, it has an average
speed of 80 miles per day.
16. Write an equation that shows the relationship between the number of days t
and the distance (in miles) it has traveled d.
17. Evaluate the equation for t= 2, 5, 8, and 10. Organize your results in an inputoutput table.
Name _________________________________________________________
Chapter 1 Practice Test
Evaluate the expression for the given value of the variable.
1.
q – 10 when q = 13
2. 4.25x when x = 6.2
Evaluate the power.
3.
26
4. 73
Evaluate the expression for the given values of the variables.
5. a2 + b when a = 4 and b = 3
6. (x + y)3 when x = 3 and y = 5.
Write each number into scientific notation.
7. 0.00000054
8. 621,000,000,000,000
Write each number into standard form.
9. 3.49 x 10-6
10. 4.312 x 109
Evaluate each expression.
11. [44 ÷ (10 – 8)2] + 7(3 + 2)
12. 9  4 
5  11
2
3 1
Place parentheses to make each statement true.
13. 5 * 4 + 6 ÷ 2 = 25
14. 3 * 42 + 8 ÷ 4 = 18
Check whether the given number is a solution of the equation or inequality.
15. 16x + 3 = 29 - 3x; 2
16. 10x – 4 ≤ 20; 5
Write the equation, inequality or expression for each verbal phrase or
sentence.
17. Four is greater than six times a number t.
18. Eight times a number y decreased by seven is less than or equal to thirty.
Write the verbal phrase to model the given expression, equation, or inequality.
19. 9(x – 4)
20. 35 › 5c + 2
Solve.
21. Calculate the amount of simple interest earned using the formula I=prt.
I deposited $1500 in an account that offers 6.25% interest. How much
interest will I have earned after two and a half years?
22. The perimeter of a rectangle is 58 feet. The length is two more than twice
the width. Find the length and width.
23. A rectangular field has a perimeter of 86 meters. The length of the field is 5
meters less than three times the width. Find the dimensions of the field.
24. The table below shows the amount of gasoline used each month for a fourmonth period. Make a bar graph of the data.
Amount of Gasoline Used
Month
Number of gallons
March April May June
58
66
50
70
Does the table represent a function? Explain.
25.
Input
Output
3
26.
Input
Output
8
7
4
4
11
4
13
8
19
22
9
3
5
7
4
Make an input-output table for the function. Use 0, 1, 2, and 3 as the
domain.
27.
y = 5x + 3
Input
Output
28. y = 32 – 3x
Input
Output
You start a portable catering business. One of your specialties is a barbecue
sandwich plate that costs $0.85 to prepare. Suppose you cater an auction where
you sell each sandwich plate for $2.00. You must also spend $50 on equipment and
supplies to cater the auction.
29. Write an equation that gives the profit you expect to make from catering the
auction.
30. Find the profit you will make if you sell 75 barbecue sandwich plates.
31. How many barbecue sandwich plates to you need to sell in order to make a
$100 profit?