Algebra 1 FINAL Exam Review
Algebra • •
• •
• • •
Equation Solving y = mx + b (writing equations and graphing) Solving Systems Includes word problems for all of above Factoring Solving by factoring Solving by graphing
Geometry (Measurement) •
• • •
Area, volume and perimeter problems where x is unknown Rectangles, circles Angles and lines Translations and rotations
Name: ___________________
Number Sense (Computation) • •
• •
Solving proportions Solving word problem proportions Order of Operations Exponent rules
Alg 2nd Trimester Review Number Sense Order of Operations. Show all work. 1)
3)
5g3 12 3 4(5 8)
8 4(10 2) 6 32
Evaluate. Show substitution and all work.
2)
4)
64 16 8 (3) 8 52
102 (10) 2 52
Data • • • • •
Line of best fit Box plots Stem & Leaf Histograms Probability
5)
15 11 x
7)
5x x2 x 5
x = 20
x = -1
6)
8)
x x2
12x x x2
x = -3
x = -5
Solve the proportion. Keep as a fraction or simplify to 3 decimal places. 9)
3 4 11 m
10)
17 x 29 31
Write a proportion and then solve. 11) A beekeeper tagged 211 bees and then took a sample of 400 bees and found 37 of them tagged. What is the total bee population?
Write a proportion and then solve.
12) Arnault is keeping a steady pace running a marathon. He’s run 17 miles in 2.5 hours. How long will it take him to run the remaining 9.2 miles of the marathon?
13) 16% of 51 is what number?
14) What percent of 47 is 103?
Write a proportion and convert. 15) 1 mile = 1.6 km. Convert 65 km into miles.
16) There are 16 oz in a pound. How many pounds is 83 oz?
Exponent Rules. Simplify completely. 17)
x 3 gx 6
20)
3 x 4 y 7 g4 xy 8
18)
y 12 y4
21)
15 x 9 y 4 3 x 2 y10
19)
22)
m
2 5
x 15 y 2 x 3 y
Alg 2nd FINAL REVIEW Algebra (Part I) Solve the equation. Show each step completely. If the answer is not an integer, leave it as a reduced improper fraction. DECIMALS WILL NOT BE ACCEPTED. 1)
12x 4 3x 7
2)
15 2x 4 3
3)
8 3( 2x 3) 15x 2
Write an algebraic equation for each problem, then solve it. Show all work. 4) The temperature dropped 12 degrees at night and then tripled the next day 57 degrees. What was the original temperature?
Equation
5) You pay $18 for Netflix service each month and you can buy movies for $5 each. Your total bill for one month was $43. How many movies did you buy?
Equation
6) The temperature increased by 23 degrees during the day and then halved at night to 20 degrees. What was the original temperature?
Equation
7) A bag of oranges costs $4.50 and lemons are $.60 each. You bought two bags of oranges and spent $15.60. How many lemons did you buy?
Equation
Write an equation that describes the relationship, and then answer the questions. Show all work. 8) You drove 500 miles in 9 hours.
9) How many hours did it take you to drive 320 miles? SHOW ALL SUBSTITUTIONS.
10) You drove for 11 hours, how far did you drive?
11) Draw the line given the ordered pair and the slope.
12) Draw the line given the equation.
y
(-2, 5) m = -4
2 x 6 5
Write an equation for the problem, graph it, and answer the questions. A taxi costs $2 to get in and $1.50 a mile. 13. Write an equation to represent this.
14. What is the y-intercept?
15. What is the slope? (fraction)
16. Circle the point on the graph where you spent$7.50. How many miles is that?
17. Use your equation to determine the cost of going 21 miles.
Equation:
18) Write the equation of the line.
19) Calculate the slope using the formula.
(8, 3) ( 101,8)
y 2 y1 x2 x1
Equation______________________ 20) Write the equation of a line that passes through the point (-12, 40) with a slope of
31 .
21) Write the equation of a line that passes through (-28, 60) and (-20, -4).
Alg 2nd FINAL REVIEW Algebra (Part II) Simplify the Radicals Completely 1. 147
2.
8
3.
18
4. 54
5.
300
6.
20
Find the equation of the line and answer the questions. Below are the costs for a phone plan per month. Cost $50.50 $63.40 7) Write the equation for the above data.
Minutes Over 15 32
8) How much is your base phone plan (what you would pay if you didn’t go over any minutes)? SHOW ALL WORK.
9) What does the company charge per minute over your plan? SHOW ALL WORK.
10) What’s the charge if you went 6 minutes over? SHOW ALL WORK.
11) Solve the system of equations by graphing.
y 3x 5
12) Use substitution to solve the system of equations.
y x 1 2x 5y 10
y 21 x 9
Solve the quadratic equations using Algebra. Graph it using a calculator and eyeball the zeroes to confirm. Sketch the graph and label. 13.
x2 9
14.
2
x 5 5
15.
11 x 2 70
16.
20 x 2 19
Solve the equations by factoring. Check by graphing. HINT: Solve each equation for zero 17.
x 2 9 x 14 0
18.
x 2 7 x 30
19.
x 2 9 x 22
20.
x 2 2 x 1
22.
x 2 10 x 25
21.
x 2 9 x 36
Solve the equations by graphing. Sketch the graph and label the zeroes. Show decimals to 3 places. 23. 9 x 2 4 x 16
24.
5 x 2 10 x 5
Systems of Equations. Write equations and solve. 25. A nursery sells 1 gallon bucket plants for $8 and 2 gallon buckets for $12. You bought 15 plants for $136. How many did you buy of each.
26. You have 200 nickels and dimes for a total of $18.85. How many do you have of each?
Evaluate the functions. Write your final answer as an ordered pair.
27.
f ( x) x 2 100 ;
x = -4
28.
f ( x) x 2 4 ;
x = -7
Find the equation of the line and answer the questions. You’re in a long distance taxi. It costs a certain amount to get in and then more for every mile. Here is some data from your ride. Miles 53 81 29) Write the equation of the line.
Cost $138.50 $208.50
30) How much does the taxi charge just to get in? SHOW ALL WORK.
31) How much was the charge at 25 miles? SHOW ALL WORK.
32) You spent $256. How many miles did you go? SHOW ALL WORK.
Alg 2nd Trimester Test B Data & Probability You reach your hand into a bag of M&Ms to pick one: 19 are red, 15 blue, and 10 green. 1) What is the probability of picking blue M&M?
2) What is the probability of picking a green or blue M&M?
3) What is the probability of NOT picking a green M&M?
4) Write the ratio of the shaded area to the whole area as a fraction, a percentage and a decimal.
5) In this carnival game, you try to drop a coin into the center circle. What are the chances of getting a coin in the center if it is randomly dropped? The radius of the small circle is 5 cm and the radius of the large circle is 20 cm.
Take the data and plot the points on the graph. Determine a line of best fit and write the equation by calculating the slope and identifying the y-intercept.
The Department of Transportation is counting cars in an intersection. Many cars had passed through before they began counting. Minutes # of Cars 5 160 10 210 15 260 20 350 25 420 30 450 35 490
5) Plot the points and draw a line of best fit.
6) Write the equation of the line.
7) Use your equation to determine how many cars would have passed through after 2 hours.
8) Use your equation to determine how long it would take 2000 cars to pass through.
9) Use your equation to determine how many cars passed through before DOT began counting.
Bob’s Savings Weeks Dollars 4 3800 5 4400 7 4500 9 4800 12 5600 15 5900 16 6400
10) Plot the points and draw a line of best fit. 11) Write the equation of the line.
12) Use the equation to determine how much money Bob started with.
13) Use the equation to determine how much money he’ll have after 1 year.
14) Use the equation to determine how long it will take Bob to save $10, 000.
15. Put the following data in a Stem & Leaf Plot 14
8
33
19
11
42
30
2
15
17
11
58
27
18
11
29
39
44
41
16
16. Find the 5 number summary from the data above (#7) and draw a box and whisker plot.
17. Construct a histogram from the following data. Snowfall in FT
Date
2 4 1 5 2 1 3 1 4
1995 1996 1998 1999 2002 2003 2004 2005 2006
Snowfall in Feet
Alg FINAL EXAM REVIEW Geometry
Name______________________ Period_______
Write an algebraic equation for each problem, then solve it. Show all work. 1) Consider these similar triangles. Solve for x.
2) The perimeter of the rectangle is 71 cm. What is the value of x?
5x - 3
30 x
4x
7 14
Find the value of the variable given the perimeter of each rectangle. Write the equation and solve. DRAW A PICTURE! 3) The length of a rectangle is eight less than one half its width. The perimeter is 80 cm.
4) The width of a rectangle is five more than one four times its length. The perimeter is 60 meters.
5) Find the sides of the rectangle. The area is 300 ft squared. 7x - 3
11
Side 1
Side 2
6) A box has the dimensions of 4 cm, 7 cm and 10 cm. a. b. c. d.
Draw a picture. Find the volume. Double the side of 10 cm. Find the volume of the new box.
7) Explain why these lines are perpendicular.
8) Lines A and B are parallel. What is the angle of X ?
A
62o
B X
C
9) Use the Pythagorean Theorem to calculate the length of the dotted line.
10) If you flip the triangle over the y-axis, what are the new coordinates of the corners of the new triangle?