Name ______Date ______Period ______
Integrated Algebra 1- semester 1 Final Exam Review Problems Show All Work for All Problems. Make sure you understand how to do all of these problems before you take your final exam.
1. In the function {(2,3)( 4,5)( 6,7)( 8,9)}, Identify the Domain and Range. Domain: ______Range: ______
2. What are the domain and range of the function? y= -2 x + 10 Domain: ______Range: ______
Find the Slope of: 1 3. line containing ( 4,8) and(- 3,9) 4. y = x - 7 5. 4 x - 2 y = 10 2
Solve the following problems. 4.f( x) = 3 x - 7, so the function has a value of 23
5.g ( x )= - 2 x + 14, so the function has a value of 56
6.- 2x + 10 = - 50 7. 7 + x + 5 = 11 8. 4 x - 13 = 7
1 4 63 11 3 10 10 7 9.+ = 10. + = 11. = 6x 18 8 x 2 4 x x+ 2 x - 4
12. 5x= - 10 13. - 6 2 x + 8 = 0 14. 4 x + 10 = 6 x - 8 Simplify the following. 15. 81x10 y 12 16. 64 x 2 y 7 17. 27
49 18. 19. 18+ 32 20. 3 4 2 + 6 36 ( )
2 21.( 2- 7) 22.( 3 + 4)( 3 - 4) 23. 18
x+3 2 x - 7 x2 + 7 x 8 - x 24.+ 25. - x-1 x - 1 x + 4 x + 4
Factor. 26.x2- 4 x - 21 27. 6 x 2 - 24 28. x 2 + 8 x + 15
29. 9x2- 36 x + 36 30. x 2 + 5 x - 6 31. x 3 + x 2 + 4 x + 4
Factor and Solve. 32.x2+ 5 x + 6 = 0 33. x 2 - 49 = 0 34. 2 x 2 - 10 x = 0
Find the product. 35.( 2x- 7)( x + 3) 36.( x - 8)2 37.( x + 2) 5
- 2 - 38. Find the perimeter and the area of the figure.
8
X
X 15
Perimeter = ______Area = ______
Divide. 39.(- 24x3 + 48 x 2 - 12 x) �( + 4 x) 40.( 2 x 2 + 19 x � 29) ( x 8)
Find the next three terms in the pattern. 41. 4, 10, 16, 22, 28, ______, ______, ______
42. 2, 7, 5, 10, 8, 13, 11, ______, ______, ______Describe the translations of each function compared to the parent function. 43.Compare y=( x + 3)2 , to y = x2 44. Compare y = x - 5, to y = x
Does the function have a local maximum point or a local minimum point? 45.y= x2 + 6 x + 7 46. y = - 2 x 2 + 3 x - 7
Does the function have a maximum or a minimum point, and what is the value? 47.y= -( x - 3)2 + 2 48. y = x2 - 7
- 3 - 49. What are the solutions 50. How many solutions do the functions of f( x) = x2 +2 and g( x) = x + 4 ? below have?
#51- 56 Label the graphs with their parent functions.
- 4 - Integrated Algebra 1- semester 2 Review Problems Show All Work for All Problems. Make sure you understand how to do all of these problems before you take your final exam. Distance and Midpoint (given two points) Name ______骣x+ x y + y distance = (x- x )2 + ( y - y ) 2 midpoint = 琪1 2, 1 2 2 1 2 1 桫 2 2 1. Find the distance and midpoint of segment AB given A(-2, 3) and B(4, 1).
AB = ______midpoint of AB = ( _____ , _____ )
2. Find the value(s) of x given that the distance from C(-2, 5) and D(x, -3) is 10. x = ______
3. Find the value(s) of y given that the distance from E(-4, y) and F(8, 6) is 13. y = ______
Inductive and Deductive Reasoning (patterns, detachment, syllogism)
Write a valid conclusion given the information and determine whether it is valid through inductive reasoning or deductive reasoning (law of detachment or law of syllogism).
3. If it is past 3 o’clock then the restaurant is not serving lunch. It is now 4:15 pm, therefore:
______reason ______
4. For the past 4 weeks the mailperson has brought the mail at exactly noon. What can you conclude about the mail today?
______reason ______
5. If a person hasn’t eaten, then they are hungry. If a person is hungry, then they will be grumpy. George has been without food all morning therefore:
______reason ______
- 5 - Conditional Statements (if-then, converse, inverse, and the contrapositive)
6. Write the statement in if-then form then write the converse, inverse, and contrapositive. Determine the truthfulness of each statement and then, if possible, write the statement as a biconditional. statement: “All triangles with two congruent sides are isosceles.” if-then form ______T / F converse ______T / F inverse ______T / F contrapositive ______T / F biconditional ______
Segment and Angle Addition Postulate (part + part = whole)
Find the value of each segment or angle given the information.
7. Given that AB = 3x + 5, BC = 2x – 1, and AC = 14, find: x = ______AB = ______BC = ______
8. Given that EDF is twice the measure of FDG and m� EDG 75 , find: m� EDF ______m� FDG ______
Supplementary, Complementary, VAT, and Linear Pairs
9. Given that m� ABC 4x + 50o and m� CBD 2x + 10o m� ABC ______m� CBD ______
Write two words that describe angles ABC and CBD ______&______
10. Given that m� BAC x + 35o and m� CAD x – 5o m� BAC ______m� CAD ______
What word would describe angles BAS and CAD?
______
- 6 - 11. Given that m� AED 5x – 40o and m� BEC 2x + 20o m� AED ______m� BEC ______
What word would describe angles AED and BEC?
______
Triangle Congruence (GOOD SSS, SAS, ASA, AAS, HL BAD SSA, AAA)
12. Determine whether each pair of triangles is congruent. If they are congruent, write the reason.
(a) (b) (c)
______
(d) (e) (f)
______
Midsegments
12. Midsegments connect two ______of the sides of a triangle.
13. Midsegments are ______to and ______the length of the side of the triangle they do not intersect.
14. Given the figure, fill in the table.
AC P______BD @______@ ______BD P______DE @______@ ______CD P______Special SegmentsBC @______in a Triangle @ ______15. The circumcenter is ______from the ______of the triangle.
16. The angle bisectors intersect at the ______which is equidistant from the ______of the triangle.
17. The segment connecting the midpoint of a side of a triangle to its opposite vertex is a(n) ______. - 7 - 18. The dotted segment to the right is a(n) ______, if all three are drawn they intersect at the ______.
19. Use the figure at the right to determine which line segment represent each special segment. G is the midpoint of AE (yes, I know its not a very good midpoint, deal with it). a. angle bisector = ______b. perpendicular bisector = ______c. median = ______d. altitude = ______
Triangle Inequality Theorem
20. Determine whether each set of lengths will work to create a triangle. Show why or why not. a. 5, 12, 6 b. 8, 12, 20 c. 19, 11, 10
______
21. Determine the possible values of the third side of a triangle made up of these lengths. a. 5, 12 b. 15, 12 c. 19, 31
______
22. Write the sides and angles of the triangles in order from least to greatest.
sides ______sides ______angles ______angles ______
Exterior Angle Inequality Theorem
23. Each exterior angle of a triangle is ______than either of the two nonadjacent interior angles.
m行 DAB______m B
- 8 - m行 DAB______m C
Hinge Theorem
24. a. AB ______BC b. m行1______m 2
Indirect Proof (proof by contradiction)
25. The first step in an indirect proof is to assume that the conclusion is ______.
26. Write the first step in an indirect proof of each statement. a. If a B is between A and C, then AB + BC = AC. ______b. If x and y are positive, then xy is positive. ______c. If x is odd and y is even, then xy is odd ______
Angle Measures in Polygons
The sum of the interior angles of a polygon with n sides = ______
If the polygon is regular then each interior angle of an n-gon = ______
The sum of the exterior angles of a polygon = ______
Complete the table: Polygon 15 hexagon nonagon Sum of the interior 3060o 5760o angles (in degrees)
Parallelograms
Find the value of each variable below.
- 9 - Rectangles, Rhombuses, and Squares
Find the value of each variable below.
BE=3 x + 1, ED= x + 7 , and EC= 5 y
Kites and Trapezoids
Find the value of each variable below.
Counting Principles
A Thai restaurant serves 25 rice dishes and 10 noodle dishes. If Simon orders either a rice dish or a noodle dish, from how many dishes can he choose?
Martina has 6 hats, 2 scarves, and 5 pairs of gloves. In how many different ways can she wear a hat, scarf, and a pair of gloves?
To log on to the school computer system, each student must choose a password with 2 letters and 2 numbers in that order. Each letter and number may be used only once. How many different passwords are possible?
Permutations and Combinations
A box contains 8 tiles, each a different color. How many ways can you select two tiles?
In how many different orders can 4 students line up in front of a whiteboard?
8P6 = ______5C3 = ______12P2 = ______9C9 = ______
- 10 - Mutually Exclusive, Independence, and Conditional Probability
In a bag of gumballs there are 5 red, 8 blue, and 3 white. What is the probability that you randomly select two without replacing and get a red on the first try and white on the second try?
In that same bag of gumballs from above, what is the probability of selecting a blue gumball second if you know you selected a red gumball first?
You roll a die three times, what is the probability that you roll a 5 on your second and third roll if you rolled a 4 on the first?
Expected Value
You and your friend are playing a game. You roll a die and if it is less than 3 you will gain $4 but if it’s 3 or more you pay your friend $2. What is the expected value of this game for you?
Buying a house in this market is risky! If you bought a house in a certain neighborhood to resell, there is a 45% chance of making $54,000, a 22% chance of breaking even, and a 33% chance of losing $70,000. What is your expected value in this situation? Would you risk it?
Measures of Central Tendency For each set of numbers find all the different characteristics listed. {12, 15, 22, 19, 12, 16, 12, 4} a. mean = ______b. median = ______c. mode = ______d. mean absolute deviation = ______e. range = ______
{6, 11, 14, 12, 9, 11, 14}
- 11 - a. mean = ______b. median = ______c. mode = ______d. mean absolute deviation = ______e. range = ______
Surveys and Samples
(1) A library wants to know more about the people that use its resources so the librarians survey every fifth person that walks through the door. population: ______method: ______
Is this a representative sample?
(2) A school wants to know what there students think about a certain issue so they ask the first 20 students that walk by the main office. population: ______method: ______
Is this a representative sample?
(3) A Georgia power company wants to know how satisfied their customers in Lawrenceville are with their service so they randomly select six houses from each neighborhood in Lawrenceville to survey. population: ______method: ______
Is this a representative sample?
- 12 -