**Final Exam Review Math 1 0910Name:______**

**Decide in each situation whether the data is continuous or discrete. Explain why or why not. **

1) A pot is put on the stove and the stove is turned on high to bring the water to boiling. Time is graphed as the independent variable and the temperature of the water as the dependent variable.

2) Juan keeps track of the odometer on his car (the mileage gauge) as a function of the time he has owned the car.

3) For a full year, Erica recorded just the high temperature of each day with input as the day and output as the temperature.

**Given the table shown, if a scatter plot was made with the indicated input and output, decide if the dependent variable would be a function of the independent variable. Explain why or why not.**

1 / Brown / Jessica / 15 / 60 / Pink

2 / Smith / Phil / 14 / 60.5 / Yellow

3 / James / Kiya / 12 / 61 / Blue

4 / Pike / Sean / 13 / 58 / Pink

5 / Johnson / Phil / 14 / 59 / Red

6 / Brown / Sal / 16 / 60 / Yellow

4) input as student number and output as age______

5) input as last name and output as age______

6) input as first name and output as age______

**Explain the meaning of each specifically within the context of the information given.**

7) If G(x) represents how far a golf ball goes (measured in yards) and the input is the number of the golf swing the person is taking, explain what G(30) = 250 means.

8) If S(x) is the number of snow days we get and the input is which month of the year we are in, then explain what S(3) = 4 means specifically.

9) L(x) represents the number of laps a student ran on the particular day of the week. If on the fifth day, Haley ran 4 laps express this in function notation.

10) Given h(x) = −2x2 + 6, find each. Show your work.

a) h(−3)b) h(0)

11) Given r(x) = −2x + 3, find each. Show your work.

a) r(−3)b) x if r(x) = −3c) r(5)d) if r(x) = 5, find x

**Write the statement in conditional form.**

12) All dolphins swim fast. ______

**For each give the converse, inverse, and contrapositive of the given original statement. **

13) If it is December 31st, then it is the last day of the year.

14) If a graph is a quadratic, then its parent graph is y = x2.

**For each graph, give the equation that it shows. Then answer the questions about it.**

15) equation:______16) equation:______

domain: ______domain: ______

range:______range:______

increasing:______increasing:______

decreasing:______decreasing:______

end behavior:______end behavior:______

x-intercept:______x-intercept:______

y-intercept:______y-intercept:______

17) equation:______18) equation:______

domain: ______domain: ______

range:______range:______

increasing:______increasing:______

decreasing:______decreasing:______

end behavior:______end behavior:______

x-intercept:______x-intercept:______

y-intercept:______y-intercept:______

**Use the graph of L(x) to answer each question. **

19) Find the value(s) when L(x) = 4.______

20) Find L(1). ______

21) Find the value(s) when L(x) = −1.______

22) Give the interval where the average rate of change is the largest.

______

23) Give the limiting values of the domain and range.

Domain______Range______

24) Give the domain and range.

Domain______Range______

25) Give the x-intercept(s) of the graph.______

26) Give the y-intercept(s) of the graph. ______

27) Is the graph increasing or decreasing for 1 < x < 3?______

28) True or False: If L(x) = 1, then x = −1. ______

29) On the interval −4 < x < −2 is L(x) > 0 or is L(x) < 0? Explain. ______

30) Give the maximum value of the function in function notation. ______

**Match each of the sequences with the correct closed form or recursive form formula shown.**

31) 3, 12, 27, 48, …______a) tn = 3n − 2 for n = 1, 2, 3,…

32) 3, −9, 27, −81, …______b) t1 = ______, tn = tn-1 + 5

33) 1, 4, 7, 10, …______c) tn = 3n2 for n = 1, 2, 3,…

34) 1, 6, 11, 16, …______d) t1 = ______, tn = −3∙tn-1

35) Explain the differences between an infinite sequence and a finite sequence. Are their domains different or the same?

36) The graph shown is a model of the height of a dolphin as it jumps up out of the water and re-enters the water. Use the graph to answer the questions about the situation. The independent variable is time measured in seconds and the dependent variable is the height the dolphin is from the surface of the water measured in feet. The function used in the situation is called d(t).

a) What is the maximum height of the dolphin

from the surface of the water? When does this occur?

b) Explain what d(1) = 5 means in this situation.

c) What is the average rate of change in the height from

when time is 0 to when time 2 sec? Explain what this

means in the context of this problem.

d) What is the average rate of change in the height from

when time is 3 seconds to when time is 5 sec. Explain

what this means in the context of this problem.

e) Find the value(s) of t when d(t) = 8. Explain what

these mean in this situation.

**Decide if the data creates a linear function or not. Decide if the equation makes a linear function or not. Give the formula for each function.**

G(x) / 5 / 11 / 17 / 23

x / 1 / 2 / 3 / 4

P(x) / 3 / 6 / 11 / 18

37) 38)

Answer each.

39) Simplify: −24 ÷ 3 ∙ 4 − 7 + 1

40) A rectangle has a length of x + 5 and a width of 2x − 3.

a) Find the area of the rectangle. ______

b) Find the perimeter of the rectangle. ______

41) Find the area of the non-shaded portion of the rectangle shown.

42) The side of a cube measures x + 4. Find the volume of the cube.

43) The area of a rectangle is 2x2 + 7x − 15 and the width is x + 5. Find the length.

44) Simplify each of the following.

a) = _____ b) (4x)(−2x) = ______c) = ______d) a3 • a • a3 = ______h) (3x)(x) =______

45) Identify the following expressions as equivalent or not. Explain why or why not.

a) 2m(m − 6) = 3m − 12mc) 3(a2 − 2a) − (a − 3) + a2 = (4a − 3)(a − 1)

46) Identify each of the following as being a monomial, binomial, trinomial, or if it is none of these, just tell how many terms it has.

a) 3 − 4x ______b) 3xy4z ______c) 7 ______d) 3x − 4x2 + 6______

47) We can also classify polynomials by their degree. Fill in the following information.

a) A polynomial that has degree 2 is called a______. Their graphs make a ______.

b) A polynomial that has degree 0 is called a ______. Their graphs make a ______.

c) A polynomial that has degree 3 is called a______. Their graphs make a ______.

d) A polynomial that has degree 1 is called a______. Their graphs make a______.

48) Identify each polynomial as a constant, linear, quadratic, or cubic function.

a) 5 − 2x______b) 5x2 − 2x3 + 1 ______c) 4x2 + x − 1 ______

d) −4______e) −2x2______f) 5x ______

**Simplify each. Show your work. **

49) 2x(x2 + 3x − 4y)50) −2y2 + 3y − y2 − 3y 51) (x + 4)(x − 4)52) (x − 5)2

53) (x − 5) − (x2 − 2x + 4)54) (x − 5)(x2 − 2x + 4)55) (x − 5) + (x2 − 2x + 4)

56) (2xy2 + 3x2y − 5) − (4 − x2y + 2xy2)57) (2x − 5)(x − 2) − (6 − 9x) + x2

58) Use the table given of the function h(x) to answer the questions.

x / −2 / −1 / 0 / 2 / 3h(x) / 4 / 1 / 0 / 4 / 9

a) Find the equation for h(x). ______

b) What is the degree of your equation?______

c) If this is a complete table of the values allowed for the function h(x), give the domain and range.Domain______Range______

59) Match the equation with the correct graph. ______

y = −x2 + 3

a) b) c)

**Perform each operation and make sure your answers are as simplified as possible. **

60) 61) 62) 63)

64) 65) 66)

67) 68) 69)

70) 71) 72)

**Simplify each. Show your work. **

73) =______74) =______75) =______

76) =______77) =______78)

**Answer each. Show your work. **

79) In the rectangle shown, find the length. ______

80) Consider the figure shown and answer the questions:

a) Find the area.______

b) Find the perimeter. ______

81) A homeowner wants to put out a layer of hay on the yard that he just planted with grass. His rectangular field measures by units. He is going to put out a layer of hay measuring units thick. Given this information, find the volume of the hay that is out on the yard.

______

82) If m(x) = find m(4) simplified.83) If p(x) = find p(−3) simplified.

______

84) The production of a factory each day is represented by the expression 2x + 3y. Using that fact write a simplified expression for each of the following.

a) The amount produced after 7 days. ______

b) The amount produced after x days.______

c) The amount produced after x + 3 days.______

85) Draw a convex pentagon? Draw a concave hexagon?

86) Identify the following as either a polygon or not a polygon.

87) Identify the following as either concave or convex.

88) Into how many triangles can a decagon be divided if diagonals are drawn from a vertex to the other non-consecutive vertices?

89) What is the measure of each interior angle of a regular dodecagon? ______

90) What is the measure of each exterior angle of a regular decagon?______

91) What is the sum of the measures of interior angles for a heptagon?______

92) How many sides does a regular polygon have if each interior angle measures 108?______

93) If each exterior angle of a regular polygon is 30, what is the measure of each interior angle? ______

94) Identify the postulate that can be used to prove these triangles congruent.

a) ______b)______

95) Give the third congruence that must be given to prove that by the indicated postulate.

a) ____________by SAS b) ____________by SSS

96) Identify each triangle by an angle name (obtuse, right, acute) and side name (scalene, isosceles, equilateral).

a) b) c)

97) An equilateral has angles that always measure ______each. The word for this is ______.

98) Using the triangle given find the missing information.

x = ______sides = ______, ______, ______perimeter = ______

99) Mark the given information on each figure. Determine if the following triangles are congruent. If so, state the appropriate postulate and fill in the congruence statement with the correct order of letters. If they are not congruent, tell why it cannot be determined.

a. b. c.

Congruent: Yes/NoCongruent: Yes/NoCongruent: Yes/No

Reason______Reason______Reason______

If they are congruent, find x.

x = ______sides:______

100) In ΔECD, mE = 136º, mC = 17º, and mD = 27º. Which statement must be true? (hint: draw picture!)

a) CD < DEb) DE < CDc) CE > CDd) DE > CE

101) Decide if each triangle exists with the given measurements for the sides. Explain why or why not.

a) 5, 5, 5b) 2.6, 4.3, 1.6c) 9, 3, 11d) 10, 13, 3

102) Solve for x in each diagram and find each unknown angle.

a) b)

x = ______x = ______

angles ______, ______, ______, ______, ______angles ______, ______, ______, ______, _____

103) Using the diagram of the triangle on each scenario, find the missing information.

a) If m4= 3x + 9, m1= x − 16, m2= x + 45,

then x=______, m1=______, m2=______, m4=______

b) If m3 = 3xº, m1 = 4xº, m2 = 3xº,

then x=_____, m1=______, m2=______, m3 = ______

c) If m3 = x + 40º and m4 = 3x º, then x = ______, m3 = ______, m4 = ______

**Use the given figures to solve each problem. (caution go by the wording/info and NOT the picture)**

104) Use square ABCD to answer the questions.

a) mCAD = ______

b) mAEB = ______

c) Is ? ______Explain. ______

d) If AE = 5x + 1 and EC = 2x + 13, then x = ______and AC = ______

105) Use parallelogram ABCD to answer the questions.

a) If mB = 70º, then mA = ______, mC = ______, mD = ______

b) Are the diagonals congruent? ______Do they bisect each other? ______

c) If mA = 3x − 10 and mB = x + 30, then x = ______, mA = ______, mB =______

106) Use rectangle ABCD to answer the questions.

a) If mABD = 42º, then mCBD = ______, mBDC =______

b) If BD = 12, then AC = ______

c) If AC = 12, then AT = ______

d) If AB = 6 and BD = 8, then AD = ______and the perimeter is ______

107) Use rhombus ABCD to answer the questions.

a) x = ______, AB = ______, and perimeter =______

b) mAMB = ______

c) Is ? ______Explain. ______

108) Use kite ABCD to answer the questions.

a) Which angles are congruent on the kite? ______

b) If mADB = 65º, then mABD = ______

c) The two isosceles triangles are ______

d) Does bisect ? ______Explain. ______

e) If KD = 12 and AK = 5, then AD = ______and the perimeter is ______

109) Use the trapezoid ABCD to answer the questions.

a) If mA = 55º, then mB = ______, mC = ______, mD = ______

e) If AD = x + 12 and BC = 4x − 18, then x = ______, AD = ______, BC = ______

110) Which point of concurrency is equidistant from each side of the triangle? Explain why.

a) orthocenterb) centroidc) circumcenterd) incenter

111) Which point of concurrency is equidistant from each vertex of the triangle? Explain why.

a) orthocenterb) centroidc) circumcenterd) incenter

112)** Point D is the centroid of ΔKLM. Answer the following.**

a) What is the name of ?______

b) If KA = 24, what is the length of ?______

c) If KD = 24, what is the length of ?______

d) If CL = 24, what is the length of ?______

e) If MA = 24, what is the length of ?______

f) If mAKD = 24º, what is mCKD?______

113) **Point P is the incenter of ΔTUV. Answer the following.**

a) What is the name of ?______

b) If mYUP = 42º, what is mXUP?______

c) If mZVU = 54º, what is mXVT?______

d) If mPTX = 52º, what is mZTU?______

114) Point P is the circumcenter of ΔXYZ. Answer the following.

a) Find the length of .______

b) What is the radius of the circumscribed circle?______

c) Find the length of .______

d) Find the length of .______

115) Explain what the graph for will look like.