Name: ____________________________________ 8:00 am – 9:30 am 6/14/2017

Teacher: (circle one): ANDERSON GOLDBERG

Math 2 (CP2)

Final Exam 2017

Lexington High School Mathematics Department

• This is a 90-minute exam, but you will be allowed to work for up to 120 minutes. If you get extra

time as an accommodation in your 504 or IEP, you will complete that extra time with your teacher

immediately after the end of the exam.

• Calculator use is permitted for the entire exam. You may NOT share calculators for any reason, even

if someone is done with the exam.

• You will given a reference sheet on GREEN paper that you may use for the exam. No other papers or

notes are allowed.

• Only work written on this exam document will be graded.

• You are NOT allowed to have phones, iPads, or any other electronic device out during the exam.

• You may leave your answers as fractions, in terms of pi, or rounded to 2 decimals.

• There are 25 questions, 5 will be thrown out. THEY ALSO COUNT AS RETAKES

(teacher use only)

Total Score: __________

Percentage: __________

Letter Grade: _________

CP2 Math 2 Final Exam 2017 Page 2 of 14

LT-1: I can define, compare, and classify different types of real numbers.

Circle all rational numbers in the list below. If you did not circle any numbers, explain why they are all

irrational.

√3 √4 5

7 – 5π

LT-2: I can use exponent rules to simplify expressions.

Simplify the expression as much as possible. Circle your final answer.

3𝑦4𝑥2

𝑦2𝑥5

LT-3: I understand rational exponents and can evaluate expressions.

Simplify as much as possible. Your final should only have bases and exponents that are integers.

(8𝑎3𝑐6)1/3

CP2 Math 2 Final Exam 2017 Page 3 of 14

LT-4: I can identify different types of functions given a graph, table, or equation.

a. Does this table represent an exponential, linear, or polynomial function? Explain how you know.

b. Write the equation of any exponential function.

LT-5: I can compose two functions and understand and find the inverse of a function.

Given the following functions:

f(x) = 2x – 7 g(x) = √3x + 4

a. Find 𝑔(𝑓(𝑥)) =

b. Find 𝑓−1(𝑥) =

x y

-3 12

-2 7

-1 2

0 -3

1 -8

CP2 Math 2 Final Exam 2017 Page 4 of 14

LT-6: I understand transformations written in function notation and can use equations to graph a

transformed function.

Given the graph to the right, create the graphs of each

of the following:

a. 𝑓(𝑥 + 2) − 1 b. 𝑓(−𝑥)

CP2 Math 2 Final Exam 2017 Page 5 of 14

LT-7: I can write an equation of a transformed function given a word description or graph.

a. Describe the transformations.

b. If the parent function is 𝑓(𝑥) = |𝑥| write the new equation for the transformed graph.

LT-8: I can identify parts of a polynomial.

Use the polynomial, 𝑦 = 4𝑥2 − 3𝑥 + 2𝑥5 + 6 to answer each question.

a. What is the degree of this polynomial? _______________

b. What is the coefficient of the x term? _______________

c. Write the polynomial in standard (normal) form:

LT-9: I can add, subtract and multiply polynomials

CP2 Math 2 Final Exam 2017 Page 6 of 14

Perform each operation. Write your final answers in standard (normal) form.

a. (2𝑥 − 3) + (4𝑥2 − 5𝑥 + 6)

b. (2𝑥 − 3) − (4𝑥2 − 5𝑥 + 6)

c. (2𝑥 − 3)(4𝑥2 − 5𝑥 + 6)

LT-10: I can identify the greatest common factor and use it to factor binomial.

Factor the following using the greatest common factor.

a. 24𝑥2𝑦 + 16𝑥𝑦3 b. 60𝑎2 + 25𝑏2

LT-11: I can factor a trinomial and use Zero Product Property to solve a quadratic using factoring.

CP2 Math 2 Final Exam 2017 Page 7 of 14

Solve by factoring. Show all work and circle final answers.

𝑥2 − 14𝑥 − 32 = 0

LTs 12, 13, 14: I can solve a quadratic word problem using algebraic methods to find y-intercept, x-

intercepts and the vertex.

You must show algebraic work to support your answers.

A diver dives from a platform. The height (in meters) of the diver over time (seconds) can be modeled by

the equation: ℎ(𝑡) = −5𝑡2 + 10𝑡 + 15

a. How high is the platform where the diver started? (y-intercept)

b. When does the diver hit the water (height = 0)? (x-intercepts)

c. What is the maximum height the diver reaches? (vertex)

CP2 Math 2 Final Exam 2017 Page 8 of 14

LT-15: I can write the equation of a quadratic in factored form or vertex form.

Write an equation of a quadratic function with a vertex of ( – 2, – 5) and passes through the point (0, 3).

LT-16: I can dilate a figure and use scale factor to solve problems.

A rectangle has side lengths 6 cm and 14 cm. Another rectangle has side lengths 15 cm and 35 cm. Are

they scaled copies? Show your work or explain how you know.

CP2 Math 2 Final Exam 2017 Page 9 of 14

LT-17: I can explain why two triangles are similar and use the definition of similarity to solve for

missing parts.

ABC ~ DEF. Solve for x.

Show your work and circle your final answer.

LT-18: I can find missing sides or angles of a right triangle using an efficient method.

a. Solve for side x. Show work and circle your final answer.

b. Solve for angle B. Show your set up and circle your final answer.

CP2 Math 2 Final Exam 2017 Page 10 of 14

LT-19: I understand and can use the volume formulas for prisms, pyramids, cylinders, cones, and

spheres.

Golf balls come in sleeves (rectangular prism packages) containing 3 balls per sleeve. A golf ball has a diameter of approximately 2 inches.

a. Find the volume of 1 golf ball.

b. Based on your answer in part a. What is the minimum volume of the sleeve? Explain in words or show your work.

LT-20: I can identify and use special angle relationships with triangles and parallel lines to find missing

angles.

Use the picture to solve for x. Show work and circle your final answer.

CP2 Math 2 Final Exam 2017 Page 11 of 14

LT-24: I can identify and compare parts and terms related to circles.

Determine whether each statement is true or false based on the diagram.

J is the center of the circle.

If false, change the underlined vocabulary to make it true.

LT-25: I can use special angle relationships in a circle to solve for missing angles.

Use the picture to solve for x. Show your work, and circle your final answer.

LT-26

Statement True or False

a.

𝐸𝐹̅̅ ̅̅ is a tangent to the circle.

b.

𝐶𝐸̅̅ ̅̅ is a radius to the circle.

c.

∠𝐸𝐶𝐷 is a central angle.

d.

𝐷�̂� is a minor arc.

CP2 Math 2 Final Exam 2017 Page 12 of 14

I can find the area of any sector and the length of any arc.

a. Find the area of the shaded sector. Show work and circle your

final answer.

b. Find the length of arc DM. Show work and circle your final

answer.

CP2 Math 2 Final Exam 2017 Page 13 of 14

LT-27: I can calculate basic probabilities and compare them in different forms.

A “litter” is a set of puppies born from the same mother at the same time. Suppose that a dog breeder

kept track of the sizes of each litter, and recorded this data:

number of puppies Tally of # of litters Probability that the #

of puppies are born

1 1

2 3

3 4

4 5

5 7

6 9

7 8

8 5

9 2

10 4

11 1

Answer these questions based on the above data.

a. What number of puppies occurred most often? What is the probability that a litter contained that

number of puppies?

b. What is the probability of having 9 or more puppies in a litter?

c. What is the probability of having neither 4 nor 8 puppies in a litter?

LT-28:

CP2 Math 2 Final Exam 2017 Page 14 of 14

Pamela’s Fine Italian Dining offers vegetarian and gluten free items on the menu.

Use the table to answer the following questions.

Appetizer Main Dish Dessert TOTALS

Vegetarian 3 5 10

Gluten Free 1 3

TOTALS 5 7 16

a. Fill in the blanks of the 2-way table.

b. If an item is chosen at random from the whole menu, what is the probability that it is a gluten free main dish.

c. If an item is chosen at random from the whole menu, what is the probability that a gluten free main dish or a vegetarian desert is chosen?

d. What is the probability that if an item is vegetarian, it is not a main dish?