Honors Algebra I / Geometry A

Final Review Packet

2018-19

Name _____________________________ Per__ Date______

This review packet is a general set of skills that will be assessed on the midterm. This review packet MAY

NOT include every possible type of problem that is assessed on the final exam.

Unit 6: Exponential Functions

1. In the graph above, each curve represents a function of the form 𝑦 = 𝑎 ∙ 𝑏𝑥.

The parameter b takes on one of these values: 0.5, 0.8, 1.25, or 2.

For each graph, identify the values of a and b:

Graph #1 a = ________ b = ________

Graph #2 a = ________ b = ________

Graph #3 a = ________ b = ________

Graph #4 a = ________ b = ________

2. Brandon’s uncle gave him $500 and told him to save it to buy a car when he is old enough to drive. He put

the money in a savings account that pays 4% interest compounded annually. He wanted to know how much

interest he would earn after 3 years. So he found the value by calculating 500 ∙ (0.04)3 = 0.032. He was

amazed that he would earn only slightly more than 3 cents! What went wrong? Explain his error and calculate

the amount of interest correctly.

3. In the last century western gray wolves were placed on the endangered species list. But after a few years the

population began to grow again. Biologists believe that the population fits an exponential model of the form

𝑃 = 𝑎𝑏𝑡 where P is the population of wolves and t is the number of years since 2000.

a) Use the data in the table below (which gives the wolf population in the state of Michigan) and the graph to

estimate values of the parameters a and b. You may use a graphing calculator if you choose.

Year Wolf

Population

2000 220

2001 250

2002 280

2003 315

2004 360

2005 405

b) Use your model to predict the wolf population in the year 2010.

4. A business discovered that their kitchen has been infested with fruit flies! The owner keeps a record of the

number of flies and finds they are growing exponentially, doubling every week. Here are the data he has

collected.

Number of weeks

since flies were

discovered

Number of fruit

flies in the

kitchen

0 10

1 20

2 40

3 80

How many flies will there be in 6 weeks? In 7.5 weeks?

5. The value of a government bond, in dollars, is given by the function 𝑦 = 1000 ∙ 1.06𝑥 where x is the number

of years the bond has been held.

a) How much was the bond originally worth?

b) What is the annual rate of interest?

c) Approximately how many years will it take the original investment to double in value?

6. From approximately 1947 to 1977, General Electric Company (GE) discharged PCBs from its capacitor

manufacturing plants at Hudson Falls and Fort Edward into the Hudson River. It was only many years later that

the Environmental Protection Agency (EPA) reached an agreement with GE to start cleaning up the river. In

the meantime, the EPA monitored fish in the river to determine the level of PCBs. The concentration (in

mg/kg) of PCBs in brown bullheads was found to be modeled by the function 𝑦 = 62 ∙ 0.927𝑥 where x is the

number of years since 1980.

a) What does 62 represent in the context of this problem?

b) What does 0.927 represent in the context of this problem?

c) By approximately what percent did the concentration of PCBs decay each year?

d) What was the concentration of PCBs in 2002 when the cleanup began?

e) If they had never started cleaning up the river, what would the concentration of PCBs be in 2013?

Solve each equation using the graphing calculator.

7. 5.77125 .76 1.5x

8. 1

6 62

x

x

Graph the following exponential functions.

9. 3 1.6x

y 10. 8 0.5x

y

Unit 7: Polynomials and Quadratics

For these questions you may use the quadratic formula.

1. The graph of 𝑦 = 𝑥2 is shown as the

thicker curve.

Match each of the other graphs (#1 – #4)

with its function rule.

a. 𝑦 = 𝑥2 − 4

b. 𝑦 = 2𝑥2

c. 𝑦 = – 𝑥2

d. 𝑦 = (𝑥 − 3)2

2. Find the x- and y-intercepts of the graph of 𝑦 = (2𝑥 − 3)(𝑥 + 7).

3. Write each function in factored form:

a. 𝑓(𝑥) = 𝑥2 − 5𝑥 − 24 b. 3 2( ) 6 16 21 56f y y y y

𝑐. 𝑓(𝑥) = 4𝑥2 + 27𝑥 + 35 d. 𝑓(𝑥) = 6𝑥3 + 32𝑥2 + 10𝑥

4. Write each function in standard form:

a. 𝑓(𝑥) = −(𝑥 + 1)2 + 5 b. 𝑓(𝑥) =1

2(𝑥 − 4)2 − 8

c. 𝑓(𝑥) = (𝑥 + 3)(𝑥 − 3) d. 𝑓(𝑥) = (3𝑥 − 1)(𝑥 + 3)

e. 2 2( ) ( 5 2)( 7 3)f x x x x x f.

2( ) 6 (2 3) 5(2 9 3)f p p p p p

5. Solve each equation using the quadratic formula. Write exact answers only.

a. 23 6 3x x b. 2 2 7x x

6. Find the discriminant of the quadratic equation and state the number and types of solutions.

a. 23 4 4 9b b b. 2 2 8 9p p

7. Solve each equation using any method. If the solutions are irrational, round to the nearest hundredth.

a. 2 14 32x x b. 22 18d d

c. 249 140 100 0x x d. 3 219 60 0x x x

e. 12112 2 xx f. 29 144 0b

g. 210 24 8 0x x h. 28 6 5h h

8. A quarterback throws a football down field to a receiver. The path of the football is given by the equation

ℎ = −0.05𝑥2 + 𝑥 + 6 where h is the height of the ball and x is the distance from where the ball is thrown.

Both h and x are measured in feet.

a. What is the maximum height of the ball?

b. How high was the ball when it was thrown?

9. Lindsey has a rectangular bedroom which she wants to carpet. The area of her room is 104 square feet. The

length of her room is three feet less than twice the width. Find the length and width of her room.

10. Graph the quadratic function using any method. State the vertex and axis of symmetry. If necessary, round

to the nearest hundredth.

a. 2 2 2y x x b.

2 6 7y x x

Vertex: Vertex:

Axis of Symmetry: Axis of Symmetry:

Unit 8: Basics of Geometry

1.

If AC= 36, then x = ________

2.

The distance between the two points is ______.

3. Identify what each of the following means:

a) AB b) ____

AB c) AB d) AB

4. Use the figure to answer the questions:

a) Name two collinear points. b) Name a line that is skew to FE .

c) Name three planes that intersect at point F. d) Name two planes that do not intersect.

e) Name four points that are not coplanar. f) Plane EFGH and CH intersect at _______.

5. a) M is a point on GS , between G and S. b) G is the midpoint of LS .

GS = 32 LG = 6x + 5

GM = 3x + 10 GS = 2x + 9

MS = x – 2 Find x, LS, GS, LG

Find: x, GM, MS

6. Matt wants to put a fence around his rectangular pool. His pool measures 21 feet by 40 feet. The pool

has a path around it that is 4 feet wide. How much fencing material does Matt need to enclose the pool and

the path?

7. Use the points below to answer the following questions

A(0, 3) B(-1, -4) C(-7, -9) D (8, 10) E (0, -2)

Find: a) AE

b) BC

c) midpoint of BE

d) midpoint of CD

8. The midpoint of QT is (-5, 1). The coordinates of point Q are (-7,4). Find the coordinates of point T.

9. Find the area of the region:

a) b) Radius of larger circle = 4

Radius of smaller circle = 2

Find the area of the ‘doughnut’

10. Find the perimeter of a four sided figure with the following vertices:

A (-4, 5), B(3, 5), C(5, -2) and D(-4, -2).

(Use the coordinate plane if necessary)

11. Find the length of each missing side. Write each answer as an exact answer and rounded to the nearest

hundredth.

a) b) c)

12. M wants to swim across a river that is 400 meters wide. She started swimming perpendicular to the shore,

but because of the current, she ended up 100 meters downstream from her target. How far did she actually

swim?

13. An isosceles triangles has two congruent legs that measure 20 cm. The base of the triangle is 10 cm. Find

the height of the triangle from the vertex to the base.

Unit 9: Parallel Lines and Triangle Congruence

1. Find the value of x.

a) b)

2. Find the value of x for which a t .

a) b)

c) d)

3. Find the value of each variable.

4. State which postulate/theorem, if any, could be used to prove the two triangles congruent? If not enough

information is given, write not possible.

a) b) c)

d) e) f)

Use the diagram to the right for # 5 – 8.

5. If r||s, then 1 ___?

a. 9 b. 11

c. 5 d. 9 and 5

6. If 11 14, then___?

a. b||c b. r||s

c. b||c and r||s d. none of these

7. If 3 12, then ___?

a. b||c b. r||s c. b||c and r||s d. none of these

8. If b||c, then 6 must be ___ to 3?

a. congruent b. supplementary c. congruent and supplementary d. adjacent

9. The sum of the measures of the exterior angles, one at each vertex, of a convex octagon is ___?

a. 135 b. 1080 c. 45 d. 360

10. Find the measure of each interior angle of a regular decagon.

a. 144 b. 180 c. 36 d. 360

11. Each interior angle of a polygon has a measure of 160°. The number of sides in the polygon is:

a. 9 b. 12 c. 18 d. 20

12. If the measure of an angle exceeds its supplement by 20, then the measure of the angle is:

a. 100 b. 80 c. 55 d. 35

13. If the vertex angle of an isosceles triangle is 40º, then each base angle is:

a. 40º b. 140º c. 70º d. 20º

14. In PQR , mQRS = 2x + 20, mP = 50, and mQ = x +20. Find mQRP.

a. 50 b. 60

c. 70 d. 120

15. If the sum of the measures of the interior angles of a polygon is 2520º, how many sides does the

polygon have?

a. 13 b. 14 c. 15 d. 16

16. Find each variable.

Unit 10: Similarity

1. List the ways you can prove two triangles similar.

2. Solve the following proportion:

1 2

3 6

x x

Determine whether the triangles are similar. If so, write the similarity statement and tell how you know.

3. a) b)

4. The triangles are similar. Find the missing side(s) in each figure.

a) b)

5. The triangles are similar. Find the missing lengths.

a) b) c)

6. If ABC ~ DEF, AB = 8, BC = 10, CA = 12, and DE = 12, then: (hint-draw a diagram!)

a. EF = 10 b. DF = 15 c. EF = 5 d. C F

7. Find EB.

a. 15 b. 60 c. 20 d. 45

8. Find x.

a. 10 b. 12 c. 1.3 d. 8

9. LUV is similar to GEO . The perimeter of LUV is 45 in. The perimeter of GEO is 105 in.

Find:

a) their similarity ratio b) the ratio of their areas

10. Two figures are similar with a similarity ratio of 4:5. The area of the larger figure is 475 in2. Find the area

of the smaller figure.

11. It cost $3.88 to print a 4” x 6” photo. If Emily wanted to print the same image on a 16” x 24” poster, how

much should it cost?

12. A model of a 180-foot tall lighthouse is built to the scale of 2 inch : 15 feet. How many inches tall is the

model?

13. Jake is 5’10’’ and at a certain time of day casts a 7’4” shadow. At the same time of day, Abe’s shadow is

6’8”. To the nearest inch, how tall is Abe? (write your answer in feet and inches)

14. Triangles IJK and TUV are similar. The length of the sides of ∆IJK are 40, 50, and 24. The length of the

longest side of ∆TUV is 275, what is the perimeter of ∆TUV?

Unit 11: Right Triangle Trigonometry

Write an equation involving sine, cosine, or tangent that can be used to find x. Then, solve the equation.

Round answers to the nearest hundredth.

1. 2. 3.

4. 5. 6.

7. Use the picture at the right to find the ratio for cos .

8. To approach runway 17 of the Ponca City Municipal Airport in Oklahoma, the pilot must begin a 3° descent

starting from an altitude of 2714 ft. Create a trigonometric equation to find how many miles the airplane is from

the runway, and then find that distance (the horizontal distance), to the nearest foot.

9. A building casts an 82-foot shadow when the angle of elevation of the sun is 42 o. How tall is the building?

21

x5

54 x

1033

5.2

x

17

x

41 x

5

8 x

8

5