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Name
Teacher/Block (circle):
Cordero - A Sheppard-Brick - D Sheppard-Brick - G
Lexington High School Mathematics Department
Math 1 Final Exam June 20, 2014
Rules
This is a 90-minute exam, but you are allowed to work for up to 2 hours. Students with an
individual plan giving them extra time may work for 2 hours and 15 minutes.
All work to be graded must be written in this test packet. You may request extra paper for
scratch work if needed.
Graphing calculators are permitted, but may not be shared between students.
Advice
Showing your work is important. The more you write, the more opportunities you will have
for partial credit.
You may leave answers as fractions or square roots where appropriate. Also, you may round
to two places where appropriate.
On many questions, there are ways to check your answers. Make sure you do this.
Don’t give up early — work for the full time that you are allowed.
Your teachers all say: We know you can do it!
Do not write in these boxes:
Q 1–3
/12
Q 4-7
/12
Q 8–10
/8
Q 11-12
/8
Q 13-16
/12
Q 17-19
/13
Q 20-21
/12
Q 22-23
/7
Q 24-25
/6
Q 26 /9
TOTAL
/99
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3
Show all steps for full credit.
1. (2 points) Simplify the following expression:
2. (8 points) Solve the following equations.
a. b.
c. d.
3. (2 points) Sam owns an ice cream shop. He charges $3 for a single scoop and $5 for a double
scoop. He earned $130 yesterday. Let s equal the number of single scoops and d equal the
number of double scoops. Write an equation to model the situation.
4
4. (2 points) Find the slope of the line between (7, 1) and (5, 16)
5. (3 points) Use slopes to determine whether the following points are collinear.
Explain and show your work.
A(–3, 7) B(–1, 5) C(6, 2)
6. a. (1 point) Write an equation for a line that b. (2 points) Write an equation for the line that
passes through the given point and has passes through the following points:
the given slope:
with an undefined slope
7. (4 points) Sketch the graph of each equation.
a. b.
5
10
8
6
4
2
2
5 101009080
10
8
6
4
2
70605040302010
Minutes
Miles
O
A BC D
E
F
8. (3 points) The graph shows Sammy’s trip to Lexington. He started in Bedford, rode his bike to
the Candy Castle in Lexington. He locked up his bike and then hung out at Candy Castle buying
lots of chocolate. Afterwards, he walked over to Orange Leaf and ate some yummy frozen
yogurt. Then, he walked back to the Candy Castle to get his Bike. Lastly, he got on his bike and
rode back to Bedford.
a. Between which pair of points is Sammy at
Candy Castle?
b. Why is the line segment from C to D horizontal?
c. What was his average speed on his way to
Lexington?
9. (3 points) Let l be the line with equation
a. Solve the equation for y. b. What is the slope of the line l?
10. (2 points) Write the following numbers in scientific notation.
a. 0.0000123 b. 880000
6
11. ( 2 points) Write each expression as a single power of x.
a. b.
12. (6 points) Solve each system.
a.
b.
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13. (3 points) Solve the inequality. Graph your solution on a number line.
14. (5 points) Draw graphs in the coordinate plane for the solutions of this system of inequalities.
Don’t forget to shade.
and
15. (2 points) Leave all of your answers as fractions and show all of your work.
Use the function formulas
and .
a. Evaluate . b. Evaluate .
16. (2 points) a. What is the domain of
? b. What is the domain of ?
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17. (4 points) Point P has coordinates . Line l has equation .
a. Write an equation for the line through P parallel to l.
b. Write an equation for the line through P perpendicular to l.
18. (5 points) Use this graph below to answer the following problems.
a. Does the table show a function? Tell why or why not.
b. What is the value(s) of ?
c. Find the x value(s) such that .
19. (2 points) a. are the endpoints of a diameter. Find the coordinates
of the center of the circle (the midpoint of ).
(2 points) b. Find the length of the diameter, .
-3 -1
-3 5
2 3
3 -3
5 3
7 7
9
0 10 20 30 40 50 60 70
Ages of Actors in a Play
20. (6 points) The boxplot below represents the ages of the actors in a play that is performed in
Belmont.
a. What is the 5 number summary represented by the boxplot.
Minimum _________________
Quartile 1 _________________
Median _________________
Quartile 3 _________________
Maximum _________________
b. What percentage of the actors are under 20 years old?
21. (6 points) The data from a survey of 100 underclassmen is shown in the two-way table. The
students were asked their current grade in school and whether they take Spanish or French.
Take Spanish Take French Total
9th
graders 30 12 42
10th
graders 42 16 58
Total 72 28 100
a. What fraction and percent of 9th
grade students take Spanish?
b. What fraction and percent of the students take French?
c. What fraction and percent of the students who take French are 9th
graders?
10
22. (3 points) The Stem and Leaf Plot below shows the number of all-time tournament wins by the
top 17 female professional golfers.
2 6 9 9
3 1 1 1 2 5 8
4 2 2 4
5 0 5 7
6
7
8 2 8
a. Find the mean number of tournament wins.
b. Find the mode of the number of tournament wins.
c. Find the median number of tournament wins.
23. (4 points) Reflect with endpoints over the line with equation y = 2.
Write the coordinates of the image.
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24. (2 points) Describe the transformation that maps to
a. Translation, reflection, or rotation?
b.
25. (4 pts) Determine if the function modeled by each table is linear or exponential and write an
equation for the function.
a. b.
Linear or Exponential Linear or Exponential
Equation: Equation:
x f(x)
0 3
1 6
2 12
3 24
4 48
x f(x)
0 12
1 9
2 6
3 3
4 0
12
A
D C
BF
E HG
L
K
I
M
J
26. (9 points) Determine whether the two triangles in each pair are congruent by looking at the sides
and angles. If they are congruent, state a congruence postulate (SAS, SSS, ASA, AAS) and
write a congruence statement.
a. b.
Part a Part b
Are the triangles
congruent?
SAS, SSS,ASA, AAS or
reason for not being
congruent
Congruence Statement,
if any
c.
Part c
Are the triangles
congruent?
SAS, SSS,ASA, AAS or
reason for not being
congruent
Congruence Statement,
if any
