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Southern Maryland Christian Academy Summer Math Assignment Options
Objectives: Retention of math skills learned from previous school year. Students will be practicing math skills
so that retention is maintained over the summer. Because each year builds upon the previous year’s math skills, it
is important that students have a solid foundation moving forward. To assist with this, SMCA requires that all
students spend time over the summer completing an online mission on khanacademy.org or complete a summer
math packet.
Due Date: 2nd day of Math Class
Assessment: Count as one test grade. Student must complete one option below in its entirety. Student may
not start one option and then finish with the other option.
Requirements: This summer there are two options for all students entering 6th-AP Calculus. SMCA strongly
recommends Option 1.
Option 1: Khan Academy Summer Program
Students are expected to spend at least 1,000 minutes AND 50% of the course mission. However; in order to prepare for success next year, students are highly encouraged to complete at least 90% of the course mission.
Students that choose the Khan Academy summer math assignments will be completing math modules through
khanacademy.org. Students can expect to spend on average a minimum of 30 minutes per week on modules.
As students complete the course, they have opportunities to earn “Badges”. “Badges” will be tallied at the beginning
of the school year and the top 5 students per course with the greatest number of “badges” will earn 5 homework
passes as a reward.
Grading for the Khan Academy will be calculated by the completion percentage of the mission and it will count as
one test grade.
Option 2: Summer Math Packet
Students must complete all problems on the summer math packet.
Students who choose the math packet will complete a paper packet that must be printed from SMCA’s website.
Students can expect to complete at least one page of the packet three times each week. Remember, it’s not
about just “checking it off” and getting it done – it’s about doing quality review that will help you “hit the ground
running” in your next math course. Students must show all work on separate sheets of paper. Answers need to
written beside each question.
Grading for the Summer Math Packet will be calculated by the number of correct answers out of number of prob-
lems and it will be counted as one test grade.
Calculator Use: Calculators may only be used for students entering Pre-Calculus and Calculus.
New SMCA Students: New SMCA students who enroll after August 1, 2018 will have until the end of the first
quarter to complete 50% of the Khan Academy summer math assignments or the entire math packet.
Option 1 and 2 – Keep Reading
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Southern Maryland Christian Academy Khan Academy Instructions
Entering Algebra/Trigonometry or Pre-Calculus
OPTION 1
“How to join your Khan Academy class.”
1. Sign up at khanacademy.org
New to Khan: “Sign-Up” - Upper right side of screen click “sign-up”
o Click “sign-up with email”
o Create Account
Use student’s real name for username – this will be the name that
helps the teacher know who to give credit to at the end of the
summer.
Parents may use their own email account if student does not have
an email account.
Returning: “Sign-In” if you already have an account
2. Click on Name in the upper right hand corner
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3. Click on Profile
4. Click on “Coaches” tab
5. In the “Add a coach” field, enter the class code: XZFQBSQK (Trigonometry)
2AAB6N7N (Pre-Calculus)
Click “Join the Class”
6. Now click on name in the upper right hand corner
7. Click “Notifications”
“Add your Parent” if parent would
like to monitor progress of stu-
dent.
Open the “Coach’s Name” menu at the top right and click “Add students”
or “Add Children” to get started!
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8. You’re set! Click “Start this Mission”
9. Complete the “Mission Warm-Up”
10. After completion of “Mission Warm-Up”, Khan Academy will generate assignments
based on individual’s needs.
11. A new window will appear with some statistics regarding the pre-test.
a. Review the statistics. Then press the green bar at the bottom of the window
to close it.
12. You are now ready to earn points and badges while completing summer math assign-
ments!
Remember: Students are expected to complete 90% of the course mission. The completion
percentage of the mission will be translated into a TEST GRADE for Quarter One.
Option 2 – Keep Reading
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Southern Maryland Christian Academy Summer Math Packet
Entering Algebra/Trigonometry or Pre-Calculus
OPTION 2
Excellent websites for fun learning and reinforcement of math skills:
If, after completing this packet, you are still struggling with a specific topic, you can visit some of the websites
listed on the next page for assistance with that topic.
www.khanacademy.com - Learn almost anything for free. With a library of over 3,000 videos covering everything from arithmetic to physics, finance, and history and 306 practice exercises, we're on a mission to help you learn what you want, when you want, at your own pace.
www.classzone.com – Curriculum used at Southern Maryland Christian Academy Grades 6-12
www.wildmath.com Select “Play the game”. Select addition, subtraction or multiplication and grade. You can
race to beat your time.
www.harcourtschool.com Click the red box, select math, select HSPMath, select Maryland, click on the skill you
need help with. Select a game.
www.aplusmath.com Go under “Flashcards” or “Game Room” on the left side of the screen. They can practice
adding, subtracting and multiplying. Very important to know the addition, subtraction, and multiplication facts
from memorization or within a couple seconds.
www.mathisfun.com Select numbers then Math Trainer for adding, subtracting and multiplication. Or at the
home screen select games and pick a game to play.
www.eduplace.com Select your state – “Michigan” press submit. Select the student tab then click on the “mathe-
matics” rectangle. Click in the center book “Houghton Mifflin Math 2007”, Click on “Grade #”. Select any games.
Extra Help and Extra Practice is good, also eGames.
www.illuminations.nctm.org Select activities then select grade level. Click on Search.
www.aaamath.com At the top pick grade for a challenge. Choose any of the activities like multiplication then
select “play” option toward the top of the screen. 20 Questions and Countdown games are good ones.
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Southern Maryland Christian Academy Summer Math Packet
Entering Algebra/Trigonometry or Pre-Calculus
OPTION 2
Write the prime factorization of the number.
____ 1. 264
a. c. b. d.
Write all of the factors of the number.
____ 2. 153
a. 1, 3, 17, 51 c. 1, 153
b. 1, 3, 9, 17, 51, 153 d. 1, 3, 17
Find the greatest common factor of the numbers.
____ 3. 56, 64
a. 2 c. 8
b. 112 d. 5
Write the prime factorization of the numbers. Then find their LCM.
____ 4. 24, 63
a. c. b. d.
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List the first few multiples of each number. Then use the list to find the LCM of the numbers.
____ 5. 12, 21
a. multiples of 12: 12, 24, 36, 48, 60, 72, 84
multiples of 21: 21, 42, 63, 84
84
b. multiples of 12: 24, 36, 48, 60, 72, 84
multiples of 21: 42, 63, 84
84
c. multiples of 12: 3, 4
multiples of 21: 3, 7
3
d. multiples of 12: 1, 3, 4, 12
multiples of 21: 1, 3, 7, 21
3
Simplify:
____ 6.
a. c. b. d.
8
Simplify:
____ 7.
a. c.
b. d.
____ 8. Simplify
a. c. b. d.
Simplify the expression using positive exponents.
____ 9.
a.
c.
b.
d.
Simplify the expression using positive exponents.
____ 10.
a. c.
b.
d.
Factor:
____ 11.
a. c.
b. d.
Solve:
____ 12.
a. p =
c. p =
b. p =
d. p =
9
Graph:
____ 13.
a.
c.
b.
d.
10–10 x
10
–10
y
10–10 x
10
–10
y
10–10 x
10
–10
y
10–10 x
10
–10
y
10
____ 14. The equation is graphed below. Which graph shows the result of changing the 3 in the equation
to
a.
c.
b.
d.
____ 15. Solve: = 32
a. 28 c. 27
b. 37 d. 36
Solve:
____ 16. = 16
a. 64 c. 4
b. –4 d. –64
Solve:
____ 17. 6x + 4 = 64
a. 68 c. 60
b. 9 d. 10
11
Solve the equation. Round your result to two decimal places.
____ 18. 0.4x – 0.2 = –2.5
a. –2.70 c. –5.75
b. –3.25 d. –6.75
Solve:
____ 19.
a. 22 c. 21
b. –21 d. –22
Solve the inequality. Then graph its solution.
____ 20.
a.
b.
c.
d.
Graph the solution:
____ 21.
a.
b.
c.
d.
0 5 100–5–10
0 5 100–5–10
0 5 100–5–10
0 5 100–5–10
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Solve and graph:
____ 22.
a.
b.
c.
d.
Solve and graph the inequality:
____ 23.
a.
b.
c.
d.
Find the product.
____ 24.
a. c. b. d.
Find the product and simplify.
____ 25.
a.
c.
b. d.
0 2 4 6 8 100
0 2 4 6 8 100
0 2 4 6 8 100
0 2 4 6 8 100
13
____ 26.
a. c. b. d.
____ 27.
a. c. b. d.
Find the difference.
____ 28.
a. 12 c. –32
b. 32 d. –12
Find the product.
____ 29.
a. 13 c. –36
b. 36 d. 5
Find the perimeter and area of the rectangle or square.
____ 30.
a.
b.
c.
d.
14
____ 31.
a.
c.
b.
d.
Find the circumference of the circle.
____ 32.
a. 18.84 in. c. 75.36 in.
b. 452.16 in. d. 37.68 in.
Find the surface area of the prism, where B is the area of the base, P is the perimeter of the base, and h is the
height.
____ 33.
a. c. b. d.
Find the volume of the rectangular prism.
____ 34.
a. 529.2 c. 88.2
b. 121.8 d. 130.8
Find the volume of the cylinder. Round to the nearest tenth.
____ 35.
a. 253.3 c. 21.6
b. 63.3 d. 88.2
Find the sum.
____ 36.
a. c. b. d.
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Simplify:
____ 37.
a. c.
b. d.
Find the difference.
____ 38.
a. c. b. d.
____ 39.
a. c. b. d.
Find the product:
____ 40.
a. c. b. d.
____ 41. What is the value of the expression for and ?
a. b. c. d.
____ 42. The formula gives the kinetic energy of an object in terms of its mass and velocity .
What is the equation for ?
a.
b.
c.
d.
____ 43. What is the solution of the inequality ?
a. or
b. or
c. or
d. or
16
____ 44. Which data set shows direct variation?
a.
b.
c.
d.
____ 45. Which linear equation approximates the best fit to the data?
a.
b.
c.
d.
____ 46. What is the solution of the linear system?
a.
b.
c.
d.
17
____ 47. What is the solution of the system?
a.
b.
c.
d.
____ 48. What is the axis of symmetry of a parabola with the equation ?
a. b. c.
d.
____ 49. What is the solution of ?
a. or
b. or
c. or
d. or
____ 50. What is the quotient of divided by ?
a. b. c. d.
18
____ 51. Which is an exponential decay function?
a.
b.
c.
d. y =
____ 52. What is the distance between the points and ?
a.
b. c.
d.
____ 53. The Venn diagram shows the number of people in a neighborhood of 40 people who use 3 town services:
the library A, the playground B, and the jogging trail C. What is the probability that a randomly selected person
from the neighborhood uses the library and playground?
a.
b.
c.
d.
____ 54. Which shows the ratio 15 to 42 as a fraction in simplest form?
a.
c.
b.
d.
19
Perform the indicated operation. Let and .
____ 55.
a. b. c. d.
____ 56.
a. b. c. d.
____ 57.
a. b. c. d.
Choose the statement that is true about the given quantities.
____ 58.
a. The quantity in column A is greater.
b. The quantity in column B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the given information.
____ 59.
a. The quantity in column A is greater.
b. The quantity in column B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the given information.
20
____ 60.
Column
A
Column
B
a. The quantity in column A is greater.
b. The quantity in column B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the given information.
____ 61.
Column
A
Column
B
16
a. The quantity in column A is greater.
b. The quantity in column B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the given information.
____ 62.
Column A Column B
where a = 1, b = -2, c = -3 where a = -1, b = 2, c = 3
a. The quantity in column A is greater.
b. The quantity in column B is greater.
c. The two quantities are equal.
d. The relationship cannot be determined from the given information.
____ 63. What is the value of ?
a.
b.
c.
d.
____ 64. Simplify .
a. b.
21
c.
d.
____ 65. What is the product ?
a.
b.
c.
d.
____ 66. Factor .
a.
b.
c.
d.
____ 67. What are all the rational zeros of ?
a. none
b.
c.
d.
22
____ 68. How many zeros does the function have?
a. none
b. 3 rational
c. 2 real, 1 imaginary
d. 3 imaginary
____ 69. How many turning points does the function have?
a. 2
b. 1
c. 3
d. 4
____ 70. What are all solutions of
a. 4, 1
b. –4, –1
c. 2, 2
d. –2, –2
____ 71. What are all solutions of
a. 4
b. –8, –2
c. 4, –4
d. 0, 16
____ 72. The graph of y = x2 is a
a. circle.
b. line.
c. parabola.
d. rectangle.
____ 73. In the quadratic formula is called the
a. denominator.
b. discriminant.
c. derivative.
d. domain.
____ 74. is
a. rational.
b. irrational.
c. real.
d. imaginary.
23
SIMPLIFYING EXPRESSIONS Simplify the following expressions.
(𝑤6𝑐)(−3𝑤4𝑐3) (𝑝8)6 53 ∙ 57 (−4
𝑞)
4
(𝑚6
𝑛3 )6
(8𝑥3𝑦2)−3 𝑥8
𝑥−2 15𝑥2𝑦
6𝑥4𝑦5 ∙6𝑥3𝑦2
5𝑥𝑦
8𝑥8 − 4 + 3𝑥4 − (6𝑥4 + 3𝑥8 + 9) (2𝑞5 + 2) − (9𝑞4 + 5) + (5𝑞5 + 4𝑞4) (6𝑥3 + 8𝑥2 + 4) − (5𝑥3 − 2𝑥2 + 8𝑥 − 5) 7𝑥 + 6(𝑥 + 5) + 5(𝑥 + 2)
√3753
+ √83
√4𝑥5 − 𝑥√𝑥3 5√12 − 3√48 + 9√28
24
F.O.I.L the following. Made sure the resulting polynomial is in descending order. (𝑥 − 9)(𝑥 + 3) (𝑥 − 4)(𝑥 + 1)(𝑥 + 3) (3𝑥 + 4)(𝑥 + 5) (5𝑐 − 2)(3𝑐 + 4) (𝑥 + 4)(𝑥2 + 3𝑥 + 4) (2 − 3𝑥)(3𝑥 − 2)
(𝑥 + 3)2 (2𝑥 − 1)2 (𝑥 − 7)2
Factor. 𝑥2 − 9𝑥 + 18 64𝑥3 + 343 2𝑥3 − 3𝑥2 + 4𝑥 − 6
1282 xx 8022 dd 372 2 xx
61910 2 xx 60288 2 yy 1212 x
4129 2 rr 1055 2 xx 49100 2 x
12119881 2 xx 1266 2 xx 1242 xx
2092 xx 1002 x 3042 2 xx
169262 xx 2136 2 xx 090192 xx
215 2 xx 64162 xx 28112 xx
25
Divide using synthetic division
(8𝑥4 + 5𝑥3 + 4𝑥2 − 𝑥 + 7) ÷ (𝑥 + 1) (12𝑥3 + 31𝑥2 − 17𝑥 − 6) ÷ (𝑥 + 3) Divide using long division (𝑥3 + 8𝑥 + 1) ÷ (𝑥 + 4) (3𝑥3 + 11𝑥2 + 4𝑥 + 1) ÷ (𝑥2 + 𝑥)
26
Solving each of the following equations. Show all of your work neatly in the space provided and put a box around your answer.
3
2
15
4
5
2k
6
5
6
5
2
1
t )1(83)4(2 hhh
−5𝑥 + 23 + 7𝑥 + 23 = 4 |13 + 2𝑥| = 5 4𝑥2 + 28𝑥 − 15 = 0 9𝑥2 + 6𝑥 + 1 = 0 9𝑝2 + 42𝑝 + 49 = 0 7𝑥2 − 3 = 11 𝑥2 − 32 = 4 𝑚2 + 8𝑚 = −3 3(𝑝 − 9)2 = 81 3𝑥4 − 11𝑥2 − 20 = 0 4𝑥3 − 8𝑥2 − 𝑥 + 2 = 0
27
Write y as a function of x. (In other words, solve for y in terms of x) 5𝑥 + 𝑦 = 7 2𝑥𝑦 + 𝑥 = 12 Find the discriminant of the function 𝑓(𝑥) = 7𝑥2 − 𝑥 + 10 and use it to say what you know about the zeros of f. Identify the x-intercepts, y-intercept, and end behavior of the function
𝑓(𝑥) =1
9(𝑥 + 3)2(𝑥 − 3)2 𝑔(𝑥) = (𝑥 − 3)(𝑥 + 1)(𝑥 + 2)
ℎ(𝑥) = 𝑥3 + 4𝑥2 + 9𝑥 + 36 𝑠(𝑥) = −𝑥3 + 5𝑥2 + 14𝑥
28
Graph each of the following functions or inequalities. Show any work necessary to produce the graph. Neatly draw and
label the axes. Find the domain and range of each.
𝑦 =2
3𝑥 + 3 5𝑥 − 2𝑦 = 10
𝑦 > 3𝑥 − 1 𝑦 = 2|𝑥| − 1
29
𝑦 = −1
3|𝑥 − 2| + 2 𝑦 = (𝑥 − 4)2 − 7
𝑦 = −2𝑥2 + 8𝑥 − 5 𝑦 = (𝑥 + 3)2 + 1
𝑦 = −1
3(𝑥 + 1)(𝑥 − 5)
30
Write an equation of the line with a slope of 1
3 that passes through the point (-6, 2)
Write an equation of the line that passes through the points (5, -7) and (1, -3)
Write an equation of the line that passes through (1, 4) and is perpendicular to the line 𝑦 = −3𝑥 + 1
Write an equation of the line that passes through (5, -2) and is parallel to the line 2𝑥 − 3𝑦 = 6
31
Geometry Review:
Write the following statement in "if-then" form. The graph of an nth degree polynomial function has at most n – 1 turning points. Write the converse of the statement. Then decide if the converse is true. If f(x) is one-to-one, then 𝑓−1(𝑥) is a function. Write the biconditional statement as a conditional statement and its converse: A quadratic function has two real zeros if and only if its determinant is positive. Write the inverse of the following statement. If the point (2, 5) is a solution to f, then the point (5, 2) is a solution to 𝑓−1. Parallel Lines cut by a Transversal For each diagram below, l||m. Find the value of x.
m l
m 65º
3xº l 75º (2x + 15)º m
144º l (3x + 5)º
Write a proof for the following.
Given: m||l and 21 1 2
32
Prove: 32 m
3 The legs of a right triangle measure 4 in and 6 in. Find the length of the hypotenuse in simplest radical form. Find the sine, cosine and tangent of the angle θ in each triangle below. (Recall SOH-CAH-TOA) 8 13 5 6 θ 10 12 θ
The angle of elevation to the top of the Ulm cathedral from a point 300 ft away from the base of its steeple on level
ground is 60º. Find the height of the steeple to the nearest hundredth of a foot.
Find the perimeter and area of a rectangle whose length is 5cm and whose width is 6cm
33
Find the circumference and area of a circle whose radius is 12 inches. Leave your answer in terms of 𝜋.
The area of the base of a right prism is 12.5 in2. The perimeter of the base is 14 inches and the height of the prism is 6 inches. Find the surface area and volume of the prism.
Find the volume of a rectangular prism with the following dimensions: 6cm x 3.5cm x 4.2cm
Find the volume of a cylinder whose radius is 2.4 yd and whose height is 3.5 yd.
