Download Southern Maryland Christian Academy Summer Math Packet Mrs

Southern Maryland Christian Academy
Summer Math Packet
Entering Pre-Calculus: Algebra and Trigonometry
Due Date:
1st day of Math Class
Assessment: Summer math packet will count as a two homework grades. One grade will be a
completion grade and the other is a correctness grade.
Requirements:
•
•
•
•
•
Complete Part 1 and Part 2 of this packet.
Complete the odd problems on Part 1; Complete all of the problems on Part 2
No calculator may be used
Show all work on separate sheet of paper
Write all answers beside each question
Dear Students,
In preparation for your next math course, it is vital that you practice your math skills so that
you retain them over the summer. Because each year builds upon the previous year’s math
skills, it is important that you have a solid foundation moving forward. Just like in your English
courses, where you need to learn the alphabet to be able to read and write, you also need to
learn the math skills and concepts in order to have success in future math courses.
To assist you with this, SMCA requires that all students spend time over the summer completing
a math packet. You will benefit from this the most if you do a little bit each day. 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. We suggest you complete at least one
page of the packet three times each week and complete the entire packet.
Your completed math packet is due to your math teacher on the first day of math class in
the fall. Please be sure to bring this completed packet with you on the first day of math
class. All work should be shown, and all work should be your own work.
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.
Please remember this is a required assignment and will be assessed the first day of math class.
Sincerely,
Mrs. Andrea L. Smith, M.Ed.
Dean of Academic Affairs
Southern Maryland Christian Academy
P.O. Box 1668
White Plains, Maryland 20695
phone: 301-870-2550
[email protected]
Excellent websites for fun learning and reinforcement of math skills:
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 Washington Christian Academy Grades 8-12
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 “mathematics” 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.
www.funbrain.com Lots of fun games to choose from.
Southern Maryland Christian Academy
Summer Math Packet
Entering Pre-Calculus: Algebra and Trigonometry
Part 1: Complete all the odds.
answers on the lines provided.
Show all your work on a separate sheet of paper.
Write final
Write the prime factorization of the number.
____
1. 264
a.
b.
c.
d.
Write all of the factors of the number.
____
2. 153
a. 1, 3, 17, 51
b. 1, 3, 9, 17, 51, 153
c. 1, 153
d. 1, 3, 17
Find the greatest common factor of the numbers.
____
3. 56, 64
a. 2
b. 112
c. 8
d. 5
Decide whether the numbers are relatively prime. If not, find the greatest common factor.
____
4. 16, 24
a. No; 4
b. Yes
c. No; 24
d. No; 8
Write the prime factorization of the numbers. Then find their LCM.
____
5. 24, 63
a.
b.
c.
d.
List the first few multiples of each number. Then use the list to find the LCM of the numbers.
____
6. 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
Write the fraction or mixed number as a decimal.
____
7.
a. 2.66667
b. 0.375
c. 3.08
d. 0.83
Use a percent proportion.
____
____
8. What is
a. 291.4
b. 2923.4
of 94?
9. 217 is what percent of 620?
a. 29%
b. 3.5%
c. 292.34
d. 29.14
c. 0.35%
d. 35%
Write the decimal or fraction as a percent.
____
10.
a. none of these
b. 87.5%
____
11. 0.399
a. 3.99%
b. 0.0399%
c. 0.00875%
d. 0.024375%
c. 39.9%
d. 0.399%
Simplify:
____
12.
a.
b.
c.
d.
Simplify:
____
____
13.
a.
c.
b.
d.
14. Simplify
a.
b.
c.
d.
Simplify the expression using positive exponents.
____
15.
a.
c.
b.
d.
Simplify the expression using positive exponents.
____
16.
a.
c.
b.
d.
Factor:
____
17.
a.
b.
c.
d.
Solve:
____
18.
a.
b.
p=
p=
c.
d.
p=
p=
Graph:
____
19.
a.
c.
y
10
–10
10
x
y
10
–10
–10
b.
d.
y
10
–10
x
10
x
–10
10
–10
10
x
y
10
–10
–10
____
20. The equation
is graphed below. Which graph shows the result of changing the 3 in the
equation to
____
a.
c.
b.
d.
21. Solve:
a. 28
b. 37
= 32
c. 27
d. 36
Solve:
____
22.
= 16
a. 64
b. –4
c. 4
d. –64
Solve:
____
23. 6x + 4 = 64
a. 68
b. 9
c. 60
d. 10
Solve the equation. Round your result to two decimal places.
____
24. 0.4x – 0.2 = –2.5
a. –2.70
b. –3.25
c. –5.75
d. –6.75
Solve:
____
25.
a. 22
b. –21
c. 21
d. –22
Solve the inequality. Then graph its solution.
____
26.
a.
–10
–5
0
5
10
–10
–5
0
5
10
–10
–5
0
5
10
–10
–5
0
5
10
b.
c.
d.
Graph the solution:
____
27.
a.
b.
c.
d.
Solve and graph:
____
28.
a.
0
2
4
6
8
10
0
2
4
6
8
10
0
2
4
6
8
10
0
2
4
6
8
10
b.
c.
d.
Solve and graph the inequality:
____
29.
a.
b.
c.
d.
Find the product.
____
30.
a.
b.
c.
d.
Find the product and simplify.
____
31.
a.
b.
c.
d.
____
____
32.
a.
b.
c.
d.
a.
b.
c.
d.
33.
Find the difference.
____
34.
a. 12
b. 32
c. –32
d. –12
Find the product.
____
35.
a. 13
b. 36
c. –36
d. 5
Find the perimeter and area of the rectangle or square.
____
36.
a.
b.
c.
d.
____
37.
a.
c.
b.
d.
Find the circumference of the circle.
____
38.
a. 18.84 in.
b. 452.16 in.
c. 75.36 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.
____
39.
a.
b.
c.
d.
Find the volume of the rectangular prism.
____
40.
a. 529.2
b. 121.8
c. 88.2
d. 130.8
Find the volume of the cylinder. Round to the nearest tenth.
____
41.
a. 253.3
b. 63.3
c. 21.6
d. 88.2
Find the sum.
____
42.
a.
b.
c.
d.
Simplify:
____
43.
a.
b.
c.
d.
Find the difference.
____
____
44.
a.
b.
c.
d.
a.
b.
c.
d.
45.
Find the product:
____
46.
a.
b.
c.
d.
____
47. What is the value of the expression
a.
b.
c.
d.
____
48. The formula
for
and
gives the kinetic energy
. What is the equation for
a.
of an object in terms of its mass
?
b.
c.
d.
____
49. What is the solution of the inequality
a.
or
b.
or
c.
or
d.
or
?
?
and velocity
____
50. Which data set shows direct variation?
a.
b.
c.
d.
____
51. Which linear equation approximates the best fit to the data?
a.
b.
c.
d.
____
52. What is the solution of the linear system?
a.
b.
c.
d.
____
53. What is the solution of the system?
a.
b.
c.
d.
____
54. What is the axis of symmetry of a parabola with the equation
a.
b.
c.
d.
____
55. What is the solution of
a.
b.
c.
d.
____
?
?
or
or
or
or
56. What is the quotient of
a.
b.
c.
d.
divided by
?
____
57. Which is an exponential decay function?
a.
b.
c.
____
58. What is the distance between the points
and
?
a.
b.
c.
d.
____
59. 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.
____
60. Which shows the ratio 15 to 42 as a fraction in simplest form?
a.
c.
b.
d.
Perform the indicated operation. Let
____
and
.
61.
a.
b.
c.
d.
____
62.
a.
b.
c.
d.
____
63.
a.
b.
c.
d.
Choose the statement that is true about the given quantities.
____
____
64.
a.
b.
c.
d.
The quantity in column A is greater.
The quantity in column B is greater.
The two quantities are equal.
The relationship cannot be determined from the given information.
a.
b.
c.
d.
The quantity in column A is greater.
The quantity in column B is greater.
The two quantities are equal.
The relationship cannot be determined from the given information.
65.
____
66.
Column A
a.
b.
c.
d.
____
The quantity in column A is greater.
The quantity in column B is greater.
The two quantities are equal.
The relationship cannot be determined from the given information.
67.
Column A
a.
b.
c.
d.
____
Column B
Column B
16
The quantity in column A is greater.
The quantity in column B is greater.
The two quantities are equal.
The relationship cannot be determined from the given information.
68.
Column A
where a = 1, b = -2, c = -3
a.
b.
c.
d.
____
Column B
where a = -1, b = 2, c = 3
The quantity in column A is greater.
The quantity in column B is greater.
The two quantities are equal.
The relationship cannot be determined from the given information.
69. What is the value of
a. 15
b.
c. 125
d. 5
?
____
70. What is the value of
?
a.
b.
c.
d.
____
71. Simplify
.
a.
b.
c.
d.
____
72. What is the product
?
a.
b.
c.
d.
____
73. Factor
.
a.
b.
c.
d.
____
74. What are all the rational zeros of
a. none
b.
c.
d.
?
____
75. How many zeros does the function
a.
b.
c.
d.
____
none
3 rational
2 real, 1 imaginary
3 imaginary
76. How many turning points does the function
a.
b.
c.
d.
77. What are all solutions of
a. 4, 1
b. –4, –1
c. 2, 2
d. –2, –2
____
78. What are all solutions of
a. 4
b. –8, –2
c. 4, –4
d. 0, 16
____
79. The graph of y = x2 is a
a. circle.
b. line.
c. parabola.
d. rectangle.
____
80. In the quadratic formula
a.
b.
c.
d.
denominator.
discriminant.
derivative.
domain.
a.
b.
c.
d.
is
rational.
irrational.
real.
imaginary.
81.
have?
2
1
3
4
____
____
have?
is called the
Part 2: Complete all problems. Show work on a separate sheet of paper neatly and highlight
your final answers. Write all final answers in the space provided underneath each problem.
SIMPLIFYING EXPRESSIONS
Simplify the following expressions.
(𝑤 6 𝑐)(−3𝑤 4 𝑐 3 )
𝑚6
6
( 𝑛3 )
(𝑝8 )6
53 ∙ 57
(8𝑥 3 𝑦 2 )−3
𝑥8
𝑥 −2
−4 4
(𝑞)
15𝑥 2 𝑦 6𝑥 3 𝑦 2
∙ 5𝑥𝑦
6𝑥 4 𝑦 5
8𝑥 8 − 4 + 3𝑥 4 − (6𝑥 4 + 3𝑥 8 + 9)
(2𝑞 5 + 2) − (9𝑞 4 + 5) + (5𝑞 5 + 4𝑞 4 )
(6𝑥 3 + 8𝑥 2 + 4) − (5𝑥 3 − 2𝑥 2 + 8𝑥 − 5)
7𝑥 + 6(𝑥 + 5) + 5(𝑥 + 2)
3
3
√375 + √8
√4𝑥 5 − 𝑥√𝑥 3
5√12 − 3√48 + 9√28
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)(𝑥 2 + 3𝑥 + 4)
(2 − 3𝑥)(3𝑥 − 2)
(𝑥 + 3)2
(2𝑥 − 1)2
(𝑥 − 7)2
𝑥 2 − 9𝑥 + 18
64𝑥 3 + 343
2𝑥 3 − 3𝑥 2 + 4𝑥 − 6
x 2  8 x  12
d 2  2d  80
2x 2  7x  3
10 x 2  19 x  6
8 y 2  28 y  60
x 2  121
9r 2  12 r  4
5 x 2  5 x  10
100 x 2  49
81x 2  198 x  121
6 x 2  6 x  12
x 2  4 x  12
x 2  9 x  20
x 2  100
2 x 2  4 x  30
x 2  26 x  169
6 x 2  13 x  2
x 2  19 x  90  0
15 x 2  x  2
x 2  16 x  64
x 2  11x  28
Factor.
Divide using synthetic division
(8𝑥 4 + 5𝑥 3 + 4𝑥 2 − 𝑥 + 7) ÷ (𝑥 + 1)
Factor using synthetic division.
𝑥 3 − 8𝑥 2 − 23𝑥 + 30
Find the inverse function
𝑓(𝑥) = −5𝑥 + 5
(12𝑥 3 + 31𝑥 2 − 17𝑥 − 6) ÷ (𝑥 + 3)
𝑥 4 + 𝑥 3 − 11𝑥 2 − 9𝑥 + 18
𝑓(𝑥) = 𝑥 3 − 2
Solving each of the following equations. Show all of your work neatly in the space provided and put a
box around your answer.
2
4
2
k 
5
15
3
1 5 5
t   
2 6 6
−5𝑥 + 23 + 7𝑥 + 23 = 4
|13 + 2𝑥| = 5
9𝑥 2 + 6𝑥 + 1 = 0
9𝑝2 + 42𝑝 + 49 = 0
7𝑥 2 − 3 = 11
𝑥 2 − 32 = 4
𝑚2 + 8𝑚 = −3
3(𝑝 − 9)2 = 81
3𝑥 4 − 11𝑥 2 − 20 = 0
4𝑥 3 − 8𝑥 2 − 𝑥 + 2 = 0
2(h  4)  3h  8(1  h)
4𝑥 2 + 28𝑥 − 15 = 0
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) = 7𝑥 2 − 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
1
𝑓(𝑥) = (𝑥 + 3)2 (𝑥 − 3)2
𝑔(𝑥) = (𝑥 − 3)(𝑥 + 1)(𝑥 + 2)
9
ℎ(𝑥) = 𝑥 3 + 4𝑥 2 + 9𝑥 + 36
𝑠(𝑥) = −𝑥 3 + 5𝑥 2 + 14𝑥
Graph each of the following functions or inequalities.
Neatly draw and label the axes.
2
Show any work necessary to produce the graph.
𝑦 = 3𝑥 + 3
5𝑥 − 2𝑦 = 10
𝑦 > 3𝑥 − 1
𝑦 = 2|𝑥| − 1
1
𝑦 = − 3 |𝑥 − 2| + 2
𝑦 = (𝑥 − 4)2 − 7
𝑦 = −2𝑥 2 + 8𝑥 − 5
𝑦 = (𝑥 + 3)2 + 1
1
3
𝑦 = − (𝑥 + 1)(𝑥 − 5)
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
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
3𝑥°
(4𝑥 + 5)°
l
65°
75°
(2𝑥 + 15)°
M
l
(3𝑥 + 5)°
Write a proof for the following.
Given: M||L and 1  2
Prove: 2  3
M
l
2
1
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
6
𝜃
10
𝜃
12
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
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.