Download Coordinate Algebra Summer Review Problems Students, please

Coordinate Algebra
Summer Review Problems
Students, please use the packets as a review to help you identify the areas where you may
need some extra practice. On one of the first three days of school next year, you will take
a prerequisite skills test. This test will identify the areas that you will need to review in
order to be successful in Coordinate Algebra and it comes directly from the material
covered in the review packet. These topics are not covered in the CA course, so any
review necessary will require time outside of class.
You need to purchase a TI -30XIIS to use in your math and science class. You may use
it on this packet… . But need to show all work.
This assignment provides a review of mathematical and algebraic skills that are required
for success in CA. You are expected to be fluent with these skills, showing complete
algebraic work where appropriate, so this assignment has been provided for your
practice toward mastery.
This packet will be your first grade in CA. Bring it to class the first day of school . All
work needs to be on a separate sheet of paper NEAT and NUMBERED and record
answers on this sheet.
Looking forward to seeing you.
SETS OF NUMBERS:
1. –2 is a rational number. __________(true or false)
2. 5 is a natural number and a whole number. __________ (true or false)
3. A number can be rational and irrational. __________ (true or false)
4. Give one number that is real and rational, but NOT an integer. __________
5. Give an example of an irrational number. __________
REAL NUMBERS & THE NUMBER LINE:
6. Graph the real numbers on the number line: –3, 0.8,
7. Put the numbers in order:
3 , -0.4, 4 , -5.
3
7.
2
ORDER OF OPERATIONS:
Evaluate.
× +4
8. ( 35 )
12.
9. 12 ¸3+28
×
d -e2 when d = 16 and e = 3
10.
éë( 9-7) 2 +5ùû+26
13.
7 y-1 wheny =1
8 4
2
11.
82
× +5
12 +22 -9
SIMPLIFYING ALGEBRAIC EXPRESSIONS:
Simplify each expression.
14. 4x + 3 + 2x + 1
15. 4 x + 5(x + 3)
17. ½ (10x – 4)
18.
16. – (2x – 5)
3x+5(x-2)+8
19.
2x+3(x+2)-(2 x+5)-1
PROPERTIES OF REAL NUMBERS:
Match.
_____ 20. 4x + 0 = 4x
a. inverse property
_____ 21. 26 + (–26) = 0
b. commutative property
_____ 22. 2a + (3b + 4c) = (2a + 3b) + 4c
c. zero property
_____ 23. –12(0) = 0
d. associative property
_____ 24. 5(3x) = (3x)5
e. identity property
SOLVING LINEAR EQUATIONS:
Solve each equation.
25. 5x + 2 = 3x + 24
26. 3(5x – 1) = 3x + 3
27. – x + 3 = 7x + 8
28. Jeff earns $4 an hour baby-sitting. He is saving to buy a pair of in-line skates that
costs $116. If Jeff already has $60 saved, how many hours m ust he baby-sit in order to
buy the skates?
29. An awards dinner costs $225 plus $5 per person. The total bill is $735. How many
people attended the dinner?
30. 11 y-9=13
31.
7x+9=10 x-12
32. 3(1 + x) =1 + 5x
GRAPHING LINEAR EQUATIONS:
Graph (on graph paper).
33. y =
-2 x + 2
3
36. y = 2x – 3
34. x – 3y = – 3
35. y = – 3
37. x = 2
38. 3x – 2y = 6
FUNCTIONS:
-
-
39. Is the following a function: { (2,4),(4,2),(2,6),(6,2)}
-
y =x2 +4
--
40. Is the following a function: { (1,6),(1,2),(2,6),(1,2)}
41. Is the following a linear function:
2x +4y =3
43. Is the following a linear function: x =4
44. Is the following a linear function: y =2
3
45. Is the following a linear function: y - =4
42. Is the following a linear function:
x
SLOPE:
Find the slope of the line passing through the given pairs of points.
46. (2, –5), (–1, 3)
47. (4, 2), (–1, 2)
48. (–7, 0), (2, 5)
49. (3, –1), (3, 0)
Identify the slope and the y-intercept
50.
4x -2y =12
51.
6y -3x =12
52.
y =12
53.
x =12
EQUATIONS OF LINES:
Write the equation of each line described in slope -intercept form.
54.
slope 5 and y-intercept -3
55.
Write the equation of the line graphed to the right.
56. Write the equation represented here.
________________
57. Write the equation represented here
_________________
58. I need to take a taxi cab ride to the airport. The taxi charges a fee of $10 and then
$.20 per mile. Write an equation of a line represented in this situation. How much
would I pay for a 42 mile ride.
59. I have $500 in my savings account. I plan on spending $10 a week on food. Write an
equation of a line represented in this situation and then find out how much will be in
there after 7 weeks.
SIMPLIFYING RADICALS:
Estimate each radical.
60.
12
61.
54
62.
- 200
Simplify each expression.
63.
121
64.
64
3
65.
8
THE PYTHAGOREAN THEOREM:
Use the Pythagorean Theorem to answer each question..
66.
Given the right triangle to the right,
what is the length of the hypotenuse?
67.
Given a right triangle, a = 4 and c = 7.
Find the length of side b.
68.
Is a triangle with sides of length 10 cm, 24 cm, and 26 cm a right
triangle?
69.
A 12 -foot ladder is leaning against the side of a house. The
base of the ladder is 5 feet from the side of the house. How far
up the side of the house does the ladder reach?
To get to the store from his house, Ralph biked 5 km
due west and then 12 km due north. On the way back
he cut across a field, taking the shortest possible route
home. How far did Ralph bike on the round trip?
70.
10
16
store
12
km
Multiply and put in simplest form.
71.
2x(4 x +5)
73. 4(8
72.
3(2
x x +4y +4)
x2 -3x-5)
74. 6x(2x2 – 5x +1)
75. (-x)(4x2 – 7x)
76. 2x 2(x 3 – x2 + 8x – 5)
78. (-5a2)(3a2 – 7a +9)
79. (1/2 x)(6x + 4x2 – 8)
80. 1/3(6x - 18)
Add, subtract, combine like terms.
81. 6x – 4(7+x)
82. 3x 2 – x(3 + 2x)
83. (3n 2 – 5n) – ( 4n3 + 5n2+n+7)
84. 2(x 2 – 4x + 5) – (x)(x – 4)
5 km
home
C
ANGLES:
85. Use the diagram to the right to label the
sides, vertex, and name the angle.
A
B
86. What does “congruent” mean? What would it mean for two angles to be congruent?
Draw an example of two congruent angles and write a congruence statement for the two
angles.
87. Supplementary angles are angles whose measures add to _______________.
88. Complementary angles are angles whose measures add to _______________.
PARALLEL LINES CUT BY A TRANSVERSAL :
Using the diagram below,
89. List all pairs of vertical angles: ________________________________
90. List all pairs of corresponding angles: _____________________________
91. List all pairs of alternate interior angles: ________________________________
92. List all pairs of alternate exterior angles: ________________________________
93. List all pairs of consecutive interior angles: ________________________________
TRIANGLES:
Classify each triangle by the angle measures.
94. A right triangle is a triangle with one _________ angle.
95. An obtuse triangle is a triangle with one __________ angle.
96. An acute triangle is a triangle with three ___________ angles.
Classify each triangle by the side lengths.
97. A scalene triangle is a triangle with 3 ________________ side lengths.
98. An isosceles triangle is a triangle with at least ____ congruent sides.
99. An equilateral triangle is a triangle with exactly ____ congruent sides.
Match the correct classification with the correct description.
100. scalene triangle
F. has a right angle
101. right triangle
H. all sides are congruent
102. isosceles triangle
I. no sides are congruent
103. acute triangle
J. has two congruent angles
104. equilateral triangle
K. all angles are acute
105. equiangular triangle
L. all angles are congruent
VOLUME Use 3.14 for p—you may use a calculator for this— round to two decimal places.
106. Find the volume of a cylinder whose height is 12 cm and radius is 3cm.
107. Find the volume of a cone whose height is 18cm. and diameter of 12cm.
108. Find the volume of a sphere whose radius is 4cm.
109. Find the height of a cylinder whose volume is 125.6 cubic centimeters and radius is
2cm.
110. Find the diameter of a cone whose volume is 84.78cubic centimeters and height is 9 cm.