Download Honors Geometry

to
An assessment will be given over the material
in this packet in your Honors Geometry class at
the beginning of the 2017-2018 school year.
Dear Future Honors Geometry Student,
Congratulations! You have completed Advanced Algebra 1 as well as earned 1.0 credit
toward your 4.0 credits of high school math.
We have learned a lot of new concepts this year and it is very important that you retain
these skills. Next year you will be taking Honors Geometry. Believe it or not, Honors
Geometry uses a lot of algebra skills. Also, Algebra 2 w/ Trig and Honors Algebra 2 w/ Trig will
be a lot easier if you keep your Algebra 1 skills up-to-date.
This packet contains necessary Algebra 1 concepts that should be practiced. An
assessment will be given over the material in this packet in your Honors Geometry class at the
beginning of the school year. This packet is meant to assist you in preparing for the quiz. You
are free to pick and choose which problems you feel that you need to work on, but we
suggest that you do all of them and check your answers.
Good luck and have a great summer!
Helpful Websites
Multiplying Integers
http://www.learningwave.com/chapters/integers/mlt.html
Operations with Fractions http://cstl.syr.edu/FIPSE/fracunit/Opfrac/Opfrac.htm
Distributive Property
http://www.algebrahelp.com/lessons/simplifying/distribution/
Writing Equations of Lines
http://www.purplemath.com/modules/strtlneq.htm
http://www.youtube.com/watch?v=CSacN28lkNI
Factoring
http://www.youtube.com/watch?v=lMU5wMDcJNg
http://www.youtube.com/watch?v=NzStCbj_kJo
Solving Quadratic Equations
http://www.purplemath.com/modules/solvquad.htm
http://www.purplemath.com/modules/quadform.htm
http://video.google.com/videoplay?docid=6750617731762388525
http://www.purplemath.com/modules/solvquad2.htm
Simplifying Radicals
http://www.purplemath.com/modules/radicals2.htm
Note: You can “google” or search these topics on “youtube” to get additional
resources to help you.
For problems 1 – 11, solve each equation. Show work.
1. -4x – 22 = 10
4. 8a – 3(2a + 5) = 13
7.
10.
3
x–9=3
4
2y + 11.4 = 2.6 – 0.2y
2. 6x – 30 = -4x + 18
3
5.
(b + 1) = 3
2
8. 2x2 + 9 = 59
11.
3. 9(x + 2) = 56
6
6.
(8k + 2) = -36
5
9. 4(2x – 5) = 4(x + 7)
1
(48  24b)  2(17  4b)
12
For problems 12 – 15, solve the proportion. Show work. Give exact answers.
12.
x  4 3x  4

8
3
13.
a  5 12

12
18
14.
x
3

6
3
15.
9 y

y 3
For problems 16 – 29, factor completely.
16. 9x2 – 16
18. 16x2 + 72x + 81
20. 12x2 – 19x – 21
22. 2x2 + 2x – 24
24. 144x2 – 81y2
26. 9x2 – 6x + 1
28. 15x2 + 29x + 12
17.3x2 – 75
19.16x2 – 40x + 25
21.3x2 + 18x + 27
23.9x2 – 25y2
25.12x2 + 13x – 14
27.25x2 + 70x + 49
29.16x2 – 100y2
For problems 30 – 45, simplify the radical expression. Leave answer in simplified radical form.
30. 32
32. 48
8
34. 25
31. 300
33. 5 6  2 2
36. 3 3  9 3  4 3
38. 8 7  9 7
 2  3 6
42. 8  2  5 
44. 2 5  8
40.
2
2
35. 3
37. 2 5  2 36  3 45
39. 3 11 2 44  11
41. 5  3 15


43.  3  5  4  3
45. 6  7 8  7 
For problems 46 – 55, find the slope. Leave answers as simplified improper fractions.
46. Find the slope of the line through the
points (3, 4) and (6, 10).
48.
x
y
3
-4
4
-1
5
2
6
5
7
8
8
11
9
14
50. Find the slope of the line with function
values f(2) = -3 and f(-6) = 9.
52. Slope of the line through the points
(-2, -5) and (7, 9).
54.
x
y
47. Find the slope of the line through the
points (3, -4) and (6, -4)
49.
51. Find the slope of the line through the
points (6, 4) and (6, -10).
53.
x
-2
1
4
7
10
13
16
y
16
14
12
10
8
6
4
55.
-2
-6
0
-3
2
0
4
3
6
6
8
9
10
12
For problems 56 – 63, write the equation of the line in slope intercept form.
56.
57.
58.
59.
60.
61.
62.
63.
For 64 – 68, graph the following equations.
64.
y = -x + 6
66.
y = 3x – 4
67.
65. x = 5
y=
3
x
4
68.
y = -4
For problems 69 – 72, write an equation, in slope-intercept form of the line that passes through the
given point and has given slope, m.
69. (2, 3); m = 2
70. (6, -4); m = -1
1
(6, 2); m = 
2
71.
72. (-3, -1); m = 
4
5
For problems 73 – 74 , write an equation in slope-intercept form that passes through the given points.
73. (2, -2); (5, 7)
74. (6, 4); (2, 1)
For problems 75 – 78, determine which lines, if any, are parallel or perpendicular.
75. Line a: y = 4x – 2
76. Line a: 4x – 3y = 2
Line b: 3x + 4y = -1
1
Line b: y =  x
Line c: 4y – 3x = 20
4
Line c: y = -4x + 1
77. Line a: y =
3
x+1
5
78. Line a: y = 3x + 6
Line b: 3x + y = 6
Line c: 3y = 2x + 18
Line b: 5y = 3x – 2
Line c: 10x – 6y = -4
For problems 79 – 82, write an equation, in slope-intercept form, that passes through the given point
and is parallel to the given line.
79. (1, -2); -5x + y = 9
80. (-3, -4); 2y = 4 + 3x
82. (9, 4); y – x = 3
3
81. (5, -1); y = – x – 3
5
For problems 83 – 86, write an equation, in slope-intercept form, that passes through the given point
and is perpendicular to the given line.
5
83. (5, -8); y = x + 4
2
85. (-5, 2); y + 3 = 2x
For problems 87 and 88, solve the system.
87. 2x + y = 40
y = 6x
84. (2, -3); 6y = -2x + 1
86. (7, 10); y = 0.5x - 9
88. 2x – 9y = 1
7x – 12y = 23
For problems 89 – 102, solve the quadratic equation. Give exact answers (leave answers in simplified
radical form). Recall: Methods to solve quadratic equations include factoring, square root method
(inverse operations), quadratic formula, and completing the square.
89. x2 – 81 = 0
90. 4x2 – 32x = 0
2
91. 4x = 45
92. x2 – 3 = 4
2
93. 7(x – 3) = 35
3
94. (n + 1)2 = 33
2
95. 4x2 + 16x = 20
97. k2 – 8k – 7 = 0
99. 3x2 – 5x – 2 = 0
101.
2x2 – 7 = x
96. –x2 + 9x – 16 = 0
98. v2 – 7v + 1 = 0
100.
2x2 – 7x = -3
102.
3n2 – 5n = -1
For problems 103 – 106, solve the radical equation. Check for extraneous solutions.
103.
104.
3 2 x  8  2  10
2 x  80  x
105.
x   9 x  14
For problems 107 – 110, solve the system.
107.
-8x – 10y = 24
6x + 5y = 2
109.
-16y = 22 + 6x
-11y – 4x = 15
106.
108.
110.
4x  1  2x
-16 + 20x – 8y = 0
36 = -18y – 22x
x = -7y
2x – 8y = 22
Answer Key:
1) x = -8
2
9
8) x = + 5
2) x = 4.8
3) x = 4
6) k = -4
11)
16)
20)
24)
28)
4) a = 14
7) x = 16
9) x = 12
20
1
b =3
12) x =
13) a = 3
14) x =
21
2
2
(3x + 4)(3x – 4)
17) 3(x + 5)((x – 5)
18) (4x + 9)
2
(4x + 3)(3x – 7)
21) 3(x + 3)
22) 2(x + 4)(x – 3)
9(4x + 3y)(4x – 3y) 25) (3x – 2)(4x + 7)
26) (3x – 1)2
(5x + 3)(3x + 4)
29) 4(2x + 5y)(2x – 5y)
30) 4 2
5) b = 1
10) y = -4
15) y = + 3 3
19) (4x – 5)2
23) (3x + 5y)(3x – 5y)
27) (5x + 7)2
2 2
5
31) 10 3
32) 4 3
33) 20 3
34)
36) 8 3
37) 11 5  12
38) 1 7
39) 8 11
41) 5 3  3 5
42) 4  2 10
43) 5 3  5 5
46) 2
47) 0
48)3
51) undefined
52)
55) -1
56) y = 2x – 1
57) y =
44) 84  32 5
2
49)
3
3
54)
2
1
59) y =  x  1
4
60) y = 2
61) y =
6
3
40) 2 3  3 2
35)
45) 41 2 7
50) 
3
2
63) Company L: y =
3
x2
2
1
x  10
4
53) 
2
x 1
3
65)
66)
67)
70) y = -x + 2
2
3
58) y =
2
x2
3
62) y = -x + 2
Company K: y =
64)
69) y = 2x – 1
14
9
1
x5
2
68)
1
71) y =  x + 5
2
4
2
72) y =  x – 3
5
5
3
1
x
4
2
76) line a  line b; no lines are //
73) y = 3x – 8
74) y =
75) line a  line b; no lines are parallel
82) y = x – 5
2
83) y =  x – 6
5
77) line a // line b; no lines are 
3
1
79) y = 5x – 7
80) y = x +
2
2
1
1
84) y = 3x – 9
85) y =  x 
2
2
87) (5, 30)
88) (5, 1)
89) x = + 9
92) + 7
93) x = 3 ±
97) x  4  23
98) x 
78) no lines are //; no lines are 
5  13
6
106) x = ½
102) x 
5
73 5
2
90) x = 0, x = 8
94) n = -1 ±
22 95) x = -5, x = 1
99) x = 2, x = -
1
3
100) x =3, x =
1
2
3
81) y =  x + 2
5
86) y = -2x + 24
3 5
2
9  17
96) x 
2
1  57
101) x 
4
91) ±
103) x = 12
104) x = 10 (x = -8 is extraneous)
105) No Solution
107) (7, -8)
108) (0, -2)
110) (7, -1)
109) (-1 ,-1)