Name: _________________________________________________________________
Honors Algebra II
Summer Assignment
Directions: This summer assignment contains material that you have learned previously. The point of the summer
assignment is to rev up your mathematical engine so that you’ll be ready to explore harder concepts when we start the
year. This assignment will be collected shortly after the school year begins, and there will be an exam over this material
soon into the school year.
ALL WORK SHOULD BE ON SEPARATE PAPER!
Formulas that will be helpful:
Slope-Intercept Form: y  mx  b
Point-Slope Form: y  m( x  x1 )  y1
Standard Form: Ax  By  C [A, B, C are integers]
Distance Formula: d 
 x1  x2 y1  y2 
,

2 
 2
Midpoint Formula: 
 x2  x1    y2  y1 
2
30-60-90 Right Triangle Pattern: x  x 3  2 x
45-45-90 Right Triangle Pattern: x  x  x 2
Definitions:
x intercepts are points where a graph intersects the x-axis. All x intercepts have 0 as their y-coordinate.
y intercepts are points where a graph intersects the y-axis. All y intercepts have 0 as their x-coordinate.
For questions 1-8, put your answer in slope-intercept form:
1) Find the equation of the line with slope 5 and y-intercept (0, -2).
2) Find the equation of the line with slope -2 that passes through the point (1, 4).
3) Find the equation of the line passing through the points (2, 6) and (-2, -10).
4) Find the equation of the line passing through the points (3, 7) and (-2, 5).
5) Find the equation of the line parallel to y  2 x  7 that has y-intercept (0, 3).
6) Find the equation of the line parallel to 2 x  y  5 that passes through the point (4, 8).
7) Find the equation of the line perpendicular to y  
2
2
x  5 that passes through the point (2, 1).
3
8) Find the equation of the line perpendicular to 4 x  7 y  28 that passes through the point (-1, 3).
9) Suppose 3 x  4 y  24. Find the x-intercepts and the y-intercepts of this line.
3
5
10) Suppose y   x  3. Find the x-intercepts and the y-intercepts of this line.
11) Put y  
2
x  1 in standard form. [HINT: You’ll want to multiply the entire equation by 5, and then get the x
5
and y variable on the same side of the equation.]
12) Find the equation of the line passing through (3, 7) and (-1, 11). Put your answer in standard form.
13) Find the equation of the line perpendicular to y  5 that passes through the point (3, 9).
14) Find the equation of the line parallel to x  1 that passes through the point (-3, 8).
15) Find the equation of the line perpendicular to x  7 that passes through the point (1, 11).
16) Find the equation of the line passing through the points (2, 5) and (9, 5).
17) Find the equation of the line passing through the points (-1, 3) and (-1, -9).
For questions 18-20, leave your answer in point-slope form.
18) Find the equation of with slope 4, passing through the point (3, -11).
19) Find the equation of the line passing through the points (1, 8) and (9, -13).
20) Find the equation of the line parallel 5 x  6 y  12, passing through the point (1, 7).
For questions 21-24, graph the following lines:
21) 3 x  4 y  12
22) y  
2
x5
3
23) y 
3
 x  1  4
2
24) x  2
For questions 25-34, solve for x.
25) 3x  4  9
26) 2  x  7   2  11
28) 3 2 x 1  9  4  5  x   7
29)
31)
1 8

x 13
34)
2x  7 1
 4
5
5
2x
4

x2 3
32) x 
x 5
7
6
27) 3x  5  6x  2
30)
x x2

5
11
33)
x 4x  5 1


2
3
2
For questions 35-39, simplify the radical expressions.
35)
50
36)
360
37)
99
38)
90
39)
72
For questions 40-42, combine like terms to rewrite the expression.
40) 2  3  x   4 x
41) x  x  5  7
42) x  2  3x   5  2  3x 
For questions 43-45, given the pair of points, calculate the distance between the points and the midpoint of the points.
43)
5,2 ,(3,9)
44)
 5,4 ,(5,  4)
45)
 5,  2 ,(7,  8)
48)
3x  9 , if x = 9
For questions 46-48, compute the value of the expression for the given variable.
46)
2x  5
, if x  2
3x  4
47) 2  x  1 , if x  3
2
For questions 49-57, identify the property that is being used. The possible properties to use are: associative property of
addition, associative property of multiplication, commutative property of addition, commutative property of
multiplication, distributive property, additive inverse, multiplicative inverse, additive identity, multiplicative identity.
49) 2x  3  3  2x
50) 2(5 x  7)  10 x  14
51) 5(1)  5
52) 3  0  3
53) 5 x  (3x  7 y )  (5 x  3x)  7 y
54) (2 x)(3 y )  (3 y )(2 x)
55) 4  (4)  0
56) a (bc )  (ab)c
57) 4    1
1
4
For questions 58-60, refer to the diagram below, and find the missing side length of the right triangle.
58) What relationship exists between sides a and b?
59) Find the lengths of sides a and c if side b has length 10.
60) Find the lengths of sides a and b if side c has length has 12.
For questions 61-63, refer to the diagram below, and find the missing side length of the right triangle.
61) Find the lengths of sides b and c if side a has length 10.
62) Find the lengths of sides a and c if side b has length 4.
63) Find the lengths of sides a and b if side c has length 12.
For questions 64-66 solve the system of equations by substitution.
2 x  y  7
64) 
6 x  21  3 y
 y  2x  5
65) 
y  4  x
x  y  z  6

66)  x  2 y
z  x 1

For questions 67-68 solve the system of equations by elimination.
2a  3b  12
5a  b  13
67) 
68)
3m  4n  13

5m  6n  19
Answers are posted under Summer Assignments on the BVN Library Media Center web page.
http://www4.bluevalleyk12.org/bvn/lmc/