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GEOMETRY HONORS
SUMMER REVIEW
Name ________________________
Evaluate each expression.
1.)
382 5
1
2.) 25  (18  9)
3
2 82  2 2 8
3.)
28
4.) 4(1  5)2  8
Name the reciprocal of each number.
7.) 
1
15
8.) 2
11.)
3x  9
3
12.)
13.) 3x  8  22
14.)
x
 2  21
3
15.) 4(2 y  1)  10( y  5)
16.)
2
1
x5  x4
3
2
5.)
2
3
6.) 0
3
7
Simplify.
9.) 7
8
10
10.)
7
2

5
Solve.
70 x  30 y
5
Solve for x.
17.)
x y
d
c
18.) 5(2a  x)  3b
Determine the slope of the line passing through each pair of points.
19.) (-3, 6), (-5, 9)
20.) (2, -5), (-7, -5)
21.) (7, -4), (9, -1)
State the slope and y-intercept of the graph of each equation.
23.) y  5 x  3
24.) 3 y  8 x  2
Graph each equation using x and y intercepts.
25.) 4 x  5 y  20
26.) x 
1
y4
2
22.) (6, -1), (6, 10)
Graph each equation using the slope and y-intercept.
27.) y 
2
x 1
3
28.)
3
1
x y 4
4
2
Write an equation in slope-intercept form of the line having the given slope that passes through the
given point.
29.) 3; (5, -2)
5
30.)  ; (3, 5)
3
Use the values from #29-30 to write the point-slope form of an equation of the line having the given
slope that passes through the given point.
31.)
32.)
Write an equation in slope-intercept form of the line that passes through each pair of points.
33.) (-1, 7), (8, -2)
34.) (-6, 2), (3, -5)
Use the values from #33-34 to write an equation in point slope form of the line that passes through
each pair of points.
35.)
36.)
37.) Write an equation of the line that is parallel to 2 x  3 y  1 and passes through (4, 2).
Use slope intercept form.
38.) Write the equation of the line that is perpendicular to 5 x  3 y  7 and passes through
(8, -2). Use slope intercept form.
Solve the systems of equations using elimination or substitution.
39.)
2x  y  1
x y 8
40.)
6x  7 y  5
2x  3y  7
41.)
9x  2  3y
y  3x  8
Simplify each radical.
42.)
75
43.) 5 40
44.)
3 5 
2
45.)
7
3
48.) 7 30
46.)
2 6
5
10
47.)
5
60
49.) 4 3  5 5  10 3
50.) 2 20  3 24  180
52.) 24a 2b 2  18ab
53.) x 2  7 x  12
55.) x 2  9 x  36
56.) 2 x 2  3x  20
1 2 9 2
x  y
4
16
59.) 9 x 2  12 x  4
Factor each polynomial.
51.) 13 x  26 y
54.)
x2  5x  6
57.) 28 x 2  13 x  6
58.)
Solve each equation by factoring.
60.) 2 x 2  98  0
61.) 2 x 2  13x  24
62.) 6 x3  29 x 2  28 x  0
Solve each equation by using the quadratic formula.
63.) 24 x 2  2 x  15  0
64.)  x 2  6 x  3  0
65.) 4 x 2  13  16 x
SOLUTIONS
1.) 2
2.) 16
11.) x + 3
3
19.)  2
3.) 6
4.) 18
12.) -14x + 6y
3
20.) 0 21.) 2
25.)
3
5.) 2
13.) x = 10
14.) x = 69
22.) undefined
15.) y = 3
23.) m = 5, b = -3
26.)
7
8
34.) y   9 x  3
44.) 45
45.)
51.) 13(x – 2y)
21
3
3
14
38.) y   5 x  5
46.)
2
2
47.) 10 3
52.) 6ab(4ab – 3)
39.) (3, -5)
48.) 84 5
53.) (x + 3)(x + 4)
35
10.)  2
7
9.)  80
17.) x = cd – y
16.) x = -6
8
18.) x 
3b  10a
5
2
24.) m  3 , b  3
28.)
5
32.) y + 5 =  3 (x + 3)
31.) y + 2 = 3(x – 5)
35.) y – 7 = -1(x + 1) OR y + 2 = -1(x – 8)
2
14
37.) y   3 x  3
7
8.)  17
27.)
5
30.) y   3 x  10
29.) y  3 x  17
15
7.)  1
6.) undefined
33.) y = -x + 6
7
7
36.) y – 2 =  9  x  6  OR y + 5 =  9  x  3
40.) (2, -1)
41.) no solution
49.) 14 3  5 5
42.) 5 3
43.) 10 10
50.) 2 5  6 6
54.) (x – 1)(x + 6) 55.) (x – 12)(x + 3)
3  1
3 
1
56.) (2x + 5)(x – 4) 57.) (7x + 2)(4x – 3)
58.)  2 x  4 y  2 x  4 y 



5 3
3

4 7

61.)  , 8
62.) 0,  ,  
63.)  6 ,  4 
64.) 3  2 3
3 2


2


59.) (3x – 2)2
65.)
4  29
2
60.) {-7, 7}
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