PreAP/IB Geometry
Summer Assignment
General instructions:
Name____________________Period______
All work must be neat and readable to receive credit.
“Guess and check” is not considered showing your work!
All answers must be exact. ie : 12π, 3 5
Repeating decimal answers must be left in fraction form.
Solve each of the following problems in the space provided.
1
2
1. 5x + 7x = 9x – 40
2. x + x = 28
2
3
4.
(4x + 7) – (12 – 9x) = 86
5.
18−6𝑥𝑥
7.
x 4
=
16 x
8.
5x + 6 4x - 8
=
10
6
12
= 9 + 2x
3. 5(3 + x) = 75
6.
2𝑥𝑥
9.
x-4
x-8
=
x+6
x-3
16
=
50
40
Solve each system of equations by substitution or elimination. Show your work.
Verify your solution by graphing each set of lines.
Be sure to use a straight edge.
10.
x + y = 12
x–y=4
11. 2x – 6y = 22
2x + 3y = 4
12 .
x = 3y - 12
4x + 30 = 6y
Solve for the indicated variable. You will not have real number answers on 13-16.
a=�
13.
a2 + b 2 = c2
Solve for a.
14.
15.
s = π r l + π r2
Solve for l.
16. v =
𝑏𝑏1 + 𝑏𝑏2
2
�h
𝟒𝟒 𝝅𝝅 𝒓𝒓𝟑𝟑
Solve for b2
Solve for r.
𝟑𝟑
Simplify.
17.
√𝟐𝟐𝟐𝟐
20.
√𝟏𝟏𝟏𝟏 • √𝟔𝟔
18. √𝟏𝟏𝟏𝟏𝟏𝟏
21.
√𝟏𝟏𝟏𝟏 • 𝟑𝟑√𝟔𝟔
19.
22.
𝟓𝟓√𝟏𝟏𝟏𝟏
𝟕𝟕√𝟏𝟏𝟏𝟏 • 𝟐𝟐√𝟐𝟐𝟐𝟐
Recall that you can find a missing side of a right triangle by applying the Pythagorean Theorem.
Find the missing side of each right triangle. Leave your answers in simplest radical form. No decimals.
23.
c = ____________
24.
a = ____________
a
9
12
c
20
12
25.
b = ____________
26.
c = ____________
12
8
c
b
6
8
Solve each of the following by factoring or by using the quadratic formula.
27.
x2 – 9x + 18 = 0
28.
x2 – 20 = 8x
29.
2x2 + 5x + 2 = 0
30.
6x2 – 11x – 10 = 0