Download Honors Algebra II Pre-Test

Name _____________________________
Aledo High School
Pre-AP Geometry Summer Assignment 2016-2017
Pre-AP Geometry is a rigorous critical thinking course. Our expectation is that each student is fully
prepared. Therefore, the following Algebra 1 concepts must be mastered prior to beginning Pre-AP
Geometry.
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Solving linear equations
Graphing linear equations
Finding slope from ordered pairs and/or linear equations.
Writing equations of lines in slope-intercept, point-slope and standard forms
Solving systems of equations
Multiplying binomials
Factoring
Solving quadratic equations by factoring and with Quadratic Formula
Simplifying, multiplying, and adding radicals
Solving right triangles using the Pythagorean Theorem
Multiplying, dividing, adding and subtracting expressions with exponents, take a power to a
power, simplifying expressions with negative exponents
Adding, subtracting, multiplying, dividing, and simplifying fractions
Solving literal equations
Be prepared to turn in this assignment on the first day of school. You are expected to show all of your
work in a clear and organized manner. I have included the correct answers on Page 8 of this packet so
that you may check your answers as you work through the assignment. Aledo ISD staff will not be
available for tutoring during the summer so you may need to look up some vocabulary through Google
or other resources. You may also use the hints and examples that have been provided on Pages 9-10 of
this packet.
A test over these concepts will take place during the first week of school,
and you will not be allowed to use a calculator to complete it.
Please leave answers in simplified radical form or improper fractions (no decimals).
I look forward to meeting you in August!
Gena Berry
Aledo High School
Pre-AP Geometry
1
This assignment should be completed without the use of a calculator.
All work must be shown to receive credit.
Solve. Use improper fractions where appropriate. (No decimals or mixed numbers).
1. 4(3n + 5) – 2(2 – 4n) = 6 – 2n
2. 3x – 12 – 5x = 5 – 6x – 9
3.
2
1
x 7
3
6
5. 2(4x) – (x – 1) = 2 (1 – x)
4.
2 3
7 2
 x  x
15 5
15 3
6.
2
5 1
a  a4
3
6 2
2
Graph each line:
2
7. y =  x – 3
5
8. 3x – 2y = 12
10
y
x
-10
y
10
10
x
-10
10
-10
-10
9. y = 3
10. x = -1
5
y
5
y
x
-5
5
x
-5
-5
5
-5
Find the slope of each line:
11. y = -2x – 4
12. a horizontal line
13. a vertical line
14. y = -x
15. The line passing through A (-2, 3) and B (2,-4)
3
Write the equation of the line described. Show all equations in slope-intercept form.
16. Slope 2, y intercept –4
17. Passing through the points (-1,3) and (5, 7)
18. With undefined slope, passing through (2, 1)
3
19. Slope  , passing through the point (5, -2)
5
Solve each system of equations using addition (elimination) or substitution.
20. 2x – 3y = 8
21. 3y – 2x = 4
x + y= 4
1
(3y – 4x) = 1
6
22. 5x – 2y = 3
2x + 7y = 9
23. 2x – 3y = 1
3x + 5y = 11
4
Multiply.
24. (x – 3) (x + 7)
25. ( 2x – 1)(5x + 3)
26. (x + 8) 2
27. (2x – 3) 2
28. (x – 2) (x + 2)
29. (7m – 1)(2m – 3)
Factor.
30. a 2 + 9a + 18
31. 2a 2 + a – 15
32. 3y 2 – 14y – 24
33. b 2 – 8b + 16
34. x 2 – 81
35. 16p 2 – 25
Solve by factoring.
36. 3x 2 + 13x – 10 = 0
37. 2a 2 + 5a = -4(a + 1)
38. a2 – 4a = 21
5
Solve using the Quadratic Formula. Give exact answers in simplified radical form.
39. a 2 – 3a – 6 = 0
40. 2a 2 + 5a + 1 = 0
Simplify.
41. 45
42. 3 72
43. 5 32
44. 7 3  3 3
45. 3 6  24
46. 7 8  5 2
Use the Pythagorean Theorem to find the value of the variable. Give exact answers in simplified
radical form.
47.
48.
y
2
x
2
4
49. In little league baseball, the distance of the paths between each pair of consecutive bases is 60
feet and the paths form right angles. How far does the ball need to travel if it is thrown from
home plate directly to second base?
6
Simplify. Use only positive exponents in your answers.
50. a5  a  a-2
16x 2 y
51.
2xy
52. (2n)4  (3n)2
54. 40 𝑐 −3
53. (3x2y)2  (-4xy3)
55. (
2𝑥𝑦 4
𝑥2
3
)
56. Find the area and perimeter of the rectangle.
A = __________________
(2a)2
P = __________________
(3b2)3
Solve each literal equation for the stated variable.
57. Solve P = 2l + 2w for w
59. Solve V   r 2h for h
58. Solve A =
1
bh for h
2
9
60. Solve F = C + 32 for C
5
7
ANSWERS:
Page 2
5
1. 11
2. 2
43
3.
4
4. –5
1
5.
9
6. – 19
Page 3
7.
11. –2
12. 0
13. Undefined
14. –1
7
15. 4
Page 4
16. y = 2x – 4
2
17. 𝑦 = 3 𝑥 +
1
1
-10
y
1
43. 20 2
20. (4, 0)
2
21. (-1, )
3
22. (1, 1)
23. (2, 1)
5
5
x
y
5
-
48. 14
49. 60 2 ft.
25. 10x 2 + x – 3
26. x 2 + 16x + 64
52. 144n 6
27. 4x 2 – 12x + 9
53. -36x 5 y 5
28. x 2 – 4
54.
29. 14m – 23m + 3
30. (a + 6)(a + 3)
31. (2a – 5)(a + 3)
32. (3y + 4)(y – 6)
y
-
10.
47. 2 5
2
-
9.
45. 5 6
46. 140
50. a 4
51. 8x
24. x + 4x – 21
1
44. 4 3
Page 7
2
-
5  17
4
3
Page 5
x
40.
42. 18 2
3
x
3  33
2
11
19. 𝑦 = − 5 𝑥 + 1
y
39.
41. 3 5
18. x = 2
-10
8.
Page 6
5
x
33. (b – 4) 2
34. (x – 9)(x +9)
35. (4p – 5)(4p + 5)
2
36. x = or x = -5
3
1
37. a = -4 or a = 
2
38. a = 7 or a = -3
55.
𝟏
𝒄𝟑
𝟖𝒚𝟏𝟐
𝒙𝟑
56. A = 108a 2 b 6
P = 8a 2 + 54b 6
P  2l
57. w 
2
2A
58. h 
b
V
59. h  2
r
5
60. C  F  32 
9
-
8
NEED HELP?
Here are some examples and hints that might point you in the right direction.
Solving Linear Equations
Multiplying everything by the common denominator & cancelling will get rid of any
pesky fractions! Then, you can solve the equation the way you normally would.
Slope & Equations of Lines
Slope-Intercept Form
y = mx +b
(m = slope, b = y-intercept)
y 2  y1
x 2  x1
Slope Formula
m=
Horizontal Lines
Vertical Lines
Slope = 0
(y = #)
Slope is Undefined. (x = #)
Solving Systems of Linear Equations
Elimination (Addition)
x+y=7
2x + y = 5
Add the equations:
 -2x – 2y = -14
 2x + y = 5
-y = -9
y=9
Plug the value of x into one of the
equations:
-2(x + y = 7)
2x + y = 5
Substitution
x+y=7
2x + y = 5
Solve one equation for a single
variable:
x + y = 7  y = -x +7
Plug the expression for y into the
other equation and solve for x.
x + (9) = 7
x = -2
2x + (-x +7) = 5
2x – x + 7 = 5
x+7=5
x = -2
Solution: (-2, 9)
Solution: (-2, 9)
(-2) + y = 7
y=9
Factoring Review
Multiplying Polynomials
Perfect Square
(a+b)2 = (a+b)(a+b) = a2 + 2ab + b2
Trinomials
(a-b)2 = (a-b)(a-b) = a2 – 2ab + b2
F.O.I.L.
9
Factoring (Special Case)
Factoring a Difference a2 – b2 = (a + b)(a – b)
of Squares
Quadratic Formula
For the quadratic equation 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 = 𝟎
𝒙=
−𝒃±√𝒃𝟐 −𝟒𝒂𝒄
𝟐𝒂
Simplifying Radical Expressions
Examples:
Pythagorean Theorem
In a right triangle, the square of the length of the hypotenuse is equal to the
sum of the squares of the lengths of the legs.
Properties of Exponents
Examples:
a.
𝑥 2 ∙ 𝑥 5 = 𝑥 (2+5) = 𝑥 7
b. (2𝑥𝑦)3 = 23 ∙ 𝑥 3 ∙ 𝑦 3 = 𝑥 2+5 = 8𝑥 3 𝑦 3
c.
(𝑦 4 )5 = 𝑦 4∙5 = 𝑦 20
d.
e.
(4) = 43 = 64
𝑧 3
𝑧3
𝑧3
f.
𝑚9
20𝑥 2 𝑦 −4 𝑧 5
4𝑥 4 𝑦𝑧 3
= 𝑚9−6 = 𝑚3
𝑚6
20
=
4
5𝑧 2
𝑥 (2−4) 𝑦 (−4−1) 𝑧 (5−3) = 5𝑥 −2 𝑦 −5 𝑧 2 = 𝑥 2 𝑦 5
10