Page 1 of 17
Post Algebra 2 Summer Packet
Simplify.
1. −5 + 8 − 9
2. −36 + (−11)
Evaluate each expression for the given value of the variable.
6( s − 2) − 4( s + 1)
;s = 3
3s + 1
3. −a2 + 4a − 17; a = 5
4.
5. 12x − 9(x − 1); x = 2
6. c(3 − a) − c2; a = 4, c = −1
Simplify by combining like terms.
7. 4m − 7n − 2m + 6n
9. t +
t2 2
+t +t
2
8.
1 2
( x + 6 y ) − (4 y − x 2 )
2
10. x(x − y) + y(y − x)
Solve each equation.
11. 4w − 17 = 3w − 11
13. 7h − 4 = 5h + 16
12. 3r + 3.7 = 5r − 2.5
14. 5(w + 2) − 11 = 2w + (9 − 7w)
Page 2 of 17
Post Algebra 2 Summer Packet
15. 3(5t + 2) = 36
16. 2(5d + 13) − 14 = 8
17. 7(a + 5) − 12 = 3(a + 2)
1
7


18. 3  x −  = 5  x +  + 4 x − 1
2
2


Solve each equation for x. State any restrictions on the variables.
19. tx − ux = 3t
20.
21. a(x + c) = b(x − c)
22.
x−3
+3= a
6
x+3 2
=t
t
Solve each formula for the indicated variable.
23. R =
1
(r1 + r2 ), for r2
2
25. S = ℓw + wh + ℓh, for w
24. P = 2ℓ + 2w, for ℓ
26. S = L(1 − r), for r
Page 3 of 17
Post Algebra 2 Summer Packet
Write an equation and solve each problem.
27. The length of a rectangle is 5 cm greater than its width. The perimeter is 106 cm. Find the dimensions of
the rectangle.
28. Two buses leave Dallas at the same time and travel in opposite directions. One bus averages 58 mi/h, and
the other bus averages 52 mi/h. When will they be 363 mi apart?
Solve each inequality. Graph the solutions on a number line.
29. 3m + 7 ≥ 4
30. 5 − 6x < 7
31. 10 − x ≥ −2(3 + x)
32. 2y + 3 < 3y − 5
Solve each compound inequality. Graph the solutions.
33. −1 < 5 − 4x < 11
34. 3x − 1 ≤ 5 or 2x − 4 ≥ x
35. −3t ≤ 12 and −2t > −6
36. −5 < 2x + 5 < 3
Page 4 of 17
Post Algebra 2 Summer Packet
Solve each equation. Check for extraneous solutions on a number line.
37. 2x + 3 = 5
38. x + 6 = 2x
39. 3x + 6 = −12
40. 5x + 1 + 6 = 21
Suppose f(x) = 3x –4 and g(x) = | x | + 3. Find each value.
1. ƒ(2)
1
2. f   + g (−2)
3
3.
f (1)
g (1)
Find the slope of each line.
5.
3x − 5y = 15
7. through (6, 1) and perpendicular to y =
8.
6.
through (−2, 7) and (4, 1)
3
1
x+
2
4
9. 5x − y = −7
Write in slope-intercept form the equation of the line with the given slope through the given point.
Page 5 of 17
Post Algebra 2 Summer Packet
1 
10. slope = 6;  , 2 
2 
11. slope =
1
; (4, 3)
4
12. slope = −2; (0, 0)
Write in slope-intercept form the equation of the line through each pair of points.
13. (0, 0) and (−2, 3)
14. (1, 5) and (−3, 3)
15. (−4, 1) and (−2, −2)
Write in point-slope form the equation of the line through each pair of points.
16. (0, 1) and (3, 0)
1 2
 3 5
17.  ,  and  − , 
2 3
 2 3
18. (−3, −2) and (1, 6)
Write an equation for each line. Then graph the line on the graphs below.
19. through (−1, 3) and parallel to y = 2x + 1
3
20. through (2, 2) and perpendicular to y = − x + 2
5
21. through (−3, 4) and vertical
Page 6 of 17
Post Algebra 2 Summer Packet
22. through (4, 1) and horizontal
Solve each system using substitution or elimination.
1.
 y = 2x + 8

 y = 3x − 1
2.
2 x − y = 2

2 x − 2 y = 4
3.
− x + y = 2

 2 x + y = −1
4.
y = x − 2

 x + y = 10
5.
y = 7 − x

 x + 3 y = 11
6.
 x − 2 y = 10

 y = x − 11
7.
y = x +3

5 x + y = 9
8.
 5x + 4 y = 2

 −5 x − 2 y = 4
9.
 y = 2x + 3

5 x − y = −3
Page 7 of 17
Post Algebra 2 Summer Packet
14 x + 2 y = 10
10. 
 x − 5 y = 11
2 y = −4 x
11. 
4 x + 2 y = −11
2 x − 5 y = 11
12. 
4 x + 10 y = 18
Factor each expression completely.
1. x2 + 4x + 4
2. x2 – 7x + 10
3. x2 + 7x – 8
4. x2 – 6x
5. 2x2 – 9x + 4
6. x2 + 2x – 35
7. x2 + 6x + 5
8. x2 – 9
9. x2 – 13x – 48
10. x2 – 4
11. 4x2 + x
12. x2 – 29x + 100
13. x2 + 5x – 24
14. x2 – x – 72
15. 4x2 – 4x – 15
Page 8 of 17
Post Algebra 2 Summer Packet
16. 2x2 – 5x – 7
17. x2 – 11x
18. 10x2 – 17x + 3
Graph each quadratic function on the graphs below. Identify the axis of symmetry and the coordinates of
the vertex.
1. y = x2 + 5
3. y = –x2 + 7x – 2
Simplify each expression.
2. y = x2 – 4x – 3
Page 9 of 17
Post Algebra 2 Summer Packet
4. (3 + i) – (7 + 6i)
6.
(–4 – 9i) + (5 – 7i)
8.
(
−9 − 2
)(
)
−4 + 1
5.
(3 – 4i)(5 + 2i)
7.
3 −25 + 4
9.
(5i + 4) – (4i – 3)
Solve each quadratic equation by taking square roots, factoring, or quadratic formula.
10. x2 – 16 = 0
11. 2x2 – 3x – 11 = 0
12. x2 + 3x – 10 = 0
13. 3x2 + 48 = 0
14. x2 – 5x + 4 = 0
15. 2x2 – x + 1 = 0
16. 3x2 + 5x = 2
17. 2x2 – 3x = –1
Page 10 of 17
Post Algebra 2 Summer Packet
18. x2 – 144 = 0
19. x2 – 6x – 7 = 0
20. 5x2 = 15x
21. 2x2 + 5 = 11x
Write each polynomial in standard form. Then classify it by degree and number of terms.
1. 4x4 + 6x3 − 2 − x4
2. 9x2 − 2x + 3x2
3. 4x(x − 5)(x + 6)
Write a polynomial function with rational coefficients in standard form with the given zeros.
4.
2, 3, 5
5.
−1, 0, 1
For each function, determine the zeros and their multiplicity.
6.
y = (x − 1)2(2x − 3)3
7.
y = (3x − 2)5(x + 4)2
8.
y = 4x2(x + 2)3(x + 1)
Page 11 of 17
Post Algebra 2 Summer Packet
Solve each equation.
9.
(x − 1)(x2 + 5x + 6) = 0
10. x3 − 10x2 + 16x = 0
11. (x + 2)(x2 + 3x − 40) = 0
12. x3 + 3x2 − 54x = 0
13. x3 − 27 = 0
14. x4 − 5x2 + 4 = 0
15. x4 − x = 0
16. x4 − 81 = 0
Divide using long division.
17. (x3 + 9x2 + 26x + 24) ÷ (x + 4)
18. (2x3 − 11x2 + 2x + 15) ÷ (x + 1)
Page 12 of 17
Post Algebra 2 Summer Packet
Divide using synthetic division.
19. (x3 + 5x2 − x + 1) ÷ (x + 2)
20. (3x3 − x2 + 2x − 5) ÷ (x − 1)
Simplify each radical expression. Use absolute value symbols as needed.
1.
4.
3
400x 2 y 6
2.
64a 6b 2
5.
3
−125a9
3.
4 81x5 y 9
50 s 2t 4
6.
4
Simplify each expression. Rationalize all denominators. Assume that all
positive.
256x16 y 28
variables are
Page 13 of 17
Post Algebra 2 Summer Packet
200 x3 y
7.
2 xy 5
8 x 3 ⋅ 2 x5
10.
8.
(8 − 3 2 )(8 + 3 2 )
9.
1
3+5
11.
63 + 2 28 − 5 7
12.
2
1+ 2
Simplify each expression. Assume that all variables are positive.
3
 16 x5 y10  4
13. 
 81xy 2 


14. (−64)
− 23
2
1
15. a 3 ⋅ a 2
Solve each equation. Check for extraneous solutions.
16.
18.
3
x−3 =1
17.
x+7 =x+1
3x − 8 = 2
19. (2 x + 1) 3 = 3
1
Page 14 of 17
Post Algebra 2 Summer Packet
20.
4
x2 − 5 = 4
21. 3( x + 1) 3 = 48
Let ƒ(x) = x2 + 5 and g(x) = x – 7. Perform each function operation.
the domain of each.
22.
f ( x)
g ( x)
23. ƒ(x) − 2g(x)
24. ƒ(x) ⋅ g(x)
For each pair of functions, find f(g(x)) and g(ƒ(x)).
25. ƒ(x) = 3x + 5, g(x) = x2 + 1
27. f(x) =
2 x − 1 , g(x) = 5x + 3
26. ƒ(x) = x2 − 5x + 2, g(x) = 2x
28. ƒ(x) = −2x2, g(x) = x + 4
Then find
Page 15 of 17
Post Algebra 2 Summer Packet
Let ƒ(x) = 5x – 4 and g(x) = x2 – 1. Find each value.
29. g(ƒ(−1))
30. f(g(2))
31. g(ƒ(0))
Give the parent function and describe the transformations for each function listed below.
32. y = | x + 3 | − 2
33. y = | x | + 2
34. ƒ(x) = (x + 2)2 − 4
35. ƒ(x) =
36. y = | x − 4 |
37.
3
x+2
9 x − 63 + 4
Simplify each expression.
1.
x2 − 5x
x 2 − 25
2.
x2 − 5x
x 2 − 25
Page 16 of 17
Post Algebra 2 Summer Packet
3.
5.
3x3
x 2 − 25
⋅
x2 + 6 x + 5
x+2
x + 4x + 4
2
x2
+
2
x+2
2
7. x
3
y
9.
4.
x 2 − 3x − 10
2 x 2 − 11x + 5
÷
x2 − 5x + 6
2 x2 − 7 x + 3
6.
8.
x+2
x + 4x + 4
2
1+
+
2
x+2
2
3
4
9
3
+ 4x
x−9
10. 3 −
1
x +5
2
Solve each equation. Check each solution.
11. 1 =
x
2
x+3
12.
3x 5x +1
=
4
3
Page 17 of 17
Post Algebra 2 Summer Packet
13.
x −1 x
=
6
4
14.
15.
7 7x
= −4
2 8
16. 4 +
17.
1
5
1
+ 2
=
2x + 2 x −1 x −1
18.
19.
2 3x − 1 5
+
=
3
6
2
20.
4 x
=
x 4
2y
8
=
y −5 y −5
2y 2 y 1
+ = −
5 6 2 6
7
x − 5x
2
+
2
3
=
x 2 x − 10