Download Honors Algebra 2 Summer Work

Summer Review
for Students
Entering
Algebra 2 Honors
Name: ________________________ Class: ___________________ Date: __________
ID: A
Honors Algebra 2 Addendum to Summer Packet
These problems are for students entering Algebra 2 Honors only.
Show all work in the space provided.
1. Evaluate
3x − y
if x = 5 and y = −3
3(x − y)
5. Express algebraically and solve:
The product of 3 and a number, decreased by 8,
is the same as twice the number, increased by
15. Find the number.
2. Multiply (−x)(−3y)(−5z)
3. Solve 3(x + 2) =
1
(12x + 4) − 5x
4
.
.
6. Use an algebraic process to find four consecutive
odd integers whose sum is 464.
4. Solve the equation.
y+1
2
1
y + (y − 4) =
5
2
4
.
.
1
Name: ________________________
ID: A
Ê 2y ˆ Ê y ˆ Ê y + 3 ˆ˜
˜˜
7. Simplify: ÁÁÁ x ˜˜˜ ÁÁÁ 2x ˜˜˜ ÁÁÁ x
Ë ¯Ë
¯Ë
¯
11. Expand (3x − 7) 2
.
8.
5x −3 y 2
x 5 y −1 z 0
⋅
(2xy 3 ) −2
xy
.
12. Multiply
ÁÊÁ x 2 + x − 3 ˜ˆ˜ ÁÊÁ 3x 2 − x + 3 ˜ˆ˜
Ë
¯Ë
¯
.
9. Subtract (−3g 2 + 2g − 9) from (g 2 − 4g − 6)
.
13. Simplify
.
10. Multiply (6n − 3)(5n − 7)
.
.
2
18xy 3
7a 2 b 2
÷
12x 2 y
35a 2 b
Name: ________________________
ID: A
15. Factor completely
14. Factor completely
a) −5x 4 y 2 + 20xy 3 + 15xy 4
a) a 2 − 6a − 40
b) 6y 2 + 13y − 5
b) 3x 3 + x 2 − 15x − 5
c) 12m3 n − 75mn
c) 20x 2 − 125y 2
d) 49x 2 − 100y 2
d) 4x 2 − 12xy + 9y 2
e) 6xp + 42x − 5yp − 35y
.
3
Name: ________________________
ID: A
17. Solve the equation.
16. Solve each equation:
|3x − 5| = 7
a) n(9 − 3n)(2n + 5) = 0
b) x 2 + 8x − 20 = 0
.
18. Solve the inequality. Graph the solution on a
number line.
|3x + 9| ≥ 6
c) 20x(x − 1) = 42 − 9x
d) −8x 2 + 46x − 30 = 0
.
19. Solve and graph your answer on a real number
line: |x − 3 | − 2 < 6
e)
3x 2 − 6x = 10
4
Name: ________________________
20. Simplify
ID: A
23.
6y + 30
Find the value of x in each problem.
2
y − 25
a)
.
21. Simplify
a2 − x2
a
⋅
2
3x − 3a
a
b)
.
.
22. Find the value of x. Then, find the perimeter of
the triangle.
24. The area of a triangle is 72 in2 and the base is 8
in. Find the height.
.
5
Name: ________________________
ID: A
26. Find the slope of:
25. Graph the line of each equation:
a) x + 3y = 6
a) a line passing through (-4, 4) and (2, -5)
b) a line parallel to y = 2x + 7
c) the line whose equation is 2x − 3y = 12
b) y = −2x + 4
d) the line whose equation is y = −5
e) a line perpendicular to 6x + 5y = 9
.
27. Determine whether the lines are parallel,
perpendicular, or neither. Explain your reasoning.
c) x = 3
2x + 3y = 12
3x + 2y = 24
6
Name: ________________________
ID: A
30. Solve the system of equations by graphing.
28. Find an equation, in point-slope form, of the line
that satisfies the given conditions.
2x + 3y = −27
11x − 3y = −12
Through (–1, –11); perpendicular to the line
passing through (3, 1) and (7, –1).
Then, rewrite the equation in standard form.
.
29. Solve the system of equations by substitution
8x − 2y = 10
3x − y = 9
.
31. Solve the system of equations by elimination
2x − 3y = 6
9y − 6x = 9
7
Name: ________________________
ID: A
34. Express algebraically and solve:
32. Solve they system of equations by any method.
0.6x + 1.6y = 2.8
An orange has 15 calories more than a
grapefruit. Twenty oranges and ten grapefruits
have 1800 calories together. Jim ate three
oranges and half a grapefruit. How many
calories did Jim eat?
−0.05x + 0.08y = −0.02
.
33. Solve the system of equations by any method.
.
5
1
2
x+ y=
6
4
3
35. Find the solution set for the following system of
inequalities.
1
−1
1
x−
y=
10
10
5
x + 2y ≤ −4
3x − 2y > −4
.
8
ID: A
Honors Algebra 2 Addendum to Summer Packet
Answer Section
CASE
1. 3 / 4
2. −15xyz
3. x = −1
45
4. y =
13
5. n = 23
6. 113, 115, 117, 119
7. 2x
8.
4y + 3
5
11
4x y 4
9. 4g 2 − 6g + 3
10. 30n 2 − 57n + 21
11. 9x 2 − 42x + 49
12. 3x 4 + 2x 3 − 7x 2 + 6x − 9
15y 2
2bx
14. a) (a − 10) (a + 4)
b) ÁÊË 3y − 1 ˜ˆ¯ ÁÊË 2y + 5 ˜ˆ¯
13.
c) 3mn (2m − 5) (2m + 5)
d) ÊÁË 7x − 10y ˆ˜¯ ÊÁË 7x + 10y ˆ˜¯
e) ÊÁË 6x − 5y ˆ˜¯ ÊÁË p + 7 ˆ˜¯
Ê
ˆ
15. a) 5x ⋅ y 2 ⋅ ÁÁ −x 3 + 4y + 3y 2 ˜˜
Ë
¯
ÊÁ 2
ˆ˜
b) (3x + 1) ⋅ Á x − 5 ˜
Ë
¯
c) 5(2x − 5y) ⋅ (2x + 5y)
2
d) ÊÁË 2x − 3y ˆ˜¯
−5
16. a) n = 0, 3, or
2
b) x = −10, 2
6
7
c) x = − ,x =
5
4
3
d) x = 5 or
4
e) x =
3±
39
3
1
ID: A
2
3
18. x ≤ −5 or x ≥ −1
17. x = 4,x = −
19. −5 < x < 11
20.
21.
22.
23.
24.
25.
6
y−5
a+x
−3a
x=12
P=102
a) x = 8
b) x = 4 5
h = 18in
a)
26. a) −
3
2
b) 2
b)
c)
2
3
d) 0
e)
c)
5
6
−2
−3
, m2 =
3
2
Since these slopes are neither equal nor opposite reciprocals, the lines are neither parallel nor perpendicular.
28. y + 11 = 2(x + 1)
27. m1 =
2x − y = 9
29. (-4, -21)
2
ID: A
30. ÊÁË −3, − 7 ˆ˜¯
31.
32.
33.
No solution.
(2, 1)
ÊÁ −4, − 7 ˆ˜
Ë
¯
34. 220 calories
35.
3