Honors Algebra 2 Summer Worksheet # 3&4.
I.
Due the first day of class.
Combine like terms (with fractions)
Like terms: have the same variable and exponent, when combining add or subtract
coefficients
Adding/Subtracting: Only add/subtract coefficients of like terms. EXPONENTS DO NOT
CHANGE!
 Ex: 3x 7  2 x 3  4 x 7  x 3 Add the numbers in front of x 7 : 3+4=7 Add the numbers in front of
x 3 : -2+1=-1 ANSWER: 7 x 7  x 3
Simplify each expression :
1) (x3 - 7x + 4x2 – 2) – (2x2 – 9x + 4)
2) (3a + 2b – 7c) + (6b – 4a + 9c)
3) (5y2 – 2xy + 6x2 – 3x + 7y – 9) + (3x2 – 4x + 5) – (5y2 – 3y + 6)
4)
5) 6(4 – 2x) – 7(-3x – 5)
6) Find the PERIMETER of the shape.
7 + 3x
3ab + 4a2
2a2
6b2 – 5ab
5x2 – 2
3b2
2x – 5 Perimeter
???
5x2 + 7x + 12
2
9x – 3y + 2
12 + 5x + 7y
7) Find the missing side of each shape.
2
2y – 3x - 3
3x + 9x
9ab + 8a2
Perimeter
9b – 2ab + 12a2 ???
2
4a2 – 4ab
7b2 – 2ab
5x2 – 3x + 2
Perimeter
14x2 + 4x – 8
Word Problems:
8) Bob mowed (2x2 + 5x – 3) yards on Monday, (4x – 7) yards on Tuesday, and (3x2 + 10) yards
on Wednesday.
a. How many yards did he mow in the three days?
b. If Bob mowed 14x2 + 12x – 3 yards total for the entire week, how many yards did
he mow during the rest of the week?
9) Molly has (4x + 10) dollars and Ron has (-5x + 20) dollars.
c. How much money do they have altogether?
d. How much more money does Molly have than Ron?
10) A triangle has a perimeter of 10a + 3b + 12 and has sides of length 3a + 8 and 5a + b, what
is the length of the third side?
11) For a rectangle with length of 3x + 4 and perimeter of 10x + 18, what is the width of the
rectangle?
12) A rectangle has a perimeter of 12y2 – 2y + 18 and has a width of 4y2 – y + 6. What is the
length of the rectangle?
13) Area of Rectangle = Length * Width, Area of Triangle = ½ *Base*Height
a. Find area of a rectangle with length of 5 and width of 3x – 5y + 6.
b. Find area of a triangle with base of 12 and height of 5a + 7b
???
II.
Order of Operations
PEMDAS
Simplify each of the following
14) 7  2  3
15)
1  23
16)
17)
7  48  3
18) 3 + 2 * 3 + 5
19)
( 7  4)  8  3
24)
20)
[18  3  6]
25) 2[5 + (30/ 6)2]
21)
(1  2)
3
7  4  ( 8  3)
26) 36/2 + 10*5 – 2-2+5
43  7 28  2 2

27)
54
23
22)
23) 2(5) + 3 ( 4+3)
28)
3  4  7  1  7 2 
III.
Laws of Exponents
Multiplying: Multiply coefficients, add exponents
 Ex: 5 y 2  3 y 5  15 y 7
Dividing: Divide coefficients, subtract exponents
 21a 2 b 3
 Ex:
7ab 6
1. Divide -21 and 7= -3
2. a : subtract the exponents 2-1= 1  a
3. b : subtract the exponents 3-6= -3  b 3
4. So far we have  3ab 3 . This is not the final answer because negative exponents are not simplified.
When given a negative exponentmove and make it positive. If the negative exponent is located in the
numerator move it to the denominator, if it is in the denominator then move it to the numerator. (Big –
 3a
little, write answer wherever big exponent was) ANSWER: 3
b
Zero: Anything to the zero power equals 1
 g0 1
 (2a 3bc 8 ) 0  1 The whole quantity has the power of zero.
  3x 0 y 2  3 y 2 Note: only x is raised to the zero power, so only x 0  1 the rest of the factor remains
29)
2 x 3n y 4
x 2n y 3
32)
3a 3 b 2
16a 2 b 3
v 3
30)  2
w
33) (2r 2 s 3 ) 3 (3rs 2 )
31) (a 3 b 3 )(ab) 2
34)
30a 2 b 6
60a 6 b 8
35)
x 3
y 2
 x2
36)  3
 3y



3
  3 x 4
37) 
2
 6y



1
IV.
FOIL
Simplify
Distribute: If possible always distribute first, then combine like terms.
 Ex: 2 x(3  4 x)  x(3x 2  1) Multiply what is on the outside of the parenthesis to each term on the inside
of the parenthesis. 6 x  8 x 2  3x 3  x Then combine like terms. The only like terms in this example are
6x and –x. ANSWER:  3x 3  8 x 2  5 x
Multiply: If given two polynomials, use FOIL or the box method to multiply.
 Ex: ( x  2)(3x  4) FOIL (First Outer Inner
Ex: (2 x  1)( x 2  3x  5) Foil or box
Last) or Box method:
+5
-3x
x2
x
+2
2x
 6x 2
3
3x
10 x
2x
6x
3x 2
+1
 3x
5
x2
+4
8
4x
Rewrite the contents of the box and then
Rewrite the contents of the box and combine
combine like terms.
like terms. 3x 2  6 x  4 x  8 ANSWER:
2 x 3  6 x 2  10 x  x 2  3x  5 Like terms in
3x 2  10 x  8
this example are  6x 2 and x 2 as well as 10 x
and  3x . ANSWER: 2 x 3  5 x 2  7 x  5
1)
(8a – 2b) (5a + 4b)
4)
(y - 5) (4y2 – 3y + 2)
2)
(3a + 4)(a2 – 12a + 1)
5)
(4y2 + 3y - 7) (2y2 - y + 8)
3)
(2b2 + 7b + 9)(b2 + 3b – 1)
6)
(2x - 5) (2x - 5)
Line #7
Equations of Lines
I.
Graphs: Sketch and write an equation
Once in slope intercept form, “b” is the
y-intercept, graph, then count rise over
run from initial ordered pair.
Write the equation of the line from the graph.
Line #8
EXAMPLE
Line #7: y-int =5, slope= up 1, left 3 to next ordered pair
1
Equation y   x  5
3
Line #9
Line #10
Graph the following.
7) 9y – 3x = 18
Line #11
11) 15 = -7x + 6y
8)
8x - 2y = 7
12) 9 = 4y – x
9)
14y – 35x = 63
13) 9x + 3y = 0
10) 21 = 7y – 2x
14) 5(7 – x) = y
Line #12
Line #13
II.
Ordered Pairs
Given two ordered pairs write the equation of the line. Find the slope (
) use this value
for m, choose one ordered pair for x and y values. Solve for b.
Find the Slope Intercept Form of the line through each of points.
15. (3, -5) and (6, 4)
4  5 9
m
 3
63 3
x = 3, y = -5
17. (0, -3) and (2, 0)
21. (6, 2) and (4, 4)
18. (2, -4) and (2, 6)
22. (4, 5) and (-3, -1)
 5  3( 3)  b
 14  b
y  3 x  14
19. (-4, -5) and (6, -1)
23. (-2, -7) and (8, 8)
16. (-2, 20) and (2, 4)
III.
20. (3, -3) and (1, -3)
Parallel/Perpendicular
Parallel Lines  SAME SLOPE
 To find slope the equation must be in slope intercept form y  mx  b (solve for y)
 Use given information: new ordered pair, y intercept, slope.
Perpendicular Lines  OPPOSITE RECIPROCAL (change the sign and flip the fraction)








1
5
3
4
Ex:  4
3
Ex: -5 
To find slope the equation must be in slope intercept form y  mx  b (solve for y)
Use given information: new ordered pair, y intercept, new slope. SPECIAL CASES:
Vertical lines have a slope that is undefined (x coordinates are the same)
Ex: x=3
Horizontal lines have zero slope (y coordinates are the same)
Ex: y=-2
24. A highway is being built parallel to the train tracks. The equation of the line for the tracks is
3x - 7y =11, what is the slope of the highway?
25. The equation of a line containing one side of a parallelogram is 2x + 5y = 8. The opposite side
contains the point (0, -4). What is the equation of the line that contains the opposite side?
26. On a map, K street is perpendicular to 5th Street. The equation y = -5x +1 represents 5th street.
What is the equation of K street if it passes through (4, 9)?
27. The line passing through points (3, 5) and (x, -2) is perpendicular to a line with a slope of -2.
What is the value of x?
Write a linear equation parallel AND perpendicular to the given equation, through the given point.
28) (9, 2), y = x + 5
29) (- 2, 5), y = - 4 x + 2
30) (- 3, 4), 3y = 2x – 3
31) (- 1, - 4), 9 x + 3 y = 8
32) (0, - 1), 2 x – y = 3
33) (- 2, 7),
34) (4, - 3),
35) (- 5, 0), x = 2
36) (4, -2) 3x – 5y = 15
y = 10
x=5