foundations of algebra 2 name: unit 1, day 1 combining
TRANSCRIPT
Foundations of Algebra 2 Name:
Unit 1, Day 1 – Combining Like Terms – Homefun Period: Date:
Simplify the following expressions completely. Must show all work to receive credit.
1. 2
3 2. 3( 2) 3. 25 4.
27 3 5.
3 21 6
6. (8x – 5) + (4x – 6) 7. (6t + 1)(t – 2) 8. (2k + 11) – (4 – 7k)
9 8 25 63 36
12 11x 26 11 2t t 9 7k
9. (x2 – x + 9) – (5x2 + 5x – 7) 10. (w + 4)(w – 6) 11. (3r – 5) 2
12. (2a – 4b)(a + 5b) 13. 4x2(3x2 – x + 2) 14. 2a – 3(a + 5)
15. (2a2 + 3)(5a2 – 2) 16. 2
3x 17. (2a – 5)(a2 – 4a + 1)
24 6 16x x 2 2 24w w 29 30 25r r
2 22 6 20a ab b 4 3 212 4 8x x x 15a
4 210 11 6a a 2 6 9x x 3 22 12 22 5a a a
Foundations of Alg 2 – Unit 1 – Day 2 Homefun Name:
Solving One Step Equations Date: Period:
Solve the equation, check your solution.
1. 9 2m 2. 3 5 a 3. 5 7t 4. 11 9b
5. 4 52q 6. 108 9 j 7. 187 17r 8. 142
m
9. 77
t
10. 3 1
4 8v 11.
318
2k 12.
8 4
5 15x
13. Describe and correct the error in solving the equation. 14. The rectangle has an area A. Write and solve
an equation to find the value of x.
254 inA
Both sides
should have
been multiplied
by 3
15. Find the value of b using the given information: 6.7 3.1 and 5a b a
7 8 12 2
13 12 11 28
49 5
812 1
6
81
Answer4.5 x inches
49
Foundations of Algebra 2 – Unit 1 – Day 3 Homefun Name:
Solving 2 Step Equations Date: Period:
Solve the equation, check your solution.
1. 3 7 19x 2. 5 4 19h 3. 7 1 13d 4. 2 13 3g
5. 10 7 m 6. 17 135
w 7. 9 11
2
b 8. 6 3
4
z
9. 5
7 86
c 10. 2
10 47
n 11. 8 3 44y y 12. 2 7 54p p
13. Describe and correct the error in solving the equation.
Unlike terms
were combined
4 3 2 8
3 20 40 12
18 21 4 6
5
4
Answer
Foundations of Algebra 2 – Unit 1 – Day 4 Homefun Name:
Solving Multiple Step Equations Date: Period:
Solve the equation, check your solution.
1. 12 14 10 80v v 2. 5 3 3 7a a 3. 9 7 13 21z z
4. 3 4 5 31z 5. 5 2 1 23m m 6. 27 3 3 6 2c c
7. 8 5 6 1 t t 8. 8 5 4 11 c c 9. 10 18 8 4 b b
10. 9 6 4 a a 11. 3 4 2 8 5 x x x 12. 15 7 3 3 7c c c
3 5 5
2 3 5
2 4 7
8 2 0
13. Find the value of x for the triangle. Perimeter 24 feet.
14. Find the perimeter of the square, write you answer in terms of x.
2 feet
28 20x
Foundations of Alg 2 – Unit 1 – Day 5 Homefun Name:
Solving Systems of Equations using Elimination Date: Period:
Find the solution to the following systems of equations.
1. –x + 2y = 12 and x + 6y = 20 2. x – y = 9 and x + y = 7
3. 2x + 5y = 14 and 4x + 5y = 8 4. x + 3y = 7 and 2x – 3y = –4
5. x + y = 1 and –x + 2y = –2 6. –3x – 2y = 6 and 3x – 2y = 6
7. Which x-coordinate is in the solution to the system of equations?
{−3𝑥 + 6𝑦 = −15
3𝑥 + 8𝑦 = 1
A. 𝑥 = −1 C. 𝑥 = 19
B. 𝑥 = 3 D. 𝑛𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛
4,4 8, 1
3,4 1, 2
4 1,
3 3
0, 3
Foundations of Alg 2 – Unit 1 – Day 6 Homefun Name:
Solving Systems of Equations using Elimination Date: Period:
Find the solution to the following systems of equations.
1. x – 5y = 0 and 2x – 3y = 7 2. 2x – 3y = 8 and –5x + 2y = 13
3. –5x + 8y = 21 and 10x + 3y = 15 4. x – y =9 and x + y = 7
5. 5x – 2y = –10 and 3x + 6y = 66 6. 5x + 3y = –10 and 3x + 5y = –6
7. 9x = 6y – 12 and x + 2y = 0 8. y = 9x – 35 and 5x + 8y = 28
9. Which of the following is the solution to the system: 2x 4y 5
3x 5y 9
a) (2, 2.25) b) (–2, 3)
c) (–0.5, 1) d) (0.5, 1.5)
8, 1
5,1
3,3
5
5, 6
2,10 2,0
11,
2
4,1
Foundations of Alg 2 – Unit 1 – Day 7 Homefun Name:
Period: Date:
Given the following information, find the domain and range for the following.
Find the domain and range of each function
Foundations of Algebra 2 Name: Unit 1, Day 8 – Notation – Homefun Period: Date:
Given the following graph, write the domain and range in inequality, set, and interval notation. Also,
describe using words.
1.
Words Inequality Set Interval
D All numbers between –6 and
9 Inclusively
6 9x | 6 9x x 6,9
R
All numbers between –4 and
1 Inclusively
4 1y | 4 1y y 4,1
5. You are trying to find the height and width of an image for a graphic design class seen to the right. Write the domain and range of
the following emoji in interval notation (round to the nearest integer).
Domain: 9,2
Range: 2,8
Foundations of Algebra 2 – Unit 1 – Day 9 Name: Date: Period:
Slope-Intercept Form of Equations Graph the following equations using the slope and y-intercept.
1. y = –2x + 3 2. y = 3
1x – 1 3. f(x) = x – 4
m = m = m =
b = b = b =
4. y = 3x 5. f(x) = 3
2x + 2 6. y = –2
m = m = m =
b = b = b =
2
3
1
3
1
1
4
3
0
3
2
2
0
2
7. f(x) = –2x 8. x = 2 9. y = x
m = m = m =
b = b = b =
2
0
undefined
none
1
0
Foundations of Algebra 2 – Homefun Name:
Unit 1 Day 10 Worksheet – Graph Piecewise Functions #1 Period: Date:
Evaluate the piecewise functions given the following domains.
5 1
3 1 1
x , if xh( x )
x , if x
1) when x = 1 2) for h(-3) 3) when x = -1
4) when x = 4 5) when 5
2x 6) g(-1) 7) (0)g
8)
2 0g( x ) x, if x
9) 3 0f ( x ) x , if x
2
1 31
2 4
1 1 4
3 4 4
x , if x
g( x ) x , if x
x , if x
2 2 4
4 1
2
0 1
10) 1
1 22
h( x ) x , if x
11) 4 1f ( x ) , if x
Foundations of Algebra 2 – Homefun Name:
Unit 1 Day 11 Worksheet – Graph Piecewise Functions #2 Period: Date:
Graph the following piecewise functions.
1) 1
2 3 0
0 g
x
x , if x( x )
x , if
2)
12 0
2
1
2
0
f x
x,
x , if x
(
if
)
x
3) 1
1 1
2
1h
x
x ,
x
if x( x )
, if
4) 3
1 3
14
3f xx
i
( )
,
, f
x
i x
f x
5)
13 2
2
2 2
g( x )
,
x, i x
i
f
f x
6) 3 1
14 2
1
2
4
2
f
x , if
(
x , i x
, i) fx
x
f
x