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- Big Ideas Math Algebra 1, 2015
- Big Ideas Math Algebra 1, 2013
- Big Ideas Math Algebra 1 Virginia
- Big Ideas Math Algebra 1 Texas
- Big Ideas Math Algebra 1 A Bridge to Success
- Core Connections Algebra 1, 2013
- Houghton Mifflin Harcourt Algebra 1, 2015
- Holt McDougal Algebra 1, 2011
- McDougal Littell Algebra 1, 1999
- McGraw Hill Glencoe Algebra 1, 2012
- McGraw Hill Glencoe Algebra 1, 2017
- McGraw Hill Glencoe Algebra 1 Texas, 2016
- Pearson Algebra 1 Common Core, 2011
- Pearson Algebra 1 Common Core, 2015
1.1 Real Numbers: Algebra Essentials
- ⓐ 11 1 11 1
- ⓒ − 4 1 − 4 1
- ⓐ 4 (or 4.0), terminating;
- ⓑ 0. 615384 ¯ , 0. 615384 ¯ , repeating;
- ⓒ –0.85, terminating
- ⓐ rational and repeating;
- ⓑ rational and terminating;
- ⓒ irrational;
- ⓓ rational and terminating;
- ⓔ irrational
- ⓐ positive, irrational; right
- ⓑ negative, rational; left
- ⓒ positive, rational; right
- ⓓ negative, irrational; left
- ⓔ positive, rational; right
- ⓐ 11, commutative property of multiplication, associative property of multiplication, inverse property of multiplication, identity property of multiplication;
- ⓑ 33, distributive property;
- ⓒ 26, distributive property;
- ⓓ 4 9 , 4 9 , commutative property of addition, associative property of addition, inverse property of addition, identity property of addition;
- ⓔ 0, distributive property, inverse property of addition, identity property of addition
- ⓒ 121 3 π 121 3 π ;
- ⓐ −2 y −2 z or −2 ( y + z ) ; −2 y −2 z or −2 ( y + z ) ;
- ⓑ 2 t −1 ; 2 t −1 ;
- ⓒ 3 p q −4 p + q ; 3 p q −4 p + q ;
- ⓓ 7 r −2 s + 6 7 r −2 s + 6
A = P ( 1 + r t ) A = P ( 1 + r t )
1.2 Exponents and Scientific Notation
- ⓐ k 15 k 15
- ⓑ ( 2 y ) 5 ( 2 y ) 5
- ⓒ t 14 t 14
- ⓑ ( −3 ) 5 ( −3 ) 5
- ⓒ ( e f 2 ) 2 ( e f 2 ) 2
- ⓐ ( 3 y ) 24 ( 3 y ) 24
- ⓑ t 35 t 35
- ⓒ ( − g ) 16 ( − g ) 16
- ⓐ 1 ( −3 t ) 6 1 ( −3 t ) 6
- ⓑ 1 f 3 1 f 3
- ⓒ 2 5 k 3 2 5 k 3
- ⓐ t −5 = 1 t 5 t −5 = 1 t 5
- ⓑ 1 25 1 25
- ⓐ g 10 h 15 g 10 h 15
- ⓑ 125 t 3 125 t 3
- ⓒ −27 y 15 −27 y 15
- ⓓ 1 a 18 b 21 1 a 18 b 21
- ⓔ r 12 s 8 r 12 s 8
- ⓐ b 15 c 3 b 15 c 3
- ⓑ 625 u 32 625 u 32
- ⓒ −1 w 105 −1 w 105
- ⓓ q 24 p 32 q 24 p 32
- ⓔ 1 c 20 d 12 1 c 20 d 12
- ⓐ v 6 8 u 3 v 6 8 u 3
- ⓑ 1 x 3 1 x 3
- ⓒ e 4 f 4 e 4 f 4
- ⓓ 27 r s 27 r s
- ⓕ 16 h 10 49 16 h 10 49
- ⓐ $ 1.52 × 10 5 $ 1.52 × 10 5
- ⓑ 7.158 × 10 9 7.158 × 10 9
- ⓒ $ 8.55 × 10 13 $ 8.55 × 10 13
- ⓓ 3.34 × 10 −9 3.34 × 10 −9
- ⓔ 7.15 × 10 −8 7.15 × 10 −8
- ⓐ 703 , 000 703 , 000
- ⓑ −816 , 000 , 000 , 000 −816 , 000 , 000 , 000
- ⓒ −0.000 000 000 000 39 −0.000 000 000 000 39
- ⓓ 0.000008 0.000008
- ⓐ − 8.475 × 10 6 − 8.475 × 10 6
- ⓑ 8 × 10 − 8 8 × 10 − 8
- ⓒ 2.976 × 10 13 2.976 × 10 13
- ⓓ − 4.3 × 10 6 − 4.3 × 10 6
- ⓔ ≈ 1.24 × 10 15 ≈ 1.24 × 10 15
Number of cells: 3 × 10 13 ; 3 × 10 13 ; length of a cell: 8 × 10 −6 8 × 10 −6 m; total length: 2.4 × 10 8 2.4 × 10 8 m or 240 , 000 , 000 240 , 000 , 000 m.
1.3 Radicals and Rational Exponents
5 | x | | y | 2 y z . 5 | x | | y | 2 y z . Notice the absolute value signs around x and y ? That’s because their value must be positive!
10 | x | 10 | x |
x 2 3 y 2 . x 2 3 y 2 . We do not need the absolute value signs for y 2 y 2 because that term will always be nonnegative.
b 4 3 a b b 4 3 a b
14 −7 3 14 −7 3
- ⓒ 88 9 3 88 9 3
( 9 ) 5 = 3 5 = 243 ( 9 ) 5 = 3 5 = 243
x ( 5 y ) 9 2 x ( 5 y ) 9 2
28 x 23 15 28 x 23 15
1.4 Polynomials
The degree is 6, the leading term is − x 6 , − x 6 , and the leading coefficient is −1. −1.
2 x 3 + 7 x 2 −4 x −3 2 x 3 + 7 x 2 −4 x −3
−11 x 3 − x 2 + 7 x −9 −11 x 3 − x 2 + 7 x −9
3 x 4 −10 x 3 −8 x 2 + 21 x + 14 3 x 4 −10 x 3 −8 x 2 + 21 x + 14
3 x 2 + 16 x −35 3 x 2 + 16 x −35
16 x 2 −8 x + 1 16 x 2 −8 x + 1
4 x 2 −49 4 x 2 −49
6 x 2 + 21 x y −29 x −7 y + 9 6 x 2 + 21 x y −29 x −7 y + 9
1.5 Factoring Polynomials
( b 2 − a ) ( x + 6 ) ( b 2 − a ) ( x + 6 )
( x −6 ) ( x −1 ) ( x −6 ) ( x −1 )
- ⓐ ( 2 x + 3 ) ( x + 3 ) ( 2 x + 3 ) ( x + 3 )
- ⓑ ( 3 x −1 ) ( 2 x + 1 ) ( 3 x −1 ) ( 2 x + 1 )
( 7 x −1 ) 2 ( 7 x −1 ) 2
( 9 y + 10 ) ( 9 y − 10 ) ( 9 y + 10 ) ( 9 y − 10 )
( 6 a + b ) ( 36 a 2 −6 a b + b 2 ) ( 6 a + b ) ( 36 a 2 −6 a b + b 2 )
( 10 x − 1 ) ( 100 x 2 + 10 x + 1 ) ( 10 x − 1 ) ( 100 x 2 + 10 x + 1 )
( 5 a −1 ) − 1 4 ( 17 a −2 ) ( 5 a −1 ) − 1 4 ( 17 a −2 )
1.6 Rational Expressions
1 x + 6 1 x + 6
( x + 5 ) ( x + 6 ) ( x + 2 ) ( x + 4 ) ( x + 5 ) ( x + 6 ) ( x + 2 ) ( x + 4 )
2 ( x −7 ) ( x + 5 ) ( x −3 ) 2 ( x −7 ) ( x + 5 ) ( x −3 )
x 2 − y 2 x y 2 x 2 − y 2 x y 2
1.1 Section Exercises
irrational number. The square root of two does not terminate, and it does not repeat a pattern. It cannot be written as a quotient of two integers, so it is irrational.
The Associative Properties state that the sum or product of multiple numbers can be grouped differently without affecting the result. This is because the same operation is performed (either addition or subtraction), so the terms can be re-ordered.
−14 y − 11 −14 y − 11
−4 b + 1 −4 b + 1
43 z − 3 43 z − 3
9 y + 45 9 y + 45
−6 b + 6 −6 b + 6
16 x 3 16 x 3
1 2 ( 40 − 10 ) + 5 1 2 ( 40 − 10 ) + 5
irrational number
g + 400 − 2 ( 600 ) = 1200 g + 400 − 2 ( 600 ) = 1200
inverse property of addition
1.2 Section Exercises
No, the two expressions are not the same. An exponent tells how many times you multiply the base. So 2 3 2 3 is the same as 2 × 2 × 2 , 2 × 2 × 2 , which is 8. 3 2 3 2 is the same as 3 × 3 , 3 × 3 , which is 9.
It is a method of writing very small and very large numbers.
12 40 12 40
1 7 9 1 7 9
3.14 × 10 − 5 3.14 × 10 − 5
16,000,000,000
b 6 c 8 b 6 c 8
a b 2 d 3 a b 2 d 3
q 5 p 6 q 5 p 6
y 21 x 14 y 21 x 14
72 a 2 72 a 2
c 3 b 9 c 3 b 9
y 81 z 6 y 81 z 6
1.0995 × 10 12 1.0995 × 10 12
0.00000000003397 in.
12,230,590,464 m 66 m 66
a 14 1296 a 14 1296
n a 9 c n a 9 c
1 a 6 b 6 c 6 1 a 6 b 6 c 6
0.000000000000000000000000000000000662606957
1.3 Section Exercises
When there is no index, it is assumed to be 2 or the square root. The expression would only be equal to the radicand if the index were 1.
The principal square root is the nonnegative root of the number.
9 5 5 9 5 5
6 10 19 6 10 19
− 1 + 17 2 − 1 + 17 2
7 2 3 7 2 3
20 x 2 20 x 2
17 m 2 m 17 m 2 m
2 b a 2 b a
15 x 7 15 x 7
5 y 4 2 5 y 4 2
4 7 d 7 d 4 7 d 7 d
2 2 + 2 6 x 1 −3 x 2 2 + 2 6 x 1 −3 x
− w 2 w − w 2 w
3 x − 3 x 2 3 x − 3 x 2
5 n 5 5 5 n 5 5
9 m 19 m 9 m 19 m
2 3 d 2 3 d
3 2 x 2 4 2 3 2 x 2 4 2
6 z 2 3 6 z 2 3
−5 2 −6 7 −5 2 −6 7
m n c a 9 c m n m n c a 9 c m n
2 2 x + 2 4 2 2 x + 2 4
1.4 Section Exercises
The statement is true. In standard form, the polynomial with the highest value exponent is placed first and is the leading term. The degree of a polynomial is the value of the highest exponent, which in standard form is also the exponent of the leading term.
Use the distributive property, multiply, combine like terms, and simplify.
4 x 2 + 3 x + 19 4 x 2 + 3 x + 19
3 w 2 + 30 w + 21 3 w 2 + 30 w + 21
11 b 4 −9 b 3 + 12 b 2 −7 b + 8 11 b 4 −9 b 3 + 12 b 2 −7 b + 8
24 x 2 −4 x −8 24 x 2 −4 x −8
24 b 4 −48 b 2 + 24 24 b 4 −48 b 2 + 24
99 v 2 −202 v + 99 99 v 2 −202 v + 99
8 n 3 −4 n 2 + 72 n −36 8 n 3 −4 n 2 + 72 n −36
9 y 2 −42 y + 49 9 y 2 −42 y + 49
16 p 2 + 72 p + 81 16 p 2 + 72 p + 81
9 y 2 −36 y + 36 9 y 2 −36 y + 36
16 c 2 −1 16 c 2 −1
225 n 2 −36 225 n 2 −36
−16 m 2 + 16 −16 m 2 + 16
121 q 2 −100 121 q 2 −100
16 t 4 + 4 t 3 −32 t 2 − t + 7 16 t 4 + 4 t 3 −32 t 2 − t + 7
y 3 −6 y 2 − y + 18 y 3 −6 y 2 − y + 18
3 p 3 − p 2 −12 p + 10 3 p 3 − p 2 −12 p + 10
a 2 − b 2 a 2 − b 2
16 t 2 −40 t u + 25 u 2 16 t 2 −40 t u + 25 u 2
4 t 2 + x 2 + 4 t −5 t x − x 4 t 2 + x 2 + 4 t −5 t x − x
24 r 2 + 22 r d −7 d 2 24 r 2 + 22 r d −7 d 2
32 x 2 −4 x −3 32 x 2 −4 x −3 m 2
32 t 3 − 100 t 2 + 40 t + 38 32 t 3 − 100 t 2 + 40 t + 38
a 4 + 4 a 3 c −16 a c 3 −16 c 4 a 4 + 4 a 3 c −16 a c 3 −16 c 4
1.5 Section Exercises
The terms of a polynomial do not have to have a common factor for the entire polynomial to be factorable. For example, 4 x 2 4 x 2 and −9 y 2 −9 y 2 don’t have a common factor, but the whole polynomial is still factorable: 4 x 2 −9 y 2 = ( 2 x + 3 y ) ( 2 x −3 y ) . 4 x 2 −9 y 2 = ( 2 x + 3 y ) ( 2 x −3 y ) .
Divide the x x term into the sum of two terms, factor each portion of the expression separately, and then factor out the GCF of the entire expression.
10 m 3 10 m 3
( 2 a −3 ) ( a + 6 ) ( 2 a −3 ) ( a + 6 )
( 3 n −11 ) ( 2 n + 1 ) ( 3 n −11 ) ( 2 n + 1 )
( p + 1 ) ( 2 p −7 ) ( p + 1 ) ( 2 p −7 )
( 5 h + 3 ) ( 2 h −3 ) ( 5 h + 3 ) ( 2 h −3 )
( 9 d −1 ) ( d −8 ) ( 9 d −1 ) ( d −8 )
( 12 t + 13 ) ( t −1 ) ( 12 t + 13 ) ( t −1 )
( 4 x + 10 ) ( 4 x − 10 ) ( 4 x + 10 ) ( 4 x − 10 )
( 11 p + 13 ) ( 11 p − 13 ) ( 11 p + 13 ) ( 11 p − 13 )
( 19 d + 9 ) ( 19 d − 9 ) ( 19 d + 9 ) ( 19 d − 9 )
( 12 b + 5 c ) ( 12 b − 5 c ) ( 12 b + 5 c ) ( 12 b − 5 c )
( 7 n + 12 ) 2 ( 7 n + 12 ) 2
( 15 y + 4 ) 2 ( 15 y + 4 ) 2
( 5 p − 12 ) 2 ( 5 p − 12 ) 2
( x + 6 ) ( x 2 − 6 x + 36 ) ( x + 6 ) ( x 2 − 6 x + 36 )
( 5 a + 7 ) ( 25 a 2 − 35 a + 49 ) ( 5 a + 7 ) ( 25 a 2 − 35 a + 49 )
( 4 x − 5 ) ( 16 x 2 + 20 x + 25 ) ( 4 x − 5 ) ( 16 x 2 + 20 x + 25 )
( 5 r + 12 s ) ( 25 r 2 − 60 r s + 144 s 2 ) ( 5 r + 12 s ) ( 25 r 2 − 60 r s + 144 s 2 )
( 2 c + 3 ) − 1 4 ( −7 c − 15 ) ( 2 c + 3 ) − 1 4 ( −7 c − 15 )
( x + 2 ) − 2 5 ( 19 x + 10 ) ( x + 2 ) − 2 5 ( 19 x + 10 )
( 2 z − 9 ) − 3 2 ( 27 z − 99 ) ( 2 z − 9 ) − 3 2 ( 27 z − 99 )
( 14 x −3 ) ( 7 x + 9 ) ( 14 x −3 ) ( 7 x + 9 )
( 3 x + 5 ) ( 3 x −5 ) ( 3 x + 5 ) ( 3 x −5 )
( 2 x + 5 ) 2 ( 2 x − 5 ) 2 ( 2 x + 5 ) 2 ( 2 x − 5 ) 2
( 4 z 2 + 49 a 2 ) ( 2 z + 7 a ) ( 2 z − 7 a ) ( 4 z 2 + 49 a 2 ) ( 2 z + 7 a ) ( 2 z − 7 a )
1 ( 4 x + 9 ) ( 4 x −9 ) ( 2 x + 3 ) 1 ( 4 x + 9 ) ( 4 x −9 ) ( 2 x + 3 )
1.6 Section Exercises
You can factor the numerator and denominator to see if any of the terms can cancel one another out.
True. Multiplication and division do not require finding the LCD because the denominators can be combined through those operations, whereas addition and subtraction require like terms.
y + 5 y + 6 y + 5 y + 6
3 b + 3 3 b + 3
x + 4 2 x + 2 x + 4 2 x + 2
a + 3 a − 3 a + 3 a − 3
3 n − 8 7 n − 3 3 n − 8 7 n − 3
c − 6 c + 6 c − 6 c + 6
d 2 − 25 25 d 2 − 1 d 2 − 25 25 d 2 − 1
t + 5 t + 3 t + 5 t + 3
6 x − 5 6 x + 5 6 x − 5 6 x + 5
p + 6 4 p + 3 p + 6 4 p + 3
2 d + 9 d + 11 2 d + 9 d + 11
12 b + 5 3 b −1 12 b + 5 3 b −1
4 y −1 y + 4 4 y −1 y + 4
10 x + 4 y x y 10 x + 4 y x y
9 a − 7 a 2 − 2 a − 3 9 a − 7 a 2 − 2 a − 3
2 y 2 − y + 9 y 2 − y − 2 2 y 2 − y + 9 y 2 − y − 2
5 z 2 + z + 5 z 2 − z − 2 5 z 2 + z + 5 z 2 − z − 2
x + 2 x y + y x + x y + y + 1 x + 2 x y + y x + x y + y + 1
2 b + 7 a a b 2 2 b + 7 a a b 2
18 + a b 4 b 18 + a b 4 b
a − b a − b
3 c 2 + 3 c − 2 2 c 2 + 5 c + 2 3 c 2 + 3 c − 2 2 c 2 + 5 c + 2
15 x + 7 x −1 15 x + 7 x −1
x + 9 x −9 x + 9 x −9
1 y + 2 1 y + 2
Review Exercises
y = 24 y = 24
3 a 6 3 a 6
x 3 32 y 3 x 3 32 y 3
1.634 × 10 7 1.634 × 10 7
4 2 5 4 2 5
7 2 50 7 2 50
3 x 3 + 4 x 2 + 6 3 x 3 + 4 x 2 + 6
5 x 2 − x + 3 5 x 2 − x + 3
k 2 − 3 k − 18 k 2 − 3 k − 18
x 3 + x 2 + x + 1 x 3 + x 2 + x + 1
3 a 2 + 5 a b − 2 b 2 3 a 2 + 5 a b − 2 b 2
4 a 2 4 a 2
( 4 a − 3 ) ( 2 a + 9 ) ( 4 a − 3 ) ( 2 a + 9 )
( x + 5 ) 2 ( x + 5 ) 2
( 2 h − 3 k ) 2 ( 2 h − 3 k ) 2
( p + 6 ) ( p 2 − 6 p + 36 ) ( p + 6 ) ( p 2 − 6 p + 36 )
( 4 q − 3 p ) ( 16 q 2 + 12 p q + 9 p 2 ) ( 4 q − 3 p ) ( 16 q 2 + 12 p q + 9 p 2 )
( p + 3 ) 1 3 ( −5 p − 24 ) ( p + 3 ) 1 3 ( −5 p − 24 )
x + 3 x − 4 x + 3 x − 4
m + 2 m − 3 m + 2 m − 3
6 x + 10 y x y 6 x + 10 y x y
Practice Test
x = –2 x = –2
3 x 4 3 x 4
13 q 3 − 4 q 2 − 5 q 13 q 3 − 4 q 2 − 5 q
n 3 − 6 n 2 + 12 n − 8 n 3 − 6 n 2 + 12 n − 8
( 4 x + 9 ) ( 4 x − 9 ) ( 4 x + 9 ) ( 4 x − 9 )
( 3 c − 11 ) ( 9 c 2 + 33 c + 121 ) ( 3 c − 11 ) ( 9 c 2 + 33 c + 121 )
4 z − 3 2 z − 1 4 z − 3 2 z − 1
3 a + 2 b 3 b 3 a + 2 b 3 b
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Table of Contents for N-Gen Math Algebra I and Standards Alignment. Unit 1 - The Building Blocks of Algebra. Unit 2 - Linear Equations and Inequalities. Unit 3 - Functions. Unit 4 - Linear Functions. Unit 5 - Linear Systems. Unit 6 - Exponential Algebra and Functions. Unit 7 - Polynomials.
The workbook for this course is a printed collection of the lessons and homework sets that can be previewed on the N-Gen Math™ Algebra I course page. The answer key is sold separately as a yearly membership. Unit 1 - The Building Blocks of Algebra. Unit 2 - Linear Equations and Inequalities. Unit 3 - Functions.
Use Mathleaks to get learning-focused solutions and answers to Algebra 1 math, either 8th grade Algebra 1 or 9th grade Algebra 1, for the most commonly used textbooks from publishers such as Houghton Mifflin Harcourt, Big Ideas Learning, CPM, McGraw Hill, and Pearson. Getting helpful and educational math answers and solutions to high school ...
formula for the an in terms of a 1 , d, and n. (a) Determine a formula for an. (b) Use the formula from (a) to determine the value of a 50. N-GEN MATH® ALGEBRA I - UNIT 4 - LINEAR FUNCTIONS - LESSON 14 ® ® 6. The second term of an arithmetic sequence has a value of 20 and the fifth term has a value of 38. APPLICATIONS 7.
In this lesson students review the concept of two expressions being equivalent. They then use the commutative, associative, and distributive properties to cr...
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N-Gen Math™ Algebra I; N-Gen Math™ Geometry; Common Core Algebra I; Common Core Geometry; Common Core Algebra II; ... LESSON/HOMEWORK. LECCIÓN/TAREA. LESSON VIDEO. ANSWER KEY. EDITABLE LESSON. EDITABLE KEY. SMART NOTEBOOK. ... please credit us as follows on all assignment and answer key pages: "This assignment is a teacher-modified ...
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Introduction to Systems of Equations and Inequalities; 7.1 Systems of Linear Equations: Two Variables; 7.2 Systems of Linear Equations: Three Variables; 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables; 7.4 Partial Fractions; 7.5 Matrices and Matrix Operations; 7.6 Solving Systems with Gaussian Elimination; 7.7 Solving Systems with Inverses; 7.8 Solving Systems with Cramer's Rule
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Circular movement around an axis. Transformation. The changing of a figure's position through rotation, reflection, or translation. Reflection. A transformation that "flips" a figure over a mirror or reflection line. Reflection over x-axis. (x,y) -> (-x,-y) Translation. Moves every point of a figure the same distance in the same direction.
In this course students increase their ability to use algebra to solve problems, including the solution of equations with variables on both sides. Extensive work is done in geometry to understand rigid motions, dilations, and their connections to congruent figures, symmetry, and similarity. The equation of a line in the coordinate plane is developed from work with proportional relationships ...
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