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Math 95 Unit 1 Review Problems: Algebra and Functions, Study Guides, Projects, Research of Mathematics

A comprehensive set of review problems for math 95 unit 1, covering key concepts in algebra and functions. It includes exercises on solving linear equations, finding intercepts and slopes, graphing linear equations, simplifying expressions, factoring polynomials, and solving quadratic equations. Designed to help students prepare for an exam or reinforce their understanding of fundamental algebraic concepts.

Typology: Study Guides, Projects, Research

2022/2023

Uploaded on 10/03/2024

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Math 95 Unit 1 Review Problems 2.4, 2.5, 4.1-4.4, 5.1-5.5, 6.1-6.3, 6.6, 6.7
1.
4
(
xโˆ’9
)
=โˆ’(x+6)
2.
8.4 rโˆ’6.3=6.3 +2.1 r
3.
d
6+1
7
=
2
4.
โˆ’2
(
4โˆ’x
)
=
6x+9โˆ’4x
5. Find the x- and y-intercepts of
5xโˆ’3y=15.
Put the points in ordered pair form.
Find the slope and y-intercept of the following. Name the y-intercept in ordered
pair form.
7. 4 xโˆ’9y=15
Graph the following.
8. y=โˆ’3x+1
9.
y=โˆ’1
2xโˆ’4
10.
5xโˆ’2y=8
11.
y=6
Find the equation of a line with the given properties in slope-intercept form.
12. Slope =
1
2
and through (2,8)
13. Goes through the points (-3,1) and (4, -6)
14. Goes through the points (3,0) and (-3,5)
pf3
pf4
pf5

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Math 95 Unit 1 Review Problems 2.4, 2.5, 4.1-4.4, 5.1-5.5, 6.1-6.3, 6.6, 6.

4 ( x โˆ’ 9 ) =โˆ’( x + 6 )

8.4 r โˆ’6.3=6.3+2.1 r

d

โˆ’ 2 ( 4 โˆ’ x )

6 x + 9 โˆ’ 4 x

  1. Find the x- and y-intercepts of

5 x โˆ’ 3 y =15. Put the points in ordered pair form.

Find the slope and y-intercept of the following. Name the y-intercept in ordered

pair form.

  1. y = 5 x โˆ’ 7
  2. 4 x โˆ’ 9 y = 15

Graph the following.

  1. y =โˆ’ 3 x + 1

y =

x โˆ’ 4

  1. 5 x โˆ’ 2 y = 8
  2. y = 6

Find the equation of a line with the given properties in slope-intercept form.

  1. Slope =

and through (2,8)

  1. Goes through the points (-3,1) and (4, -6)
  2. Goes through the points (3,0) and (-3,5)

Simplify each expression.

  1. 5 x

4

โˆ™ 7 x

2

(โˆ’ 3 x y

2

3

24 p

7

3 p

3 a

4

b

6 a

3

b

5

3

(โˆ’ 6 p q

4

2

( 2 p q

7

( 4 x

0

) ( โˆ’ 3 x

2

0

21. ( 4 c

3

d

โˆ’ 2

โˆ’ 2

v โˆ™ v

โˆ’ 7

โˆ™ v

2

30 x

6

y

โˆ’ 5

45 x

โˆ’ 1

y

โˆ’ 3

b

4

c

โˆ’ 2

2 d

โˆ’ 3

โˆ’ 1

Perform the indicated operations.

6 x + 4

2 x

2

โˆ’ 5 x โˆ’ 3

y

2

โˆ’ 7 y + 3

4 y

2

โˆ’ 5 y โˆ’ 2

27.โˆ’ 5 d (โˆ’ 3 d + 7 )

  1. ( 6 p โˆ’ 5 )

2

5 x + 8

3 x โˆ’ 4

3 y โˆ’ 5

2 y

2

  • 4 y โˆ’ 5

โˆ’ 18 x

2

โˆ’ 6 x + 5

โˆ’ 3 x

12 x

2

  • 7 x โˆ’ 12

4 x + 5

3.5 ร— 10

โˆ’ 6

7.0 ร— 10

2

7.94 ร— 10

6

2.0 ร— 10

โˆ’ 2

Answers (non-graphing)

  1. x = 6 2) r = 2 3) d =
  1. no solution

  2. (3,0) and (0, -5) 6) slope = 5 and y-intercept is (0,-7)

  3. slope =

and y-intercept is (0,

) 8-11) Graphs

y =

x + 7

  1. y =โˆ’ x โˆ’ 2 14)

y =

x +

35 x

6

โˆ’ 27 x

3

y

6

p

6

a

3

8 b

12

p

3

q

15

d

4

16 c

6

v

4

2 x

7

3 y

2

2 c

2

b

4

d

3

2 x

2

  • x + 1

โˆ’ 3 y

2

โˆ’ 2 y + 5

15 d

2

โˆ’ 35 d

36 p

2

โˆ’ 60 p + 25

15 x

2

  • 4 x โˆ’ 32

6 y

3

  • 2 y

2

โˆ’ 35 y + 25

6 x + 2 โˆ’

3 x

3 x โˆ’ 4 +

4 x + 5

2 x

2

โˆ’ x โˆ’ 4 +

x โˆ’ 1

y

3

5 a

2

b

6 a

2

b

2

( b โˆ’ 3 a

2

4 a

2

b ( 2 a โˆ’ 3 b + 7 )

  1. ( 4 x + 1 ) ( x โˆ’ 5 )

  2. ( x โˆ’ 4 z ) ( x โˆ’ 5 z ) 40) ( r + 6 ) ( r + 4 ) 41) ( 5 x โˆ’ 6 ) ( x + 2 )

( 5 a โˆ’ 3 b ) ( 5 a + 2 b )

y ( 2 y โˆ’ 3 ) ( y + 1 )

x =โˆ’ 3 โˆจ x =

y =โˆ’ 2 โˆจ y =

  1. x = 0 โˆจ x = 6

  2. x =โˆ’ 9 โˆจ x = 9 48) 3. ( 10

9

ร— 10

โˆ’ 3

ร— 10

8