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Geometry Answer Key, Exercises of Geometry

Continental Theological SeminaryGeometry

The following problems represent many of the algebraic skills that are needed throughout your geometry course. I. Solving Quadratic Equations.

Typology: Exercises

2021/2022

Uploaded on 08/05/2022

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Geometry Prerequisite Skills Practice Worksheet
Name: ____Key______________________________ Date: _________________
The following problems represent many of the algebraic skills that are needed throughout your geometry course.
I. Solving Quadratic Equations
Solve. Check your solutions. Simplify your answer whenever possible.
1. ๐‘ฅ๐‘ฅ2=500
๏ฟฝ๐‘ฅ๐‘ฅ2=โˆš500
x = ยฑโˆš500
x =10โˆš5, x =โˆ’10โˆš5
2. ๐‘ฅ๐‘ฅ2+ 3๐‘ฅ๐‘ฅโˆ’28 = 0
(x+7)(x-4) = 0
x+7 = 0, x-4 = 0
x = -7, x=4
3. ๐‘ฅ๐‘ฅ2= 5๐‘ฅ๐‘ฅ
x2-5x = 0
x(x-5) = 0
x = 0, x-5 = 0
x = 0, x = 5
4. ๐‘ฅ๐‘ฅ2โˆ’9๐‘ฅ๐‘ฅ=โˆ’18
x2-9x+18 = 0
(x-6)(x-3) = 0
x-6 = 0, x-3 = 0
x = 6, x = 3
5. 2๐‘ฅ๐‘ฅ2+11๐‘ฅ๐‘ฅโˆ’21 = 0
(2x-3)(x+7) = 0
2x-3 = 0, x+7 = 0
x = 3
2 , x = -7
6. 2๐‘ฅ๐‘ฅ2+ 4๐‘ฅ๐‘ฅโˆ’7 = 0
Discriminant is 72
Use Quadratic Formula ๐‘ฅ๐‘ฅ=โˆ’4ยฑ๏ฟฝ16โˆ’4(2)(โˆ’7)
4
๐‘ฅ๐‘ฅ=โˆ’4 ยฑ โˆš72
4
๐‘ฅ๐‘ฅ=โˆ’4ยฑ6โˆš2
4 = โˆ’2ยฑ3โˆš2
2
II. Systems of Equations โ€“
Solve the following systems of equations. Check your solutions.
7. ๏ฟฝ3๐‘ฅ๐‘ฅโˆ’2๐‘ฆ๐‘ฆ=16
5๐‘ฅ๐‘ฅ+ 2๐‘ฆ๐‘ฆ= 8
8x = 24
x = 3
pf3
pf4
pf5

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Download Geometry Answer Key and more Exercises Geometry in PDF only on Docsity!

Geometry Prerequisite Skills Practice Worksheet

Name: ____Key______________________________ Date: _________________

The following problems represent many of the algebraic skills that are needed throughout your geometry course.

I. Solving Quadratic Equations

Solve. Check your solutions. Simplify your answer whenever possible.

2

2

x = ยฑ โˆš

x =10โˆš5, x =โˆ’ 10 โˆš 5

2

(x+7)(x-4) = 0

x+7 = 0, x-4 = 0

x = -7, x=

2

x

2

-5x = 0

x(x-5) = 0

x = 0, x-5 = 0

x = 0, x = 5

2

x

2

-9x+18 = 0

(x-6)(x-3) = 0

x-6 = 0, x-3 = 0

x = 6, x = 3

2

(2x-3)(x+7) = 0

2x-3 = 0, x+7 = 0

x =

3

2

, x = -

2

Discriminant is 72

Use Quadratic Formula ๐‘ฅ๐‘ฅ =

โˆ’4ยฑ๏ฟฝ16โˆ’4( 2 )(โˆ’7)

4

โˆ’4ยฑ6โˆš

4

โˆ’2ยฑ3โˆš

2

II. Systems of Equations โ€“

Solve the following systems of equations. Check your solutions.

8x = 24

x = 3

3(3)-2y = 16

9-2y = 16

-2y = 7

y = โˆ’

7

2

Check

7

2

Answer is (3, โˆ’

7

2

(x+2y = 6)(-2)

3x+4y = 10

-2x-4y = -

3x+4y = 10_

x = -

-2+2y = 6

2y = 8

y = 4

Check

Answer is (-2,4)

(y = -3x-13)(-1)

2x+7 = y

3x+13 = -y

5x+20 = 0

5x = -

x = -

y = 2(-4)+

y = -8+

y = -

Check

Questions 12 โ€“ 15 refer to the points in Question 11.

  1. Find the slope of the line passing through A and B.

A(3, -5) B(7, 2)

๐‘ฆ๐‘ฆ

2

โˆ’๐‘ฆ๐‘ฆ

1

๐‘ฅ๐‘ฅ

2

โˆ’๐‘ฅ๐‘ฅ

1

2โˆ’(โˆ’5)

7โˆ’

7

4

  1. Find an equation of the line passing through D with a slope of โˆ’

4

3

D(0, -6)

Point-Slope Form

(y-y1)=m(x-x1)

y+6 = -

4

3

(x-0)

  1. Find an equation of the line passing through E that is parallel to the graph of ๐‘ฆ๐‘ฆ = 3๐‘ฅ๐‘ฅ + 5.

Parallel lines have the same slope

Line passes through E(2, -8) with m = 3

y+8 = 3(x-2)

  1. Find an equation of the line passing through E that is perpendicular to the graph of ๐‘ฆ๐‘ฆ =

2

3

Perpendicular lines have slopes that are opposite reciprocals of each other

Line passes through E(2, -8) with m = โˆ’

3

2

y+8 = โˆ’

3

2

(x-2)

  1. Graph the equation ๐‘ฆ๐‘ฆ = โˆ’

1

2

๐‘ฅ๐‘ฅ + 3. Identify the slope, the y- intercept, and the x- intercept.

slope: โˆ’

1

2

y-i ntercept: (0,3)_

x- intercept: (6,0)_

value of x when y = 0

1

2

x+

1

2

x

-2(-3) = x

6 = x

IV. Simplifying Rational Expressions

Simplify. Rationalize denominators.

2

3

2

3

3

3

6

9

โˆš

3

8

โˆš

8

โˆš

โˆš

โˆš

8โˆš

2

V. Solving Linear Equations

Solve. Check your solutions.

15x-7 = 8

15x = 15

x = 1

3y+3 = -

3y = -

y = -

-3y-9 = 2y+

-9 = 5y+

-12 = 5y

12

5

= y

-6a+10 = -4a-

10 = 2a-

26 = 2a

a = 13

6x-4 = 6x-

All real numbers

-6x+9 = 20-4x

9 = 20+2x

-11 = 2x

x = โˆ’

11

2

3x+6 = -5-2x+

3x+6 = 1-2x

5x+6 = 1

5x = -

x = -