geometry summer prerequisites test · · 2015-07-02please complete the enclosed summer assignment...

Name:___________________________________

GEOMETRY SUMMER PREREQUISITES TEST

Dear Geometry Student,

As a student who has successfully completed Algebra 1, you have studied numerous topics that

will be crucial to your success in a Geometry course. There are many skills that you will be expected to

know before beginning Geometry. We encourage you to visit the resources listed below and within the

assignment to refresh the prerequisite skills listed below. On the Classzone site you may follow the

links to an Algebra 1 textbook to reinforce your skills.

The prerequisite skills for a Geometry course are:

• Solving one-step and two-step equations and inequalities

• Identifying and working with the domain and range of functions

• Writing linear equations

• Graphing linear equations and inequalities

• Solving systems of two linear equations

• Simplifying exponential expressions

• Adding, subtracting, multiplyi ng and dividing polynomials

• Factoring polynomials

• Simplifying radicals

Please complete the enclosed summer assignment and have a parent or guardian sign the packet

once they have reviewed it. Please refer to the rubric at the back of the section of the assignment to

review the grading requirements. The completed assignment must be handed in to vour Geometry

teacher on the first day of school and will count as an extra test grade for the first marking

period.

Options for late Summer Project: This project is due the first day of class in the fall semester and will be considered an extra test grade for the first six

weeks. As these skills are necessary for the course, the completion of this project is not only an easy A on a test

grade but is also indicative of the grade that a student will make in this class. Any student transferring into

Smithville High School will be given one week to do this project for an extra test grade.

Resources:

• www.classzone.com

• http://www.montgomeryschoolsmd.org/departments/itv/mathdude/MD Algebra! 3-l.shtm

• www.math.com

• www.freemathhelp.com

http://www.classzone.com/

http://www.montgomeryschoolsmd.org/departments/itv/mathdude/MD

http://www.math.com/

http://www.freemathhelp.com/

Section

Possible Points

Points Earned

Part 1: Skills Packet

40

Part 2: Quadratic & Square Roots 41

Part 3: Parent Signatures

19

TOTAL:

100

Scoring Rubrics

Part 1 : Skills Packet Remember that this portion of your summer project makes up only 40% of your grade.

Total Points Criteria

Points Earned

5 points (1 pt. per question)

Task 1: Evaluating

I 5

5 points (1 pt. per question)

Task 2: Solve

I 5

5 points (2 pts. per question)

Task 3: Write equations

I 10

5 points (2 pts. per question) Task 4: Graphing lines

I 10

5 points (2 pts. per question)

Task 5: Solve systems

I 10

40 Points Total I40

Part 2: Quadratic & Exponent Remember that this portion of your summer project makes up only 30% of your grade.

Total Points Criteria Points Earned

20 points (4 pts. per question) Task 1: Solve Quadratics /20

20 points (3 pts. per question) Task 2: Square Roots /21

41 points Total /41

Part 3: PARENT SIGNATURE __________________________

STUDENT SIGNATURE __________________________

High Geometry Prerequisites Test

3

PART 1: SKILLS PACKET

Task 1: Evaluating

EXAMPLE:

Evaluate 8xy 3z

For x = -5, y = 2 and z = -1

SOLUTION:

8(-5)(2)3 (-1) =

8(-5)(8)(-1) =

Final solution: 320

EXAMPLE:

Given V = n r2 h ,

If V = 3140 in3

and r = 10 in, find h

SOLUTION:

3140 = (3.14)(10)2h

3140 = 314 h

Final solution: h = 10 in

Now you try! Evaluate and show all steps for full credit. Work must be shown even if using a calculator.

(2 points each)

1. Evaluate the expression: 3x2 + 8y for x = -2 and y = 10 1. ____________

2. Evaluate the expression:

for a =-1 and b = 4 2. ____________

3. A = ( )

If A = 60 cm

2, b1 = 20 cm and b2 – 10 cm, find h. 3. H = ________


4

4. F =

If F = 68°, Find C 4. C = ___________

5. y =2x2 + r If y = 11r and r = 5, find x. 5. x = ___________

Task 2: Solving Equations and Inequalities

EXAMPLE:

Solve: -2x+3=5

SOLUTION:

-2x+3=5

-2x=2 -x = 1

Final solution: x = -1

CHECK:

EXAMPLE: Solve: -2x+3<5

SOLUTION:

-2x + 3 < 5

-2x < 2

X > -1

Final solution: x > -1

CHECK:


5

EXAMPLE:

Solve: -n+6<7n+4

SOLUTION:

-n+6<7n+4

-7n -7n -8n+6 < 4

-6 < -6

-8n < - 2

n

CHECK:

Final solu t ion: n =

*Remember to switch the inequality sign when dividing or multiplying both sides by a negative number

EXAMPLE:

Solve: 2x+3 < 5 or 4x -7 > 9

SOLUTION:

2x+3 < 5 or 4x-7 > 9

-3 -3 +7 >+7 2x < 2 4x > 16

2x < 2 4x > 16

2 2 4 4

x < 1 x > 4

Final solution: x < 1 or x > 4

CHECK:

EXAMPLE:

Solve: -2 ≤ 3t – 8 ≤ 10

SOLUTION:

-2 ≤ 3t – 8 ≤ 10 +8 +8 + 8 6 ≤ 3t ≤ 18

3 3 3

2 ≤ t 6

Final Solution: 2 ≤ t ≤ 6

CHECK


6

Now you try! Solve. Show all steps to receive full credit.

1. Solve: Check:

-4x + 5 = 25

2. Solve:

-4x + 5 > 25

Check:

1. Final solution: ____________

2. Final Solution: ___________

3. Solve:

5 - 5x > 12 - 4x

Check:


4. Solve:

-16 ≤ 3x – 4 ≤ 2

Check:

4. Final Solution: __________

5. Solve: Check: x – 1 ≤ 5 or x + 3 ≥ 10



7

Task 3: Writing Equations

EXAMPLE: SOLUTION:

Write an equation of the line with a slope

of - 4 and a y-intercept of 11.

Plug in the slope for m and the y-intercept for b

in the equation y = mx + b

Final equation: y = -4x + 11

EXAMPLE: SOLUTION:

Write an equation of the line passing

through the two given points: (2, 4), (4, 3)

Use the formula y2 – y1 to find the slope.

x2 – x1

m =

After finding the slope, use one point and the slope to

find the y-intercept:

y = mx + b given m =

and (4, 3)

3 = (

) ( )

3 = -2 + b so b = 5

Final equation: y =

x + 5

*********************************************************************************************************************

Now you try! Find the equation of the line passing through the given pair of points. Show all steps for full

cred it.

I. Slope of and a y-intercept of -5

1. Equation: _

2. (4, 5), (0, -3)

2. Equation: __


8

3. (-3, 2), (-2, 4)

3. Equation: _

4. (1, -4), (4, -2)

4. Equation: _______

5. (3, -3), (2, -2)

5. Equation: ______


9

x

2

Task 4: Graphing Equations!

EXAMPLE: Graph the equation using a table of values:

2x + y = 4

SOLUTION: Choose values for x and substitute into the

original equation to find y:

Choose x = -2, -1, 0, 1, 2 (any values can be chosen):

Substitute the x values into the

original equation to obtain the

y-values

_

*****************************************************************************************************

EXAMPLE: Graph the equation using slope

and y-intercept:

y = 2x -3

SOLUTION:

Identify the slope as the number in front of x

so, m =

and the y-intercept is the value added

to the x term, so b = -3

So you plot -3 on the y axis and then use the

slope to go up 2 spaces and right 1 space


10

-3 -2

-2

********************************************************************************** EXAMPLE:

Graph the absolute value equation

y = │x + 2 │- 3

SOLUTION:

Make a table of values by plugging in values and creating

at-chart of points

,

OR you can use the equation: y = a│x ± b│ ± c

And shift the graph of y = │x│two units to the left and three

units down

Now you try!

1. Graph: y = -x + 3

2. Graph: y =

Smithville High Geometry Prerequisites Test

3. Graph: y = │x + 5│ 2

4. Graph: y = 4

5. Graph: x = -2


Task 5: Systems of Linear Equations

EXAMPLE: SOLUTION:

Solve the equation by graphing: x + y = 5 See where the lines intersect:

x – y = 7 Plot points for each line OR put both into

y = mx + b form: y = -x + 5 slope: -1, y-int: (0, 5)

y = x – 7 slope: 1, y-int: (0, -7)

Solution is where they intersect: (6, -1)

********************************************************************************** EXAMPLE: Solve the system by linear combination:

x + y = 5

x + y = 7

SOLUTION: Line up the variables, create opposite

coefficients then add columns.

x + y = 5

x y = 7

2x = 12, so x = 6

Now plug x = 6 back in the problem to find y:

6 + y = 5, so y = -1 Final solution: (6, -1)

********************************************************************************** EXAMPLE: Solve the system by substitution:

x + y = 5

x y = 7

SOLUTION:

Solve for one variable, then plug that into

the other equation to get final answer:

Given: x + y = 5

x y = 7

x + y = 5, so x = 5 y

Now, plug that into the other equation for x:

(5 – y) y = 7

5 - 2y = 7

-2y = 2, so y = -1

Now find the other variable:

x + y= 5, so x + (-1) = 5

Final solution: (6, -1)


Now you try! Show all steps for full credit.

1. Solve by graphing: x + y = 3

x y = 1

2. Solve by linear combinations/elimination: x + y = 3

x y = 1

3. Solve by substitution: x + y = 3

x y = 1

4. Solve using any method: y =

y =





5. Solve using any method:

4x + 3y = 16

2x 3y = 8



Name:

______________________________

PART 2: QUADRATICS & SQUARE ROOTS

Task 1: Quadratics

Show all work to receive credit.

Solve by Factoring. Answers

1. 1.)___________________

2. 2.)___________________

3. 3.)___________________

Use the Quadratic Formula ( √

) to solve for x.

4. 4.)___________________

5. 5.)___________________


Find each part of the Quadratic Function. Show all work to get credit.

6. a.) Graph Function

Opens Up or Down______________

b.) Axis Of Symmetry___________________

c.) Vertex_____________________

d.) X-Intercepts_______________________

e.) Y-Intercepts______________________

f.) Maximum or Minimum___________________

Task 2: Simplifying Square Roots

Simplify each, and leave in radical form.

1. √ 1.)___________________

2. √ 2.)___________________

3. √ 3.)___________________


Rationalize each fraction.

4.

√ 4.)___________________

5.

√ 5.)___________________

Multiply each, and put in simplest radical form.

6. ( √ )(√ ) 6.)__________________

7. ( √ )(√ ) 7.)__________________

geometry summer prerequisites test · · 2015-07-02please complete the enclosed summer assignment...

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