getting ready forjvettermath.weebly.com/uploads/8/8/3/1/88313054/geometryreadinessprep... · the...

20 DIFFERENT SKILLS AND TOPICS THAT STUDENTS SHOULD BE PROFICIENT IN BEFORE ENTERING GEOMETRY

GETTING READY FOR

TABLE OF CONTENTSPAGE TOPIC

1 THE NUMBER PROPERTIES

2 CALCULATING SLOPE

3 GRAPHING IN SLOPE-INTERCEPT FORM

4 DETERMINING PARALLEL AND PERPENDICULAR LINES

5 SOLVING MULTI-STEP EQUATIONS

6 SOLVING INEQUALITIES

7 SUBSTITUTION TO SOLVE SYSTEMS OF EQUATIONS

8 FACTORING TRINOMIALS

9 SIMPLIFYING RADICALS

10 OPERATIONS WITH RADICALS

11 CLASSIFYING SEGMENTS, RAYS, and LINES

12 NUMBER OF EDGES & VERTICES

13 ANGLE MEASUREMENTS

14 TYPES OF TRIANGLES

15 TYPES OF QUADRILATERALS

16 PARTS OF A CIRCLE

17 AREA FORMULAS OF BASIC SHAPES

18 VOLUME FORMULAS OF BASIC FIGURES

19 BASIC TRANSFORMATIONS

20 CONGRUENT OR SIMILAR

@iteachalgebra

THE NUMBER PROPERTIES1

@iteachalgebra

Match each expression with the property that it shows.

5 + 0 = 5

Additive Identity

5(1) = 5

Multiplicative Identity

5(0) = 0

Zero Product Property

2 + 3 = 3 + 2

Commutative Property

of Addition

2(3) = 3(2)Commutative Property

of Multiplication

2 + (3 + 4) = (2 + 3) + 4

Associative Property

of Addition

2(3•4) = (2•3)4


of Multiplication

3(2 + 5) = 6 + 15

Distributive Property

CALCULATING SLOPE2

@iteachalgebra

Find the slope between the given points or on the graph.

(1, 3) and (5, 8) (-2, 7) and (5, 4) (1, -3) and (0, 8)

(-1, -9) and (4, 0) (-8, 8) and (-2, 8) (-4, 9) and (-4, -8)

GRAPHING IN SLOPE-INTERCEPT FORM

3

@iteachalgebra

y = x + 3 y = x - 1

y = -2x y = -x + 3

y = 1

2x - 4 y = −

3

2x + 1

y = 2x + 3

y = -3x + 3

y =4

3x - 3

PARALLEL & PERPENDICULAR4

@iteachalgebra

Circle whether each pair of equations is parallel, perpendicular, or neither.

y = x + 3

y = x - 2{slope:

parallel perpendicular neither

y = 2x + 3

2x – y = 4{slope:


y = -x

y = x + 4{slope:


y = 3x + 3

x – 3y = 9{slope:


2x + 3y = 6

3x - 2y = 4{slope:


y = 2

5x + 3

2x – 5y = 10{slope:


4x + y = 6

y = -4x - 2{slope:


y = 5x + 3

x + 4y = 8{slope:


SOLVING MULTI-STEP EQUATIONS

5

@iteachalgebra

Solve each equation. Simplify your answer.

3(x + 4) = 2.5(x – 6) 2(x - 5) + 7 = -3(2x – 6)

1

2(4x - 8) =

3

4(8x + 4)

1

2x + 5 =

2

5x - 8

2

3(5x + 6) =

3

2(8x - 4)

1

3x +

1

4=

2

3x -

1

6

SOLVING INEQUALITIES6

@iteachalgebra

Solve the inequalities.

30 + 2x < 17 15 < -4x + 18 6 ≤ 4x + 80

10 - 2x ≤ 17 -12 > -3x - 12 -9 ≤ -5x - 33

8 + 2x < -x + 17 4x - 9 ≤ 5x + 80

5 - 2x 6(x – 3) -3(3 + x) ≤ -6x - 11

SUBSTITUTION TO SOLVE SYSTEMS

7

@iteachalgebra

Solve each system by substitution.

y = -2x

y = x + 3{ y = 3x + 3

x – 3y = 9{

2x + y = 6

x = 2y - 1{ y = 2

5x + 3

2x – 5y = 10{

x = -4

y = 5{ 2x + 3y = 6

y = -3x - 1{

FACTORING TRINOMIALS 8

@iteachalgebra

Factor each trinomial.

Solve the polynomial equation.

x2 + 5x + 4 x2 + 8x + 16 x2 - 6x + 8

x2 - 6x - 7 x2 + 5x + 6 x2 - 10x + 25

2x2 + 7x + 3 3x2 - 13x + 4 5x2 + 7x - 6

x2 + 9x = -8 2x2 = 7x - 3 3x2 + 15x = -18

SIMPLIFYING RADICALS9

@iteachalgebra

Simplify each radical expression.

4 6 8 9 10

12 18 25 28 32

40 48 50 55 60

64 72 90 99 120

150 160 200 256 300

OPERATIONS WITH RADICALS10

@iteachalgebra


2 + 2 4 3 + 3 5 6 + 2 6

2 - 2 4 3 - 3 5 6 - 2 6

2 • 2 4 3 • 3 5 6 • 2 6

72 + 50 4 45 - 125 5 27 + 2 5

CLASSIFYING SEGMENTS, RAYS, & LINES

11

@iteachalgebra

Determine the segments, rays, and lines from the diagram.

SEGMENTS RAYS LINES

A

B

CD

Determine whether each statement is true or false.

Two lines can intersect at exactly one point.

Two lines can intersect at exactly two points.

The are an infinite number of points on a line.

A ray has an arrow at one end.

A segment and a line are identical.

NUMBER OF EDGES & VERTICES12

@iteachalgebra

List the number of edges and vertices for each figure.

edges:

vertices:

edges:

vertices:

edges:

vertices:

rectangular prism

square pyramid

cylinder

ANGLE MEASUREMENTS13

@iteachalgebra

Circle the type of angle shown and the best approximate measure of the angle.

acute

obtuse

right

60

100

90

acute

obtuse

right

60

100

90

acute

obtuse

right

60

100

90

acute

obtuse

right

60

100

90

TYPES OF TRIANGLES14

@iteachalgebra

Name the triangle based on its sides and angles.

Names include equilateral, isosceles, and scalene, acute, obtuse, and right.

60

60 6090

60 30

120

30 30

45

4590

40

70

70

55

8045

TYPES OF QUADRILATERALS15

@iteachalgebra

Determine if the quadrilateral is a square, rectangle, rhombus, trapezoid,

isosceles trapezoid, parallelogram, or more than one of those names.

>

>

>

>

>

>

> >

PARTS OF A CIRCLE16

@iteachalgebra

Given the circle, name each part.

Find the circumference and area of each circle.

5

8

Circumference: C = 2𝜋r Area: A = 𝜋r2

Circumference: C = 𝜋d Area: A = 𝜋r2

AREA FORMULAS17

@iteachalgebra

Calculate the area of each figure.

A = lw

13.5

4

10

3

A = 1

2bh

16

9.8

A = bh

rectangle triangle

parallelogram

A = 1

2h(b1 + b2)

trapezoid

5

9

4

VOLUME FORMULAS18

@iteachalgebra

Calculate the volume of each figure.

V = s3 V = lwh

V = r2h

cube rectangular prism

cylinder

V = 4

3r3

sphere

4

3

5

6

6

6

5

4

8.5

TRANSFORMATIONS19

@iteachalgebra

Determine the type of transformation shown in each diagram as a translation,

rotation, reflection, or dilation.

CONGRUENT OR SIMILAR20

@iteachalgebra

Determine whether the figures shown are congruent or similar.

ANSWERKEY

THE NUMBER PROPERTIES1

@iteachalgebra

Match each expression with the property that it shows.

5 + 0 = 5

Additive Identity

5(1) = 5

Multiplicative Identity

5(0) = 0

Zero Product Property

2 + 3 = 3 + 2

Commutative Property

of Addition

2(3) = 3(2)Commutative Property

of Multiplication

2 + (3 + 4) = (2 + 3) + 4


of Addition

2(3•4) = (2•3)4


of Multiplication

3(2 + 5) = 6 + 15

Distributive Property

ANSWER KEY

CALCULATING SLOPE2

@iteachalgebra

Find the slope between the given points or on the graph.

(1, 3) and (5, 8) (-2, 7) and (5, 4) (1, -3) and (0, 8)

(-1, -9) and (4, 0) (-8, 8) and (-2, 8) (-4, 9) and (-4, -8)

m = 8 − 3

5 − 1= 5

4m =

4 − 7

5 −(−2)= −3

7 m = 8 −(−3)

0 − 1= 11

−1

m = -11

m = 0 −(−9)

4 −(−1)= 9

5m =

8 − 8

−2 −(−8)= 0

6

m = 0

m = −8 − 9

−4 −(−4)= −17

0

m = undefined

𝑟𝑖𝑠𝑒

𝑟𝑢𝑛= 2

1= 2

𝑟𝑖𝑠𝑒

𝑟𝑢𝑛= −1

3

2

1

-1

3

ANSWER KEY

GRAPHING IN SLOPE-INTERCEPT FORM

3

@iteachalgebra

y = x + 3 y = x - 1

y = -2x y = -x + 3

y = 1

2x - 4 y = −

3

2x + 1

y = 2x + 3

y = -3x + 3

y = 4

3x - 3

ANSWER KEY

PARALLEL & PERPENDICULAR4

@iteachalgebra

Circle whether each pair of equations is parallel, perpendicular, or neither.

y = x + 3

y = x - 2{slope:


y = 2x + 3

2x – y = 4{slope:


y = -x

y = x + 4{slope:


y = 3x + 3

x – 3y = 9{slope:


2x + 3y = 6

3x - 2y = 4{slope:


y = 2

5x + 3

2x – 5y = 10{slope:


4x + y = 6

y = -4x - 2{slope:


y = 5x + 3

x + 4y = 8{slope:


m = 1

m = 1

m = 2

m = 2

m = -1

m = 1

m = 3

m = 1

3

m = −2

3

m = 3

2

m = 2

5

m = 2

5

m = -4

m = -4

m = 5

m = −1

4

ANSWER KEY

SOLVING MULTI-STEP EQUATIONS

5

@iteachalgebra

Solve each equation. Simplify your answer.

3(x + 4) = 2.5(x – 6) 2(x - 5) + 7 = -3(2x – 6)

1

2(4x - 8) =

3

4(8x + 4)

1

2x + 5 =

2

5x - 8

2

3(5x + 6) =

3

2(8x - 4)

1

3x +

1

4=

2

3x -

1

6

ANSWER KEY

3x + 12 = 2.5x – 15-2.5x -2.5x

0.5x + 12 = – 15-12 = – 12

0.5x = – 270.5 0.5

x = -54

2x - 10 + 7 = -6x + 18

2x - 3 = -6x + 18 + 6x + 6x

8x - 3 = 18 + 3 + 3

8x = 21

8 8 x = 2.625

2x – 4 = 6x + 1-2x -2x

– 4 = 4x + 1- 1 - 1

– 5 = 4x

4 4

-1.25 = x

10(1

2x + 5) = 10(

2

5x – 8)

5x + 50 = 4x - 80-4x -4x

x + 50 = - 80- 50 - 50

x = - 130

6[2

3(5x + 6)] = 6[

3

2(8x - 4)]

4(5x + 6) = 9(8x - 4)

20x + 24 = 72x - 36-72x -72x

-52x + 24 = - 36- 24 = - 24

-52x = - 60-52 -52

x = 15

13

12(1

3x +

1

4) = 12(

2

3x -

1

6)

4x + 3 = 8x - 2-4x -4x

3 = 4x - 2+ 2 + 2

5 = 4x4 4

1.25 = x

SOLVING INEQUALITIES6

@iteachalgebra

Solve the inequalities.

30 + 2x < 17 15 < -4x + 18 6 ≤ 4x + 80

10 - 2x ≤ 17 -12 > -3x - 12 -9 ≤ -5x - 33

8 + 2x < -x + 17 4x - 9 ≤ 5x + 80

5 - 2x 6(x – 3) -3(3 + x) ≤ -6x - 11

ANSWER KEY

-30 -30

2x < -132 2

x < -6.5

- 18 - 18

-3 < -4x-4 -43

4> x x <

3

4

- 80 - 80

-74 ≤ 4x4 4

-19 ≤ x x -19

-10 -10

-2x ≤ 7-2 -2

x -3.5

+12 +12

0 > -3x-3 -3

0 < x x > 0

+33 +33

24 ≤ -5x-5 -5

-4.8 x x ≤ -4.8

-8 -8

2x < -x + 9+x +x

3x < 9

x < 3

-4x -4x

- 9 ≤ x + 80-80 - 80

- 89 ≤ x

x - 89

5 - 2x 6x - 18-5 -5

- 2x 6x - 23- 6x - 6x- 8x - 23- 8 - 8

x ≤ 2.875

-9 – 3x ≤ -6x - 11+9 + 9

– 3x ≤ -6x - 2+ 6x + 6x

3x ≤ - 23 3

x ≤ -2

3

SUBSTITUTION TO SOLVE SYSTEMS

7

@iteachalgebra

Solve each system by substitution.

y = -2x

y = x + 3{ y = 3x + 3

x – 3y = 9{

2x + y = 6

x = 2y - 1{ y = 2

5x + 3

2x – 5y = 10{

x = -4

y = 5{ 2x + 3y = 6

y = -3x - 1{

ANSWER KEY

-2x = x + 3-x -x

-3x = 3

x = -1

y = -2x

y = -2(-1)

y = 2

(-1, 2)

x – 3(3x + 3) = 9x – 9x – 9 = 9

-8x – 9 = 9

-8x = 18

x = -2.25

y = 3x + 3

y = 3(-2.25) + 3

y = -6.75 + 3

y = -3.75

(-2.25, -3.75)

2(2y – 1) + y = 6

4y – 2 + y = 6

5y = 8

y = 1.6

x = 2y - 1

x = 2(1.6) - 1

x = 3.2 - 1

x = 2.2

(-4, 5)

2x – 5(2

5x + 3) = 10

2x – 2x + 15 = 10

15 = 10

no solution(2.2, 1.6)

2x + 3(-3x – 1) = 6

2x – 9x – 3 = 6

-7x – 3 = 6

-7x = 9

x = −9

7

y = -3x - 1

y = -3(−9

7)- 1

y = 27

7- 1

y = 20

7

(−9

7, 20

7)

FACTORING TRINOMIALS 8

@iteachalgebra

Factor each trinomial.

Solve the polynomial equation.

x2 + 5x + 4 x2 + 8x + 16 x2 - 6x + 8

x2 - 6x - 7 x2 + 5x + 6 x2 - 10x + 25

2x2 + 7x + 3 3x2 - 13x + 4 5x2 + 7x - 6

x2 + 9x = -8 2x2 = 7x - 3 3x2 + 15x = -18

ANSWER KEY

(x + 1)(x + 4)

(x + 1)(x - 7)

(x + 4)(x + 4)

(x + 4)2

(x - 2)(x - 4)

(x + 2)(x + 3) (x - 5)(x - 5)

(x - 5)2

(2x + 1)(x + 3) (3x - 1)(x - 4) (5x - 3)(x + 2)

x2 + 9x + 8 = 0

(x + 1)(x + 8) = 0

x + 1 = 0 x + 8 = 0- 1 - 1 - 8 - 8

x = -1 x = -8

2x2 - 7x + 3 = 0

(2x – 1)(x – 3) = 0

2x – 1 = 0 x - 3= 0+ 1 + 1 +3 +3

2x = 1 x = 3

x = {-8, -1}2 2

x = {1

2, 3}

3x2 + 15x + 18 = 0

3(x2 + 5x + 6) = 0

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

x + 2 = 0 x + 3 = 0

- 2 - 2 - 3 - 3

x = -2 x = -3

x = {-3, -2}

SIMPLIFYING RADICALS9

@iteachalgebra


4 6 8 9 10

12 18 25 28 32

40 48 50 55 60

64 72 90 99 120

150 160 200 256 300

ANSWER KEY

2 6 4 2

2 2

3 10

4 3

2 3

9 2

3 2

4 7

2 7

5 16 2

4 2

4 10

2 10

16 3

4 3

25 2

5 2

55 4 15

2 15

8

16

36 2

6 2

9 10

3 10

9 11

3 11

4 30

2 30

25 6

5 6

16 10

4 10

100 2

10 2

100 3

10 3

OPERATIONS WITH RADICALS10

@iteachalgebra


2 + 2 4 3 + 3 5 6 + 2 6

2 - 2 4 3 - 3 5 6 - 2 6

2 • 2 4 3 • 3 5 6 • 2 6

72 + 50 4 45 - 125 5 27 + 2 5

ANSWER KEY

2 2 5 3 7 6

0 3 3 3 6

4 = 2 4 9 = 4(3)

= 12

10 36 = 10(6)

= 60

36 2 + 25 2

6 2 + 5 2

11 2

4 9 5 + 25 5

4(3) 5 + 5 5

17 5

12 5 + 5 5

5 9 3 + 2 5

5(3) 3 + 2 5

15 3 + 2 5

CLASSIFYING SEGMENTS, RAYS, & LINES

11

@iteachalgebra

Determine the segments, rays, and lines from the diagram.

SEGMENTS RAYS LINES

A

B

CD

Determine whether each statement is true or false.

Two lines can intersect at exactly one point.

Two lines can intersect at exactly two points.

The are an infinite number of points on a line.

A ray has an arrow at one end.

A segment and a line are identical.

ANSWER KEY

𝐴𝐶 𝐵𝐶 𝐴𝐵

𝐶𝐷

true

false

true

true

false

NUMBER OF EDGES & VERTICES12

@iteachalgebra

List the number of edges and vertices for each figure.

edges:

vertices:

edges:

vertices:

edges:

vertices:

rectangular prism

square pyramid

cylinder

ANSWER KEY

12

12

8

5

none

none

ANGLE MEASUREMENTS13

@iteachalgebra

Circle the type of angle shown and the best approximate measure of the angle.

acute

obtuse

right

60

100

90

acute

obtuse

right

60

100

90

acute

obtuse

right

60

100

90

acute

obtuse

right

60

100

90

ANSWER KEY

TYPES OF TRIANGLES14

@iteachalgebra

Name the triangle based on its sides and angles.

Names include equilateral, isosceles, and scalene, acute, obtuse, and right.

60

60 6090

60 30

120

30 30

45

4590

40

70

70

55

8045

ANSWER KEY

acute

acute

acuteright

isosceles

isosceles

obtuse

equilateral

right

scalene

isosceles

scalene

TYPES OF QUADRILATERALS15

@iteachalgebra

Determine if the quadrilateral is a square, rectangle, rhombus, trapezoid,

isosceles trapezoid, parallelogram, or more than one of those names.

>

>

>

>

>

>

> >

ANSWER KEY

parallelogram

rectangle, square

parallelogram

trapezoid parallelogram

parallelogram

rhombus

trapezoid

PARTS OF A CIRCLE16

@iteachalgebra

Given the circle, name each part.

Find the circumference and area of each circle.

5

8

Circumference: C = 2𝜋r Area: A = 𝜋r2

Circumference: C = 𝜋d Area: A = 𝜋r2

ANSWER KEY

chord

center

radius

diameter

C = 2𝜋r

C = 2𝜋(5)

C = 10𝜋

C ~ 31.4 units

C = 𝜋d

C = 𝜋(8)

C = 8𝜋

C ~ 25.1 units

A = 𝜋r2

A = 𝜋(5)2

A = 25𝜋

A ~ 78.5 units

A = 𝜋r2

A = 𝜋(4)2

A = 16𝜋

A ~ 50.3 units

r = 4

AREA FORMULAS17

@iteachalgebra

Calculate the area of each figure.

A = lw

13.5

4

10

3

A = 1

2bh

16

9.8

A = bh

rectangle triangle

parallelogram

A = 1

2h(b1 + b2)

trapezoid

5

9

4

ANSWER KEY

A = (13.5)(4)

A = 56 units2A =

1

2(10)(3)

A = 15 units2

A = (16)(9.8)

A = 156.8 units2A =

1

2(4)(5 + 9)

A = 2(14)

A = 28 units2

VOLUME FORMULAS18

@iteachalgebra

Calculate the volume of each figure.

V = s3 V = lwh

V = r2h

cube rectangular prism

cylinder

V = 4

3r3

sphere

4

3

5

6

6

6

5

4

8.5

ANSWER KEY

V = (6)3

V = 216 units3

V = (8.5)(4)(5)

V = 170 units3

V = (3)2(4)

V = (9)(4)

V = 36 units3

V ~ 113.1 units3

V = 4

3(5)3

V = 4

3(125)

V = 500

3 units3

V ~ 523.6 units3

TRANSFORMATIONS19

@iteachalgebra

Determine the type of transformation shown in each diagram as a translation,

rotation, reflection, or dilation.

ANSWER KEY

rotation translation

reflection or rotation dilation

CONGRUENT OR SIMILAR20

@iteachalgebra

Determine whether the figures shown are congruent or similar.

ANSWER KEY

congruent

congruent

congruent similar

similar

similar

getting ready forjvettermath.weebly.com/uploads/8/8/3/1/88313054/geometryreadinessprep... · the...

Documents