Topics 1-7 Cumulative Review

Topics 1-7 Cumulative Review

Topic 1: Solve Problems Involving Real Numbers
Topic 2: Apply Laws of Exponents
Topic 3: Solve Equations and Inequalities
Topic 4: Understand Linear Relationships
Topic 5: Define, Evaluate, and Compare Functions
Topic 6: Understand Relationship Involving Triangles
Topic 7: Understand Congruence and Similarity

​Draw each graph under its correct transformation

Draw

What is the solution to the equation −125 = x³?

Multiple Choice

Consider the numbers:

$$\sqrt[]{9},\pi,\ -\frac{5}{8},\ 7.875$$



Which number is irrational?

• $$\sqrt[]{9}$$

• $$\pi$$

• $$-\frac{5}{8}$$

• $$7.875$$

Multiple Choice

Xavier asked 18 players on his baseball team whether they prefer using a wood or an aluminum bat. He used a calculator to compare the number of players who said they prefer using a wood bat to the total number he surveyed.
The calculator results are shown below.
0.22222222

Choose the number that shows the decimal as a fraction.

• $$\frac{2}{10}$$

• $$\frac{2}{11}$$

• $$\frac{22}{100}$$

• $$\frac{2}{9}$$

Multiple Choice

Choose the best number of solutions for the lines pictured.

• • One. The lines intersect at only one point.

• • Infinitely many. The lines are the same.

• • Infinitely many. The lines are parallel.

• • None. The lines are parallel.

Multiple Select

From the table display, choose the relations that are functions.

• (-2,5), (0, 7), (3,3), (4,9)

• (-1,0), (0,1), (2,6), (-1,8)

• (1,7), (3,5), (3,0), (5,9)

• (-5,9), (-3,9), (0,9), (8,9)

Multiple Select

Choose the set(s) that are NOT possible side lengths of a unique triangle?

• 4, 7, 12

• 6, 6, 10

• 5, 8, 12

• 7, 9, 16

Multiple Choice

Triangle ABC has coordinates A(0, 0), B(1.5, 4), and C(3, 0). A’B’C’ is the image of ABC after a dilation with center at the origin and a scale factor of 4. What are the coordinates of B’?

• (5.5, 8)

• (12, 0)

• (5.5, 8)

• • (6, 16)

Multiple Select

Select all that are true

• • The slope is positive.

• • The y-intercept is 2.

• • The relationship is proportional.

• • The equation of the line is y = 2x.

• • The equation of the line is $$y=\frac{1}{2}x$$

Multiple Choice

The slope represents a(n)   increase  of   $0.79 for each mile driven.
The y-intercept represents that the truck rental company charges $27  for a truck rental when 0 miles are driven.

Which equation best represents this?

• y= 27x + 0.79

• y = 27 (0. 79x)

• y = 0.79x + 27

• y= 27 + 0.79

• y= 0.79b (27)

Fill in the Blanks

Reminder: be sure your answer is in slope-intercept form:

y=mx+b where m and b are replaced by numbers.

Multiple Choice

Which ordered pair is the solution to the system of equations?

y = 2x − 4
y = −2x + 4

• • (0, 2)

• • (0, 0)

• • (2, 0)

• • (8, 0)

Fill in the Blanks

What is the sum of the interior angle measures of a regular polygon with 11 sides?

Fill in the Blanks

What is the solution to the system of equations?

Fill in the Blanks

Tibor is 5.5 feet tall and casts a shadow that is 7 feet long. Tibor’s sister casts a shadow that is 5.25 feet long. How many feet tall is Tibor’s sister? Express your answer as a decimal.

Multiple Choice

What is the solution to the inequality?

1.5x – 8.3 ≤ –2.3

• • x ≤ 9

• • x ≤ 4

• • x ≥ –9

• • x ≥ –4

Multiple Choice

Apply the Laws of Exponents to write an equivalent expression of −3a⁴b⁶⋅(−5a³b²).

• • −8a⁷b⁸

• • −8a¹²b¹²

• • 15a⁷b⁸

• • 15a¹²b¹²

Fill in the Blanks

The star Bellatrix is 1.4 × 10¹⁵ miles from Earth. Barnard’s star is $3.5x10^{13}$ miles from Earth.

How far is Barnard’s star from Earth, in standard form?

Multiple Choice

The perimeter of a garden is 88 feet. The length is 12 feet greater than the width.

Which system of equations represents the situation?

• • 2L + 2W = 88
    L = W + 12

• • 2L + 2W = 88
    L = W – 12

• • 2L + 2W = 88
    L + W = 12

• • L + W = 88
    L + W = 12

Multiple Select

Select the intervals that are decreasing.

• Interval 1

• Interval 2

• Interval 3

• Interval 4

• Interval 5

Fill in the Blanks

Multiple Choice

Consider the system of equations.

y = −3x + 8
y = −2x + 4

Multiple Select

Consider vertical and straight angles to help solve this problem.

• • 
    

    m∠1 = 84.7°

• • m∠1 = 115.2°

• • m∠2 = 30.5°

• • m∠2 = 64.8°

• • m∠3 = 30.5°

Multiple Choice

Which expression is equivalent to (4x − 1)(−3.4x)?

• • −17x² − 1

• • −13.6x² + 3.4x

• • 13.6x² − 3.4x

• • 17x² + 1

Multiple Choice

Factor the expression 6x⁵y⁴ − 8x⁶y⁷ completely.

• x⁵y⁴(8 − 8xy³)

• 2x⁵y⁴(3 − 4xy³)

• 2xy(3 − 4x⁵y⁷)

• 2x⁵y⁷(3 − 4xy)

Multiple Select

Which angles are congruent to angle 5?

• $$\angle1$$

• $$\angle2$$

• $$\angle3$$

• $$\angle6$$

• $$\angle7$$

Fill in the Blanks

Angle 6 and Angle 3 form a supplementary angle. If m $\angle6$ = 85 $\degree$ , what is the measure of $\angle3$ , in degrees? $\degree$

Multiple Choice

Which of these tables represent a nonlinear function?

Multiple Choice

Describe the translation that maps ABCD onto A’B’C’D’?

• Left 6, up 5

• • Left 6, down 5

• • Right 6, up 5

• Right 6, down 5

Fill in the Blanks

The vertices of figure KLMN are K(1, 1), L(4, 1), M(2, 3), and N(5, 3). If KLMN is reflected across the line 

y = –1, find the coordinates of vertex L’. Enter your answers in the boxes.

Multiple Choice

What is the coordinate for POINT B of the resulting image A’B’C’D’E’ after ABCDE is rotated 90° counterclockwise about the origin.

• (-2,2)

• (-4,6)

• (-2,6)

• (-4,2)

• (-6,4)

Draw

Draw the image of figure RSTU after a reflection across the line x=1

Name your points.

Multiple Choice

Which two figures are congruent?

• Figures A and B

• Figures B and C

• Figures C and D

• Figures A and C

• Figures B and D

Fill in the Blanks

Multiple Choice

What is the transformation that maps ABCD to EFGH?

• • 
    

    
    Reflection across the x-axis

• • 
    
    Rotation 270° counterclockwise about the origin

• • 
    Rotation 180° counterclockwise about the origin

• • 
    Translation down 6 and right 5

Multiple Select

Triangles ABC and JKL are similar. Which proportion could be used to find KL? Select all that apply.

• $$\frac{12}{2.4}=\frac{KL}{10}$$

• $$\frac{AB}{JK}=\frac{BC}{KL}$$

• $$\frac{AB}{JK}=\frac{KL}{BC}$$

• $$\frac{2.4}{12}=\frac{10}{KL}$$

• $$\frac{12}{2.4}=\frac{10}{KL}$$