Algebra 2 Quarter 1 Test Flashcards

Questions and Answers

Select all of the irrational numbers.

√2 (correct)

√34 (correct)

π (correct)

All of the above

Which inequality and graph represent all possible solutions of: |−3x|≤6?

{-2≤x≤2}

What is the probability of tossing heads using Jeff and Kevin's results?

11/20

What is the correct solution mentioned in the problem?

7 Signup and view all the answers

Select all sets of numbers that √31 belongs to.

Irrational numbers Signup and view all the answers

What is the value of 1/6 ÷ (-3/18)?

-1 Signup and view all the answers

What is the value of 4(3h-6)/1+h for h = -2?

48 Signup and view all the answers

What is the opposite and the reciprocal of 500?

Opposite: -500, Reciprocal: 1/500 Signup and view all the answers

What is the solution to 3y+20= 3+2y?

-17 Signup and view all the answers

What does the graph represent for: −6≤2x≤6?

{-3≤x≤3} Signup and view all the answers

Which points represent the graph for y = 2x + 1?

(0, 2) Signup and view all the answers

What is the slope of the line represented by the equation 3x + 5y = -15?

-3/5 Signup and view all the answers

Choose the set of ordered pairs that represents a function.

{(-3,-5),(-5,-3),(-7,-7)} Signup and view all the answers

Which ordered pair is a solution to the equation represented by the graph?

(0,-1) Signup and view all the answers

What is the slope of the line passing through the points (-8,3) and (-7,-5)?

-8 Signup and view all the answers

Select all true statements about the graph.

The line has an equation of y = 4 Signup and view all the answers

What are the slope and y-intercept of the line given by 12x - 4y = -96?

m = 3, y-intercept = 24 Signup and view all the answers

What is the vertex of the equation y = |x + 2| - 4?

-2, -4 Signup and view all the answers

What is the y-intercept of the line 9x + 6y + 1 = 0?

-1/6 Signup and view all the answers

What is the solution set for the system of equations: x + 2y + z = 5, 2x - 6 + 5z = 3, x + 3z = 3?

0, 2, 1 Signup and view all the answers

What is the solution set for the equations: x - y + z = -1, x + y + 3z = -3, 2x - y + 2z = 0?

4, 2, -3 Signup and view all the answers

What is the solution set for the equations: 6x + y = 7, x + 12y = 13?

1, 1 Signup and view all the answers

What is the solution set for the equations: 2x + 3y = 12, 3x + 4y = 17?

3, 2 Signup and view all the answers

What is the solution set for the system of equations: x + 2y + z = 4, 2x - y + 4z = -8, -3x + y - 2z = -1?

3, 2, -3 Signup and view all the answers

What is the solution set for the equations: 5z + 4y = 4, 3x - 2y = 0, x + 3z = -8?

4, 6, -4 Signup and view all the answers

What is the solution set for the equations: 4x - y + z = -5, -x + y - z = 5, 2x - z - 1 = y?

0, 2, -3 Signup and view all the answers

What is the solution set for the equations: 2x + 7y = 15, 3x - 6y = 6?

4, 1 Signup and view all the answers

What is the solution set for the equations: x - y + z = -1, x + y + 3z = -3, 2x - y + 2x = 0?

4, 2, -3 Signup and view all the answers

What is the answer to the video game word problem?

5 Signup and view all the answers

Identify the vertex and the y-intercept of the function y = -3(x + 2)^2 + 5.

Vertex: (-2, 5), Y-Intercept: (0, -7) Signup and view all the answers

Write in the vertex form: y = 2x^2 + 12x + 8.

y = 2(x + 3)^2 - 10 Signup and view all the answers

What is the vertex and y-intercept of the function y = 2(x - 2)^2 - 4?

Vertex: (2, -4), Y-Intercept: 4 Signup and view all the answers

Factor the expression: -15x^2 + 15x + 20.

5(-3x + 3x + 4) Signup and view all the answers

Select an equivalent expression to x^2 + 10x + 16.

(x + 2)(x + 8) Signup and view all the answers

Select an expression equivalent to 3x^2 + 14x + 16.

(x + 2)(3x + 8) Signup and view all the answers

Write 3 + √-49 in the form of a + bi.

3 + 7i Signup and view all the answers

Write -3 - √-180 in the form of a + bi.

-3 - 6i√5 Signup and view all the answers

Find the absolute value of |-5 + i|.

√26 Signup and view all the answers

Simplify (3i)(-i).

3 Signup and view all the answers

Given the function y = 2x^2 - 8x + 4, find the y-intercept and the vertex.

y-intercept: 4, Vertex: (2, 4) Signup and view all the answers

Enter the value equivalent to (-3 + 4i) - (2 + 6i).

-5 - 2i Signup and view all the answers

Simplify (-4 - 4i)(3 + 2i).

-4 - 20i Signup and view all the answers

Indicate whether the equation 5/20x = 1/4x has solutions.

Infinitely many real solutions Signup and view all the answers

Indicate whether the equation 3x = 4x + 5x has solutions.

One real solution Signup and view all the answers

Indicate whether the equation √2x + 3 + 6 = 0 has solutions.

No real solutions Signup and view all the answers

How long will it take the stone to hit the ground as modeled by y = −16t^2 + 358?

Round to the nearest hundredth of a second. Signup and view all the answers

Study Notes

Irrational Numbers

Examples include √2, √34, and π.
√31 belongs to irrational and real numbers.

Inequalities

The inequality |−3x|≤6 translates to the solution set {-2≤x≤2}.
The graph for −6≤2x≤6 corresponds to {-3≤x≤3}.

Probability

The probability of tossing heads, based on Jeff and Kevin's coin toss results, is 11/20.

Mistakes in Solutions

In a multi-step problem, the first mistake occurs in step 1; the correct solution is 7.

Algebraic Evaluations

The value of 1/6 ÷ (-3/18) is -1.
For h = -2 in the expression 4(3h-6)/(1+h), the result is 48.

Opposites and Reciprocals

The opposite of 500 is -500, and the reciprocal is 1/500.

Graph Representations

The graph of the equation y = 2x + 1 passes through points (-1,0) and (0,2).
The slope of the line defined by 3x + 5y = -15 is -3/5.

Function and Ordered Pairs

The ordered pairs {(-3,-5), (-5,-3), (-7,-7)} represent a function.
The ordered pair (0,-1) is a solution to the equation represented by the graph.

Slope Calculations

The slope of the line through points (-8,3) and (-7,-5) is -8.
For the equation 12x - 4y = -96, the slope is 3 and the y-intercept is 24.

Vertex and Intercepts

The vertex of y = |x+2| -4 is at (-2,-4).
The y-intercept of 9x + 6y + 1 = 0 is -1/6.

Systems of Equations Solutions

For x + 2y + z = 5, 2x - 6 + 5z = 3, x + 3z = 3, the solution set is (0, 2, 1).
The systems of equations yield solutions (4,2,-3), (1,1), and (3,2) for other specified sets.

Polynomial Factoring and Forms

Vertex form of the polynomial y = 2x² + 12x + 8 is y = 2(x + 3)² - 10.
(x^2 + 10x + 16) can be factored to (x+2)(x+8) and (3x^2 + 14x + 16) to (x+2)(3x+8).

Complex Numbers

Convert 3 + √-49 to the form a + bi gives 3 + 7i.
Simplifying -3 - √-180 results in -3 - 6i√5.

Absolute and Imaginary Values

The absolute value of |-5 + i| is √26.
Simplifying (3i)(-i) results in 3.

Graph Heights and Time

In the function y = −16t² + 358, it models the height of a stone dropped from a cliff. The time to hit the ground can be calculated using a quadratic equation setup.

Solutions Types for Equations

The equation 5/20x = 1/4x has infinitely many solutions.
The equation 3x = 4x + 5x has one real solution.
The equation √(2x+3) + 6 = 0 has no real solutions.

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Test your knowledge with these flashcards covering topics from Algebra 2, Quarter 1. Each card challenges you on key concepts such as irrational numbers, inequalities, and probability. Perfect for revision or self-assessment before your upcoming exam!