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S22 Midterm Exam

Last updated almost 4 years ago
40 questions
Note from the author:
Directions:
0) Make sure you've turned in your study guide.
On your desk - paper, pencil, calculator
On your browser - this test, Desmos links below.
In your backpack - phones, electronics, notes.
1) Take the test. If you're struggling, come back to the directions and formulae. Give it your best shot, but keep moving through the questions.
2) Some questions allow you to show your work. For these, just type what steps you took to get your answer. I may be able to give you partial credit if some of your steps are correct. You don't have to show your work.
3) Check your answers. Pay careful attention that you gave what the question was asking for. You can come by my desk and ask for your score before you submit.
4) Submit the test.
5) Close your Chromebook. Read, draw, or work on paper schoolwork quietly.

Desmos - Graphing
Desmos - Scientific

Formulae:

Discriminant: d = b^{2} - 4ac
Quadratic formula: x = \frac{-b\pm \sqrt{b^{2}-4ac}}{2a}
Difference of squares: a^{2} - b^{2} = (a-b)(a+b)
Difference of cubes: a^{3} -b^{3} = (a-b)(a^{2}+ab+b^{2})
Sum of cubes: a^{3} + b^{3} = (a+b)(a^{2}-ab+b^{2})

Desmos Graphing
Directions:
0) Make sure you've turned in your study guide.
On your desk - paper, pencil, calculator
On your browser - this test, Desmos links below.
In your backpack - phones, electronics, notes.
1) Take the test. If you're struggling, come back to the directions and formulae. Give it your best shot, but keep moving through the questions.
2) Some questions allow you to show your work. For these, just type what steps you took to get your answer. I may be able to give you partial credit if some of your steps are correct. You don't have to show your work.
3) Check your answers. Pay careful attention that you gave what the question was asking for. You can come by my desk and ask for your score before you submit.
4) Submit the test.
5) Close your Chromebook. Read, draw, or work on paper schoolwork quietly.

Desmos - Graphing
Desmos - Scientific

Formulae:

Discriminant: d = b^{2} - 4ac
Quadratic formula: x = \frac{-b\pm \sqrt{b^{2}-4ac}}{2a}
Difference of squares: a^{2} - b^{2} = (a-b)(a+b)
Difference of cubes: a^{3} -b^{3} = (a-b)(a^{2}+ab+b^{2})
Sum of cubes: a^{3} + b^{3} = (a+b)(a^{2}-ab+b^{2})

Desmos Graphing
1

Match the functions with their inverses.

Draggable itemCorresponding Item
x+2
subtraction
x2
division
x*2
x-2
multiplication
x/2
addition
\sqrt{x}
1

What is the order for evaluating the expression below?

5 - |4+3^{2}|

  1. subtract
  2. perform the absolute value
  3. add
  4. perform the exponent
1

A bottle of soda has 30 grams of sugar; a bottle of juice has 15 grams of sugar. Anna purchased 13 bottles of drinks, which collectively contain 300 grams of sugar. How many bottles of juice did Anna buy?

Hint: you will need to write two equations.

Write your answer as a number, no spaces.

1

At a very fancy bakery, Sam bought 4 cupcakes and 2 donuts and paid $23. Lyric bought 3 cupcakes and 7 donuts and paid $28.25. What is the cost, in dollars, of a donut at this bakery?

Hint: you will need to write two equations.

Write your answer as a number, no spaces.

4

Match the symbols to their shading requirements.

Draggable itemCorresponding Item
>
dashed, above
>
dashed, below
<
solid, above
<
solid, below
1

Which are solutions to the following system of inequalities?

y < 2x
y > -\frac{1}{4}x+9

Consider the function

f(x) = \frac{5}{3}(x+3)^{2}
1

How does the graph of f(x) compare with the graph of x^{2}?

1

What is the vertex of f(x)?

Use (x, y) format with one space after the comma.

1

On what interval does the function decrease?

1

Select the end behaviors for the function. (2)

1

What is the value of f(3)?

Enter your answer as a number, no spaces.

Consider the function

f(x) = \sqrt{x - 1} -2
1

How does the graph of f(x) compare with the graph of \sqrt{x}?

1

What is the domain of the function?

1

What is the inverse function of f(x)?

Use y=... format, no spaces. You may leave your answer in vertex form.

1

What is the value of f(5)?

Enter your answer as a number, no spaces.

1

Simplify by combining like terms.

2(3 - i) - 4(1 - 2i)

Use a+bi format, no spaces, where a and b are simplified real numbers.

1

Simplify.

(2 + 5i)(1 - i) - (4 + 6i)

Use a+bi format, no spaces, where a and b are simplified real numbers.

1

The discriminant of a quadratic equation is 34. Find the number and type of roots.

1

The discriminant of a quadratic equation is -64. Find the number and type of roots.

1

The discriminant of a quadratic equation is -5. Find the number and type of roots.

1

The discriminant of a quadratic equation is 108. Find the number and type of roots.

For the polynomial below, predict the end behaviors. Find its roots and their multiplicities.

f(x) = -(x+1)2
1

Select the end behaviors for the function. (2)

1

What are the roots of the polynomial? Check all that apply.

0

Do any of the roots have multiplicity greater than 1?

If so, type the roots that have multiplicity in an increasing list. Separate roots with a comma and a space.

If not, type no.

For the polynomial below, predict the end behaviors. Find its roots and their multiplicities.

f(x) = x2 + 4x - 5
1

Select the end behaviors for the function. (2)

1

What are the roots of the polynomial?

Check all that apply.

0

Do any of the roots have multiplicity greater than 1?

If so, type the roots that have multiplicity in an increasing list. Separate roots with a comma and a space.

If not, type no.

For the polynomial below, predict the end behaviors. Find its roots and their multiplicities.

f(x) = 2x4 - x2 - 3
1

Select the end behaviors for the function. (2)

1

What are the roots of the polynomial?

Check all that apply. (# roots = degree)

0

Do any of the roots have multiplicity greater than 1?

If so, type the roots that have multiplicity in an increasing list. Separate roots with a comma and a space.

If not, type no.

For the following polynomial, predict the end behaviors. Find its roots and their multiplicities.

f(x) = 24x3 - 3
1

Select the end behaviors for the function. (2)

1

What are the roots of the polynomial? Hint: you will need the quadratic formula.

Check all that apply.

For the following polynomial, predict the end behaviors. Find its roots and their multiplicities.

f(x) = 5 - \frac{1}{3}x
1

Select the end behaviors for the function. (2)

1

What are the roots of the polynomial?

Check all that apply.

For the following polynomial, predict the end behaviors. Find its roots and their multiplicities.

f(x) = -x5 + 4x3
1

Select the end behaviors for the function. (2)

1

What are the roots of the polynomial?

Use x={#, ...} format, using exactly one space after each comma.

0

Do any of the roots have multiplicity greater than 1?

If so, type the roots that have multiplicity in an increasing list. Separate roots with a comma and a space.

If not, type no.

For the following polynomial, predict the end behaviors. Find its roots and their multiplicities.

f(x) = 4x3 + 2x2 - 6x - 3
1

Select the end behaviors for the function. (2)

1

What are the roots of the polynomial?

Check all that apply.

0

Do any of the roots have multiplicity greater than 1?

If so, type the roots that have multiplicity in an increasing list. Separate roots with a comma and a space.

If not, type no.