Alg. 1 mock test 4

​Positive Association	​Negative Association	​No Correlation
​Both variables are increasing.	One variable is increasing, the other is decreasing.​	There is no relationship between the variables.​

​Types of Correlation

Standard Deviation

A measure of how far the numbers is a dataset are from the mean.

See this video for calculator help: https://youtu.be/ptQ6IKVYP6I

Measures of Spread

By Ally Gniadek

Vocabulary

• Outlier- a value that is very different from the other values in a data set

• ex: 7,12,64,10,9 {64 would be considered the outlier}

Effects of outliers: 7,20,54,9,12,8,5

• Write the data in numerical data: 5,7,8,9,10,12,54

• Determine Outlier: 54

• What is the mean median mode range with and without outlier

• How does the outlier affects mean median mode & range

Which measure of central tendency is best?

• Kobe Bryant's scores during a 6 game stretch were: 40,24,32,61,13,32

• Which measure gives Kobe's average?

• How many times did he score the same amount?

• Which measure best describes Kobe's typical points in a game?

Multiple Choice

Which has a larger IQR?

• Zach

• Steven

• They have the same IQR

Multiple Choice

If a number is added to the set that is in the middle of the data, how does this affect the range?

• increase

• decrease

• stay the same

• both increase and decrease

Multiple Choice

Which dot plot shows a larger spread of data?

• Basketball Players

• Softball Players

Multiple Choice

Which inference about the two populations is true

• Both sets of data have the same interquartile range

• Both sets of data have the same median

• Ander's data centers areound 6 and Marcus's data centers around 7

• The interquartile range for Ander's data is .5 greater than the interquartile range for Marcus's data

How can we use the measures of center to compare data sets or populations?

• Compare the medians

• Compare the range of each

• What does the range tell you?

• The correct answer is A

Multiple Choice

At a pet store, the lizards in aquarium A have a mean length of 13 cm and a range from 9 cm to 15 cm. In aquarium B, the lizards have a mean length of 15 cm and a range from 14 cm to 17 cm. Which statement BEST compares the lizards in the two aquariums?

• On average, the lizards in aquarium A are longer.

• On average, the lizards in aquarium B are longer.

• Aquarium A has the longest lizard at this pet store.

• The lizards in aquarium B vary in length more than aquarium A.

Multiple Choice

The annual salary for a computer technician at Company A ranges from $41,000 to $63,000, with a mean of $58,000. At Company B, the annual salary for the same position ranges from $45,000 to $$65,000, with a mean of $56,000. Which statement is TRUE when comparing the salaries of computer technicians for the two companies?

• The highest paid computer technician works at Company A.

• B)On average, a computer technician at Company A earns more than at Company B.

• On average, a computer technician at Company B earns more than at Company A.

• Salaries for computer technicians at Company B vary more than salaries at Company A.

Multiple Choice

Brad and Tom are comparing their classes' scores on a math test. Both of their classes had mean scores of 80 on the test, but Brad's class had a range of 6 while Tom's class had a range of 30. If the highest possible score was 100, which class had the LOWEST score in it?

• Brad's class had the lowest score in it.

• Tom's class had the lowest score in it.

• The lowest score occurred in both classes.

• It cannot be determined from the information.

The closer to 0, the weaker the correlation. Very close to 0 is no correlation. The closer to -1 or 1, the stronger the correlation. -1 and 1 are perfect.

Multiple Choice

Estimate the correlation coefficient for this scatterplot.

• r = 1.2
• r = 0.89
• r = 0
• r = -0.89

Multiple Choice

Estimate the correlation coefficient for this scatterplot.

• A) r = -0.9

• B) r = 1

• C) r = 0.9

• D) r = -1

Multiple Choice

Average time spent listening to music per day and average time spent watching TV per day.  $$r=-.17$$  

• strong positive

• strong negative

• weak positive

• weak negative

Multiple Choice

Score on science exam and number of words written on the essay question.  $$r=.28$$  

• strong positive

• strong negative

• weak positive

• weak negative

Study Time and Grades

As study hours increase, grades increase. There is a positive correlation between hours and grades.

So....Do hours spent studying cause higher grades?

To show the overall trend of a data set, we can use a ​Line of Best Fit.

​

A line of best fit should:

• Follow the trend of the data

• Split the data in half

• Help to estimate or predict values that are not already given in the set.

Line of Best Fit

​

​Use desmos to give you this information! (6.3 gives you steps)

Multiple Choice

Using your graphing calculator determine the line of best fit and the correlation coefficient of the data in the table.

• y = 4.6x - 347

  r = .942

• y = 4.6x - 347

  r = .888

• y = 4.6x + 347

  r = .942

• y = 4.6x + 347

  r = .888

Multiple Choice

As shown in the table, a person's target heart rate during exercise changes as the person gets older. Use the graphing calculator to find the correlation coefficient (r).

• -0.999

• -0.664

• 0.998

• 1.503

Multiple Choice

What is the line of best fit?

• f(x)= 5x+1.82
• cannot be determined
• f(x)= 1.82x + 5.02
• f(x)= 1.1x + 4.2

Multiple Choice

D) Use the line of best fit to determine the profit in thousands if the cost of the product was $15. (Round to the nearest tenth.)

• $$y=-49.9$$  

• $$y=49.9$$  

• $$y=-0.5$$  

• $$y=5.8$$  

Multiple Choice

D) Use the line of best fit to determine the profit in thousands if the cost of the product was $15. (Round to the nearest tenth.)

• $$y=-49.9$$  

• $$y=49.9$$  

• $$y=-0.5$$  

• $$y=5.8$$  

You have your basic one step equations where you use the opposite operator to solve for the variable.

Always maintain balance by doing the same operation to both sides.

When you have more than one step to do, start by adding or subtracting any constants by themselves.

Then follow that with multiplying and dividing to isolate the variable.

Sometimes you have a variable on both sides of the equation.

you can add and subtract variables just like constants. I suggest always starting with the smaller coefficient. notice 3 is smaller than 5, so we can subtract 3x from both sides. Then it becomes an easy two step equation. Try a few for practice.

Solving Inequalities is like Solving Equations

• Distribute First

• Get Like Terms together

• Do Opposite Operations

• BUT... If you divide or multiply by a NEGATIVE NUMBER you must flip the inequalitiy sign

​Use the video if needed!
Reminder, inequalities are similar to linear equations with exception of the "-" rule

Multiple Choice

Solve for x. (Use the image to identify the correct inequality and graph.)

$$\frac{x}{8}\ >\ 4$$  

• A

• B

• C

• D

Multiple Choice

What inequality does the number line graph represent?

• x ≤ -4
• x ≥ -4
• x < -4
• x < 4

​Graphing Inequalities... REMINDER

​Set up the inequality like we would     y = mx + b where “ y ” is all alone.

1. Graph the line (same as a linear equation)

2. Plot the points on a graph and connect the dots.

3. Make the line dotted or straight based on the inequality symbol

   1. < or >  use  dotted

   2. ≤ or ≥  use straight

4. Determine which side of the line will be shaded by plugging in random points on either side and seeing which ones make the inequality true

Multiple Choice

Which of the following equations match the given graph?

• y ≤ -3/4 x + 3
• y ≥ -3/4 x + 3
• y < -3/4 x + 3
• y > -3/4 x + 3

Multiple Choice

What graph matches this inequality?

Parallel and Perpendicular Lines

Multiple Select

Which line(s) are perpendicular to the line:  $$8x+2y=22$$  

• $$y=\frac{1}{4}x-1$$  

• $$y=-\frac{1}{4}x+13$$  

• $$y-12=-\frac{1}{4}\left(x+13\right)$$  

• $$y-5=4\left(x+8\right)$$  

• $$y-2=\frac{1}{4}\left(x+3\right)$$  

Multiple Select

Which lines are parallel to the line:  $$5x+8y=32$$  

• $$y=\frac{5}{8}x-1$$  

• $$y=-\frac{5}{8}x+13$$  

• $$y-12=\frac{5}{8}\left(x+13\right)$$  

• $$y-5=\frac{5}{8}\left(x+8\right)$$  

• $$y-2=-\frac{5}{8}\left(x+3\right)$$  

Secret: You solve them the same way as other equations.

Here we have a literal equation already solved for H.

But what if we want to solve for A?

we can use the same opposite operations method we have been using to achieve this.

Our goal to get A by itself on one side of the equal sign and everything else on the other side.

on the next slide we will go over this step by step.

Why do we even need this?

Some common literal equations involve converting temperature from celsius to fahrenheit or vice versa. There are also lots of literal equations in geometry. They will save you time.

Maybe you should try a few yourself.

Use paper and pencil if needed.

Multiple Choice

Solve for b. 

$$A\ =\ \frac{1}{2}bh$$  

• $$\frac{2A}{h}$$  

• $$2Ah$$  

• $$\frac{2}{h}$$  

• $$\frac{Ah}{2}$$  

Multiple Choice

Solve for W.

$$A=LW$$  

• $$A=\frac{L}{W}$$  

• $$W=A$$  

• $$W=\frac{L}{A}$$  

• $$W=\frac{A}{L}$$  

Multiple Choice

Solve for a.

• $$a=\frac{1-3c}{2}$$

• $$a=\frac{2}{-3c+1}$$

• $$a=-3c+3$$

• $$a=\frac{3c-1}{2}$$

Multiple Choice

This is a...

• Relation

• Function

Multiple Choice

This is a...

• Relation

• Function

Multiple Choice

This is a...

• Relation

• Function

Multiple Choice

What is the domain of the graph?

How far left and right the graph goes on the x-axis.

• $$−5\le x\le7$$

• $$−5\le x\le6$$

• $$−5\le x\le4$$

• $$−5\le x\le5$$

Multiple Choice

What is the range of the graph?

How far up and down the graph goes on the y-axis.

• $$−4\le y\le9$$

• The y-values are -5, -2, 0, 2 and 5

• The y-values are -4, 0, 9

• $$−5\le y\le4$$

Multiple Choice

What is the domain of the graph?

How far left and right the graph goes on the x-axis.

• $$−7\le x\le7$$

• x values are:

  {-7, -4, 0, 4, and 7}

• x values are:

  {-3, 0, and 4}

• $$−3\le x\le4$$

Multiple Choice

Which graph represents a function. Whose domain is the set of non-negative real numbers?

Function Notation from an equation

• f(2) --> You were given an input --> plug 2 in for x in the equation

• f(x) = 2 --> You were given an output --> plug 2 in for f(x) and solve

Solve the function

​This problem is asking us to replace all the X's (inputs) we see with (8) --> yes include the parenthese to avoid mistakes.

​Using Desmos Calculator (above), the calculator will do all the hard work for us and pop out an answer.

Do not include the f(x)=

Multiple Choice

Find f(7) for the following function: f(x) = 4x-9

• f(7) = 4

• f(7) = 37

• f(7) = 19

• f(7) = -0.5

Multiple Choice

Find x if f(x) = -5 for the following function: f(x) = 4x - 9

• f(-3.5) = -5

• f(11) = -5

• f(-29) = -5

• f(1) = -5

Multiple Choice

Find g(-6) for the following function: g(x) = 3(x - 1)

• g(-6) = -21

• g(-6) = -15

• g(-6) = -1

• g(-6) = -3

Adding Polynomials

Multiple Choice

Find the sum.

(2x² + 5x - 7) + (3 - 4x² + 6x)

• 2x² + 3x + 1

• -2x² - 11x - 4

• 2x²+ 5x - 7

• -2x² + 11x - 4

Subtracting Polynomials

Multiple Choice

Add or Subtract to Simplify:

(4n⁴ - 8n + 4) - (8n² + 4n⁴ + 1)

• -8n² - 8n + 3

• -7n² - 8n + 3

• -6n² - 8n + 3

• -7n² - 4n + 3

Match

F(x) = 2x³ - 3x² - 7x + 8 and G(x) = x³ + 4x²​ - 2x - 5

Which is the Step 1

• (G - F)x

• (G + F)x

• (F + G)x

• (F - G)x

x³ + 4x²​ - 2x - 5 - 2x³ + 3x² + 7x - 8

x³ + 4x²​ - 2x - 5 + 2x³ - 3x² - 7x + 8 +

2x³ - 3x² - 7x + 8 + x³ + 4x²​ - 2x - 5

2x³ - 3x² - 7x + 8 + x³ - 4x²​ + 2x + 5

• x³ + 4x²​ - 2x - 5 - 2x³ + 3x² + 7x - 8

• x³ + 4x²​ - 2x - 5 + 2x³ - 3x² - 7x + 8 +

• 2x³ - 3x² - 7x + 8 + x³ + 4x²​ - 2x - 5

• 2x³ - 3x² - 7x + 8 + x³ - 4x²​ + 2x + 5

Multiplying with variables

(x+3)(x+4)

Multiple Choice

Write the expanded (general) form of the product (x+3)(x+6).

• x²+18x+9

• x²+9x+18

• x²+18x+18

Multiple Choice

Simplify
(p − 8)²

 Hint: (p − 8)² = (p − 8)(p − 8)

• p ² − 16p − 64 
• p ² + 16p + 64 
• p ² − 16p − 8
• p ² − 16p + 64 

Multiple Choice

Find the Product.
(2x + 3)(2x - 3)

• 4x² - 9 
• 4x² + 9
• 4x²- 12x - 9
• 4x² + 12x - 9

​Over the next few slides, you will review how to factor a quadratic equation from standard form to factored form. In addition, you will learn how to take vertex form and convert it to standard form. Furthermore, you will review how to multiply a polynomials together using the array method. Lastly, you will review how to find the solutions to the quadratic equation. Let's review...

​Standard Form

​Factored Form

​Vertex Form

​Example problem: Factoring Quadratics with a leading coefficient greater than 1.

​Array Method

​First

​Outside

Inside

Last

​Factors

Match

Match the following factored quadratic expressions to their standard form.

• $$\left(2x-1\right)\left(x+2\right)$$

• $$\left(3x-1\right)\left(x-4\right)$$

• $$\left(3x+1\right)\left(x-4\right)$$

• $$\left(2x+1\right)\left(x-2\right)$$

• $$\left(3x+1\right)\left(x-2\right)$$

• $$2x^2+3x-2$$

• $$3x^2-13x+4$$

• $$3x^2-11x-4$$

• $$2x^2-3x-2$$

• $$3x^2-5x-2$$

Quadratic Formula

• Must be in standard form and =0

• Use when equation is not factorable

• ALL QUADRATICS CAN BE SOLVED WITH THE QUADRATIC FORMULA!

Multiple Choice

Solve the equation using the quadratic formula.

$$-10k^2-6k+6=0$$  

• $$x=\frac{-3\pm\sqrt{69}}{10}$$  

• $$x=\frac{6\pm2\sqrt{69}}{-20}$$  

• $$x=\frac{-3\pm\sqrt{51}}{10}$$  

• $$x=\frac{6\pm2\sqrt{51}}{-20}$$  

Parabola with a Minimum

• 2 x-intercepts (aka roots, zeros)

• Note that the vertex IS the minimum

• It occurs at the bottom

• See that the axis of symmetry goes THROUGH the vertex

Parabola with a Maximum

• Axis of symmetry still goes THROUGH the vertex

• The vertex IS the maximum, at the top

• 2 x-intercepts (aka roots, zeros)

Multiple Choice

What is the equation for axis of symmetry?

• y=3

• x=3

• x=5

• x=1

Multiple Choice

What are the x-intercepts?

• 0 and 2

• -4 and 0

• 2 and 3

• 0 and 4

Multiple Choice

Use the graph to determine the roots:

• -1 and -3

• 1 and -3

• 1 and 3

• -1 and 3

Multiple Choice

What is another word for zeros?

• y-intercepts

• roots

• vertex

• axis of symmetry

Multiple Choice

Calculate the zeros of the quadratic.

• x = 6 and 3

• x = 1 and 0

• x = 0 and 3

• x = 3 and 1

Multiple Choice

Find the vertex.

y = -x² -10x + 3

• (5,-72)

• (28,-5)

• (-5, 78)

• (-5, 28)

Key Features of Standard Form

Multiple Choice

What is the vertex of y=x²+4x+3?

• (2,1)
• (-2,1)
• (0,0)
• (-2,-1)

Multiple Choice

Elaine shoots an arrow upward at a speed of 32 feet per second from a bridge that is 28 feet high. The height of the arrow is given by the function h(t) = -16t² + 32t + 28, where t is the time in seconds. What is the maximum height that the arrow reaches?

• A. 24 ft.

• B. 30 ft.

• C. 44 ft

• D. 32 ft.

Multiple Choice

The height of a water balloon that is launched into the air is given by h(t) = -5t² + 40t + 2. From what height was the balloon released?

• 2 meters

• 5 meters

• 40 meters

• 20 meters

Multiple Choice

The height of a water balloon that is launched into the air is given by h(t) = -5x²+20x+25. When will the balloon explode on the ground?

• 5 seconds

• 1 second

• 2 seconds

• 3 seconds

Multiple Choice

Jason launched a rocket for a physics experiment. This equation can be used to find the height (h), in feet, of the rocket after t seconds.

h = -16t2 + 288t + 8

How many seconds will it take for the rocket to reach a height of 1,304 feet?

• 9.0 seconds

• 9.6 seconds

• 81.0 seconds

• 82.0 seconds

Multiple Choice

Rafael drops a ball from a third-story window. This equation represents the approximate height, h, in meters, of the ball above the ground after it falls for t seconds.

h = -5t² + 45

When is the ball at ground level?

• only at t = 0 seconds

• only at t = 3 seconds

• only at t = 9 seconds

• at both t = 0 seconds and t = 3 seconds