Quarter Catch-Up Pre-AP Algebra 1

Sequences,
Function Notation,
Slope

Drag and Drop

Can you predict the pattern?



3, 9, 15, 21, 27, 33, ​ ​

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Drag these tiles and drop them in the correct blank above

39

45

51

36

44

50

40

46

52

Drag and Drop

What about this one? 12, 24, 36, 48, 60, 72​

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Drag these tiles and drop them in the correct blank above

84

96

108

82

86

94

98

100

110

106

Cue Math defines as “the sequence where the common difference remains constant between any two successive terms.” 

https://www.cuemath.com/algebra/arithmetic-sequence/

​

​Arithmetic Sequences

​Basically it is a group of numbers which contain a pattern with the same difference between a number and the one next to it.

• Can start with any first term

• Must increase or decrease by a constant amount between each term in the sequence.

• Cannot skip any terms

​

​Characteristics of an arithmetic sequence:

​Look for the same amount being added or subtracted with each new term.

Multiple Select

Which of the following would be an arithmetic sequence?

• 1, 3, 6, 10, 15
• 5, 10, 15, 20, 25
• 3, 6, 9, 12, 15
• 1, 2, 4, 6, 10, 16

Multiple Choice

Which of the following is an example of an arithmetic sequence?

• 4, 8, 16, 32, 64

• 1, 2, 4, 7, 11

• 15, 13, 11, 9, 7

• 3, 6, 12, 24, 48

Multiple Choice

Which sequence is NOT an arithmetic sequence?

• -7, -13, -19, -25,...

• -10, -6, -2, 2,..

• 6, 8, 10, 12,...

• 3, 15, 75, 375,...

Multiple Choice

The first three terms of an arithmetic sequence are as follows

13, 19, 25

What are the next two terms of the sequence?

• 31 and 37

• 31 and 36

• 30 and 37

• 30 and 36

Multiple Choice

The first three terms of an arithmetic sequence are as follows.

3, -4, -11

Find the next two terms of this sequence

• -17 and -25

• -18 and -26

• -18 and -25

• -17 and -26

Multiple Choice

The difference between two terms in an arithmetic sequence is called ___________________.

• Formula

• Common Ratio

• Common Difference

• Common Factor

Multiple Choice

What is the common difference of the sequence 2, -1, -4, -7,...?

• -3

• -1

• -2

• 3

Multiple Choice

What is the common difference of the following sequence?

7, 27, 47, 67,...

• 10

• 20

• 3

• -20

Multiple Choice

Identify the common difference. 
10, 20, 30, 40, ...

• 5
• 10
• 15
• 20

Multiple Choice

What is the common difference of the following sequence?

7, 27, 47, 67,...

• 10

• 20

• 3

• -20

Multiple Choice

Find the common difference: 29, 21, 13, 5, ...

• d = -10
• d = -9
• d = -8
• d = -7

STOP!!!
Work on SEQUENCES ACTIVITY 1. When finished, continue with this Quizizz.

If you were to take $25 out of your paycheck each week and put it in a savings account, the growth of the savings account would be an arithmetic sequence.

In Banking: regular deposits of same amount

​When starting an exercise plan it is recommended that you start slowly, adding to your plan at a gradual pace. This can be done as an arithmetic sequence, add 2 new sets each week, until they hit their desired set total. So, if a person starts with 3 sets, he can move to 5 sets the next week, 7 sets the third week, and so on.

In Health: An increasing exercise plan

​Where we might see an arithmetic sequence: Daily Life

With pyramid like patterns in stadiums and auditoriums where seats are designed around a center location, the amount of seats in each row are often in an arithmetic sequences. For example, a seat might be added to each side of a row as the rows get further from the center point, this would be an arithmetic sequence of +2 each row.

In Structures: Building seats in auditoriums and stadiums

“For example, if a company purchased a truck for $35,000 and it depreciates at the constant rate of $700 per month, its value for each month will follow an arithmetic sequence.” (The Boffins Portal Team. (2022, January 5).

In Accounting: Calculating depreciating assets

“A company may embark on a production expansion over a period of time. For example, it can increase its production by 20 units each week.  If its production in the first week was 200, its production for the first 4 weeks is 200, 220, 240, 260…which follows an arithmetic sequence.” (The Boffins Portal Team. (2022, January 5).

In Factories: Production Plans

Where we might see an arithmetic sequence: In Companies

There is a formula for that!

Lets look at the sequence 7, 12, 17, 22, 27
a₁ = 7
a₂= 7+5
a₃= 7+5+5
a₄= 7+5+5
a₅= 7+5+5+5+5

We can see that the number of 5s added to the 7 is one less than the term's number in the sequence.
This is what gives us the formula to the left.

What if we want to find a future term but not all the terms in between?

We can see that that a₁ is 6 which is the first term.

Next we need to figure out the difference between each term. We can solve -30-(-12) = -18 and -48-(-30) = -18

So we can input that into the formula so that
a_n = a₁ + d (n-1)

a_n = 6 + -18 (n-1)

Write the general term of each arithmetic sequence 6, –12, –30, –48, –66, ...

We can see that that a₁ is 13 which is the first term.

Next we need to figure out the difference between each term. We can solve 22-13 = 9 and 31-22 = 9

So we can input that into the formula so that
a_n = a₁ + d (n-1)

a_n = 13 + 9 (n-1)

Write the general term of each arithmetic sequence 13, 22, 31, 40, 49, ...

Let's look at some examples

First we need to find out general term formula:

a₁ = 45 and the difference is -6

So we can input that into the formula so that
a_n = 45 + -6 (n-1)

Then we can input the 30 in for the nth term.
a₃₀ = 45 + -6 (30-1) => 45 + -174 = -129

Find the 30th term of the sequence 45, 39, 33, 27, 21, ...

First we need to find out general term formula:

a₁ = -121 and the difference is 34

So we can input that into the formula so that
a_n = -121 + 34 (n-1)

Then we can input the 27 in for the nth term.
a₂₇ = -121 + 34 (27-1) => -121 + 884 = 763

Calculate the 27th term in the arithmetic progression –121, –87, –53, –19, 15, ...

How about a few more?

Now it is time for you to try....

Multiple Choice

Write the general term of each arithmetic sequence –199, –99, 1, 101, 201, ...

• a_n = -199 + -100 (n-1)

• a_n = -199 + 100 (n-1)

• a_n = 100 + -199 (n-1)

• a_n = -199 + 100 (n+1)

Write the general term of each arithmetic sequence –199, –99, 1, 101, 201, ...

We can see that that a₁ is -199 which is the first term.

Next we need to figure out the difference between each term. We can solve -99-(-199) = 100 and 1-(-99) = 100

So we can input that into the formula so that
a_n = a₁ + d (n-1)

a_n = -199 + 100 (n-1)

Multiple Choice

Write the general term of each arithmetic sequence 57, 52, 47, 42, 37, ...

• a_n = 57 + 5 (n-1)

• a_n = -5 + 57 (n-1)

• a_n = 57 + -5 (n+1)

• a_n = 57 + -5 (n-1)

Write the general term of each arithmetic sequence 57, 52, 47, 42, 37, ...

We can see that that a₁ is 57 which is the first term.

Next we need to figure out the difference between each term. We can solve 52- 57 = -5 and
52- 47 = -5

So we can input that into the formula so that
a_n = a₁ + d (n-1)

a_n = 57 + -5 (n-1)

​Calculate the 47th term in the arithmetic progression 25, 16, 7, –2, –11, ...

First we need to find out general term formula:

a₁ = 25 and the difference is -9

So we can input that into the formula so that
a_n = 25 + -9 (n-1)

Then we can input the 47 in for the nth term.
a₄₇ = 25 + -9 (47-1) => 25 + -414 = -389

Given the arithmetic progression 131, 159, 187, 215, 243, ... find the 22nd term.

First we need to find out general term formula:

a₁ = 131 and the difference is 28

So we can input that into the formula so that
a_n = 131 + 28 (n-1)

Then we can input the 22 in for the nth term.
a₂₂ = 131 + 28 (22-1) => 131 + 588 = 719

Multiple Choice

Which of the following is the correct formula in finding the nth term of an arithmetic sequence?

• a_n = a₁ + (n - 1)d

• a_n = a₁ + (n + 1)d

• a_n = a₁ - (n - 1)d

• a_n = a₁ +- (n + 1)d

Multiple Choice

What is a₁ in the following sequence?

-6, -14, -22, -30, ...

• -6

• -14

• -22

• -30

Multiple Choice

What is the 67^th term of the following arithmetic sequence.

13, 22, 31, 40, ...

• -445

• 67

• 625

• 607

Multiple Choice

What is the 76^th term of the following arithmetic sequence?

8, 14, 20, 26,...

• 76

• 452

• 458

• 476

​STOP!!!
Work on Arithmetic Sequences ACTIVITY 2. When finished, continue with this Quizizz

Function Notation

Objective: Evaluate functions written in function notation.

Multiple Choice

Evaluate f(-2) if f(x) = x²+ 3

• -1
• 1
• 7
• -7

Function Notation

a specific way to write a relation when it is a function. ​

General Function Notation: f(x)

Said out loud: "f of x"

​

Example:

y = 3x + 2 is a function.

So it can be written as f(x) = 3x + 2

Math Response

Given h(x) = 5 - 9x, find h(8). 

Type answer here

Correct Answer: -67

Deg^°

Rad

Multiple Choice

For the function f(x) = -3(x-1) find f(0).

• 0
• -3
• 3
• -1

EXAMPLE​

​Given f(x) = 4x - 9, find f(2).

Multiple Choice

Evaluate f(-5) if f(x) = -2x - 12

• -22
• -2
• -19
• -5

Multiple Choice

Find f(10). If f(x)= -4x -10

• x = -5

• x = 40

• x = -40

• x = -50

Multiple Choice

If f(x) = 7, what is the value of x?

f(x) = 3x+1

• 2

• $$\frac{8}{3}$$

• 3

• 22

Multiple Choice

For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. Write an equation in function notation to represent this situation, where the total amount she earns would be represented by m(x).

• $$m\left(x\right)=3x+5$$

• $$m\left(x\right)=5x+3$$

• $$m\left(x\right)=8x$$

• $$m\left(x\right)=5x-3$$

Multiple Choice

If f(x) = -4, what is the value of x?

$$f\left(x\right)=-4+\frac{x}{4}$$  

 

• 0

• 1

• -5

• -3

Multiple Choice

Find $$f\left(-3\right)$$

• -2

• 10

• 8

• no solution

Multiple Choice

$$f\left(n\right)=4-10n$$  

If f(n) = 14, what is the value of x?

• 1

• -1

• -136

• -6

Multiple Choice

What is f(8)?

• 8

• 0

• 3

• -2

Dropdown

$$7x+8=29$$

The first step to solve this equation is to ​

Select answer

. The next step is to ​

Select answer

. The answer is ​

Select answer

.

Multiple Choice

Find f(-1)

• -3

• 15

• 19

• 17

Math Response

If f(x) = 1, what is the value of x?

$$f\left(x\right)=x-7$$

Type answer here

Correct Answer: 8

Deg^°

Rad

Multiple Choice

If f(x) = 19, Find the value for x.

• 0

• 1

• 2

• 3

Multiple Choice

Let's Try it:

If the input is -3, determine the corresponding output.

• f(x) = -2

• y = -2

• f(x) = 10

• y =10

Multiple Choice

If f(x) = 3 Find the value of x.

• 2

• 4

• 6

• 0

Multiple Choice

Find f(x) if x=-2.

• f(x)=9

• f(x)=-15

• f(x)=-9

• f(x)=21

Multiple Choice

f(5) = ?

• 25

• 125

• 5

• 10

Multiple Choice

Given f(x) = -4x - 10 and f(x) = 10. Find x

• x = -5

• x = 5

• x = -50

• x = 30

Multiple Choice

Find the value of y in the equation $$y=4x-1$$ when $$x=2$$

• 4

• 5

• 7

• 0

Multiple Choice

Write an equation to represent the scenario.

The cost of renting a bike is $10 to take the bike and $4 for every hour it spends in our possession.

• y = 10x + 4

• y = 10 + 4x

• y = 14x

• 4x = 30

Multiple Choice

Find $$f\left(-3\right)$$

• -2

• 10

• 8

• no solution

Multiple Choice

Find $$f\left(-2\right)$$

• f(x) = 9

• f(x) = -9

• f(x) = -15

• f(x) = 21

Multiple Choice

Find f(10). If f(x)= -4x -10

• x = -5

• x = 40

• x = -40

• x = -50

Multiple Choice

For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. Write an equation in function notation to represent this situation, where the total amount she earns would be represented by m(x).

• $$m\left(x\right)=3x+5$$

• $$m\left(x\right)=5x+3$$

• $$m\left(x\right)=8x$$

• $$m\left(x\right)=5x-3$$

STOP!!!
Work on Function Notation ACTIVITY 3. When finished, continue with this Quizizz.

Slope formula and finding slope from a graph

​

​How to find slope

Slope is the measure of the "steepness" of a line

How much a line changes UP or DOWN as it moves from left to right

​

Define Slope

Slope Formulas

Multiple Select

Slope is found by the ratio of....

Choose all that apply

• $$\frac{run}{rise}$$

• $$\frac{Change\ in\ x}{Change\ in\ y}$$

• $$\frac{rise}{run}$$

• $$\frac{Change\ in\ y}{Change\ in\ x}$$

Movement RIGHT is positive

Movement LEFT is negative

​Run

Movement UP is positive

Movement DOWN is negative

Rise

Movement Positive or Negative

Count the rise and the run between 2 points on the line

​

​Finding the slope from a graph

Dropdown

This is a ​

Select answer

slope

Pick ANY point on the line to be point one

​

​Finding the slope from a graph

Pick ANOTHER point on the line to be point two

​

​Finding the slope from a graph

​Point 1

COUNT the movement Up (+) or down (-) from point 1 to point 2

​

​Finding the slope from a graph

​Point 1

​Point 2

Fill in the Blanks

COUNT the movement right (+) or left (-) from point 1 to point 2

​

​Finding the slope from a graph

​Point 1

​Point 2

Fill in the Blanks

Put numbers together in fraction form and reduce


LEAVE IMPROPER!!

​

​Finding the slope from a graph

​Point 1

​Point 2

Math Response

What is the slope of this line $$\frac{rise}{run}$$

Type answer here

Correct Answer: -\frac{5}{3}

Deg^°

Rad

Positive: When counting from point 1 to point 2

Movement for positive slope

​OR

Negative: When counting from point 1 to point 2

Movement for negative slope

​OR

Multiple Choice

Find the slope:

• 2

• -2

• 1/2

• -1/2

Multiple Choice

Find the slope of the line.

• Undefined

• 0

• 1

• -1

Multiple Choice

Find the slope:

• 3/4

• 4/3

• -3/4

• -4/3

Multiple Choice

What is the slope?

• 3/5

• 5/3

• -3/5

• -5/3

• -6/10

Explanation Slide...

count rise over run; the line is rising from left to right so the slope is positive

Multiple Choice

What is the slope?

• -1

• 1

• 3/3

• -3/3

• -1/1

Explanation Slide...

count rise over run;the line is falling from left to right so the slope is negative; slopes must be reduced to lowest terms

Multiple Choice

What is the slope?

• -2/5

• -5/2

• 2/5

• 5/2

• -2 1/2

Explanation Slide...

count rise over run; the line is falling from left to right so the slope is negative

Multiple Choice

what is the slope

• -3/4

• 4/3

• 3/4

• -4/3

• -1 1/3

Explanation Slide...

count rise over run; the line is falling from left to right so the slope is negative

Multiple Choice

What is the slope?

• -1/2

• 1/2

• 2/1

• -2

• undefined

Explanation Slide...

count rise over run; the line is falling from left to right so the slope is negative

Multiple Choice

• -1

• 1

• undefined

• zero

• -1/1

Explanation Slide...

count rise over run; the line is falling from left to right so the slope is negative

Multiple Choice

What is the slope?

• 2

• 1/2

• 2/1

• -2

• -1/2

Explanation Slide...

count rise over run; the line is rising from left to right so the slope is positive

Multiple Choice

What is the slope?

• 2/3

• 3/2

• -2/3

• -3/2

• 4/6

Explanation Slide...

count rise over run; the line is rising from left to right so the slope is positive

Multiple Choice

What is the slope?

• undefined

• zero

• 4/1

• 4/0

• 0/4

Explanation Slide...

a vertical line always as an undefined slope because a vertical line has no "run"; slope is rise over run and anything divided by zero is undefined because you can not divide by zero

Multiple Choice

What is the slope?

• zero

• undefined

• 4/0

• 0/4

Explanation Slide...

a horizontal line always has a slope of zero because there is no rise and slope is rise over run; 0 divided by any number is zero

Multiple Choice

What is the slope?

• 3/24

• 1/8

• 1/2

• -1/2

• 8

Explanation Slide...

​

Multiple Choice

What is the slope?

• undefined

• zero

• -4/0

• 0/-4

• -12/26

Explanation Slide...

you can not divide by zero; anything divided by zero is undefined

Multiple Choice

What is the slope?

• 11/15

• -27/15

• -15/27

• 15/11

Explanation Slide...

​

Multiple Choice

What is the slope?

• -5/22

• -22/5

• 5/22

• 5/14

• 14/5

Explanation Slide...

​

Multiple Choice

What is the slope?

• 0

• undefined

• -16/3

• -3/16

• 0/3

Explanation Slide...

zero divided by anything is zero

STOP!!!
Work on SLOPES ACTIVITY 4. When finished, continue with this Quizizz.

Congratulations!
You have officially finished the Quarter Catch-Up!

Your Grade Will Officially be a 70!