Algebraic Thinking

Question 1

Polynomial example

Answer 1

Question 2

What is an Algebraic expression

Answer 2

A mathematical phrase that contains terms and numbers terms are separated by a+ or a- sign

Question 3

What is the degree of the polynomial represented by ‘ab = ab’?

Answer 3

6

Question 4

What type of polynomial is ‘3a’b3’?

Answer 4

monomial

Question 5

What is a trinomial?

Answer 5

A polynomial with three terms

Question 6

Define a binomial.

Answer 6

A polynomial with two terms

Question 7

What is a polynomial?

Answer 7

An algebraic expression that does not have a variable in the denominator of a fraction

Question 8

How may polynomials be named?

Answer 8

By the number of terms they have or their degree

Question 9

What is the largest exponent in a polynomial called?

Answer 9

Degree

Question 10

Identify the characteristics that may be required in exam questions about polynomials.

Answer 10

Name and degree

Question 11

What is the term for a polynomial with one term?

Answer 11

Monomial

Question 12

Fill in the blank: A polynomial with two terms is called a _______.

Answer 12

binomial

Question 13

Fill in the blank: A polynomial with three terms is called a _______.

Answer 13

trinomial

Question 14

What is the sum of exponents in a polynomial used for?

Answer 14

To determine the degree

Question 15

What is an independent variable?

Answer 15

An independent variable is a variable that is changed or controlled in a scientific experiment to test its effects on the dependent variable.

Question 16

True or False: The dependent variable is the factor that the experimenter measures.

Answer 16

True

Question 17

Fill in the blank: In the equation y = mx + b, y is the ________ variable.

Answer 17

dependent

Question 18

Short answer: How does changing the independent variable affect the dependent variable?

Answer 18

Changing the independent variable directly influences the outcome measured by the dependent variable.

Question 19

What does the expression ‘Four times the difference of two numbers’ indicate?

Answer 19

It indicates the need to subtract two numbers in the order they appear before multiplying by 4.

This requires parentheses to show that subtraction comes first in the order of operations.

Question 20

How is Emily’s number of coins represented if Jessica has ‘c’ coins and Emily has four less than twice as many coins as Jessica?

Answer 20

2c - 4

This is calculated by finding two times the number of coins Jessica has and then subtracting four.

Question 21

Which expression represents the phrase ‘four less than twice as many coins as Jessica’?

Answer 21

2c - 4

The phrase indicates to first calculate twice Jessica’s coins and then subtract four.

Question 22

In the expression 4(x-12) = 87, what operation is being performed?

Answer 22

Multiplication after subtraction.

The parentheses indicate that subtraction occurs before multiplication.

Question 23

What is represented by the verbal statement ‘the sum of a number and twelve is eighty-seven’?

Answer 23

An equation where a number plus twelve equals eighty-seven.

This translates to x + 12 = 87.

Question 24

What does the symbol ‘<’ represent in the context of ‘4 < 2c’?

Answer 24

It represents ‘is less than’.

This indicates that 4 is less than 2 times c.

Question 25

Which word could Jarrod use to represent addition in a verbal statement?

Answer 25

Sum ## Footnote 'Sum' is commonly used to indicate the addition of two terms.

Question 26

Fill in the blank: Four less than twice a number can be expressed as _____ .

Answer 26

2x - 4

Question 27

True or False: The phrase '4 less than 5' is represented mathematically as 4 - 5.

Answer 27

False ## Footnote '4 less than 5' is equivalent to 5 - 4.

Question 29

What is the cost of a gym membership per month?

Answer 29

$18

Question 30

What is the application fee for the gym membership?

Answer 30

$10

Question 31

Which equation represents the total cost of the membership after m number of months?

Answer 31

y = 18m + 10

Question 32

In the equation y = 18m + 10, what does 'm' represent?

Answer 32

The number of months

Question 33

In the equation y = 18m + 10, what does 'y' represent?

Answer 33

The total cost of the membership

Question 34

Fill in the blank: The total paid after any given number of months can be found using the equation _______.

Answer 34

y = 18m + 10

Question 35

True or False: The application fee is a variable cost.

Answer 35

False

Question 36

What type of fee is the application fee for the gym membership?

Answer 36

A flat rate

Question 37

Performing operations on expressions

Answer 37

Question 38

Formula: F= 9/5 C +32

Question 39

What is the temperature in °F when the temperature is 8°C?

Answer 39

46.4°F ## Footnote The conversion formula used is F = (9/5)C + 32.

Question 40

What formula is used to convert Celsius to Fahrenheit?

Answer 40

F = (9/5)C + 32 ## Footnote C represents temperature in Celsius and F represents temperature in Fahrenheit.

Question 41

If the temperature is 8°C, what is the first step in the conversion to Fahrenheit?

Answer 41

Substitute C with 8 ## Footnote This leads to the equation F = (9/5)(8) + 32.

Question 42

In the conversion formula, what does the '+32' represent?

Answer 42

+32 represents the adjustment needed to convert Celsius to Fahrenheit ## Footnote It accounts for the difference in the zero points of the two scales.

Question 43

Fill in the blank: To simplify the fraction in the conversion, you divide _____ and 5.

Answer 43

72 ## Footnote This step helps in calculating the temperature in Fahrenheit more easily.

Question 44

True or False: The result of converting 8°C to Fahrenheit is 46.4°F.

Answer 44

True ## Footnote This is the final result after performing the conversion.

Question 45

What is the final step after substituting 8 for C in the Celsius to Fahrenheit formula?

Answer 45

Multiply by 9/5 and then add 32 ## Footnote This gives the final Fahrenheit temperature.