Transcript ALGEBRA GAMEx - Long Island City High School

Polynomials
Properties
Functions
Find x
Definitions
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Polynomials for 100
The expression 2x² - x² is equivalent to
Answer: x²
Polynomials for 200
What is the sum of 3x² + x + 8 and x² - 9 ?
Answer:
4x² + x - 1
Polynomials for 300
What is the answer when (x² - 5x - 2) is
subtracted from (-6x² - 7x - 3) ?
Answer:
-7x² -2x - 1
Polynomials for 400
What is the difference between a binomial
and a trinomial?
Answer:
A binomial has two terms and the
trinomial has three terms.
Polynomials for 500
Which expression is equivalent to
-3x(x - 4) - 2x(x + 3)?
Answer:
-5x² + 6x
Polynomials for 600
What is (5x – 4y) – (5x + 4y) equivalent to?
Answer:
-8y
Polynomials for 700
What is the answer when (x² - 5x - 2) is subtracted
from (-6x² - 7x - 3) ?
Answer: -7x²
-2x - 1
Polynomials for 800
When (c + 8) and (c - 5) are multiplied, what
type of polynomial do we get as the product?
What is its degree?
Answer: The product is a trinomial (c² + 3c – 40) of degree two.
Polynomials for 900
• What is the difference when 5g² - 4g + 11 is
subtracted from 9g² - 4g?
• What do we call an expression like this?
Answer:
4g² - 11 and we call it a binomial (two terms).
Polynomials for 1000
Use a geometric diagram to compute the following products:
3𝑥 2 + 4𝑥 + 2 × 2𝑥 + 3
3x²
4x
2
𝟐𝒙
𝟑
6x³
9x²
8x²
12x
4x
6
Answer:
6x³ + 17x² + 16x + 6
Properties for 100
ab + cd
cd + ab
Which property is illustrated above?
Answer:
Commutative for addition
Properties for 200
To show that (𝒘 + 𝟓)(𝒘 + 𝟐) is equivalent 𝒘𝟐 + 𝟕𝒘 + 𝟏𝟎.
Which property do we need to use?
Answer: The
Distributive Property
Properties for 300
Name the property illustrated below
Answer: The
Distributive Property
Properties for 400
If M, P and Q represent integers,
M +(P + Q) = (M + P) + Q
is an example of which property?
Answer:
The Associative Property
Properties for 500
Indicate if the following equation is sure to have a solution
set of all real numbers. Explain your answer.
𝒙+𝟐=𝟐+𝒙
Answer: Yes,
the two expressions are algebraically equivalent by
application of the Commutative Property.
Properties for 600
The statement 2 + 0 = 2 is an example of the use of which
property of real numbers?
1) associative
2) additive identity
3) additive inverse
4) distributive
Answer:
2) The Additive Identity Property
Properties for 700
While solving the equation 4(x + 2) = 2, Kim wrote
4x + 2 = 28. Which property did she use?
1) distributive
2) associative
3) commutative
4) None of the above
Answer:
4) None of the above since the statement is false.
Properties for 800
Identify the property illustrated by each statement:
a) 4 (m + 2) = 4m + 8
b) 3(4x) = (4x)3
c) ¼(4) = 1
d) -8 (1) = -8
Answer:
a) The Distributive Property
b) The Commutative Property for Multiplication
c) The Inverse for Multiplication
d) The Identity for Multiplication
Properties for 900
Indicate the properties illustrated in the following
statements:
1) a + (-a) = 0
2) a (0) = 0
Answer:
1) The Additive Inverse Property
2) The Zero Property
Properties for 1000
Identify the two properties used to obtain each of the two indicated steps
Answer: The
Distributive and Associative
Properties.
Functions for 100
What type of function is y = x² + 51x ?
Answer: This an example of a quadratic function because its
highest degree is 2.
Functions for 200
(1)
Which is a graph of a Quadratic Function?
(2)
(3)
Answer: (3) The
graph of a parabola.
(4)
Functions for 300
Compare the rates of change for A and B.
B
A
Profit
Year
Which one has a greater change?
Answer: The
rate of change for B.
Functions for 400
This table gives data from a plant growth experiment.
Time (weeks)
Height (cm)
3
4.6
4
5.8
7
9.4
What is the rate of growth of the plant?
Answer: The
rate of growth is 1.2 cm per week.
Functions for 500
Organize the following function in ascending order:
m(x) = x² + 11x³ - 5 + 20x.
Answer:
m(x) = -5 + 20x + x² + 11x³
Functions for 600
Which type of function is graphed below?
Answer: This is an exponential function (y = ab^x).
Functions for 700
In a linear equation, the independent variable increases at a
constant rate while the dependent variable decreases at a
constant rate. What type of slope does this line have?
Answer: The
slope of this line is negative.
Functions for 800
Organize the following function in descending
order and determine its degree:
m(x) = x² + 11x³ - 5 + 20x.
Answer:
m(x) = 11x³ + x² + 20x – 5
and third degree
(cubic).
Functions for 900
Kevin leaves a cup of hot chocolate on the counter in his kitchen. Which
graph is the best representation of the change in temperature of his hot
chocolate over time?
(1)
(2)
(3)
(4)
Answer: (1) The temperature of the chocolate goes down exponentially.
Functions for 1000
Amy tossed a ball in the air in such a way that the path of the ball
was modeled by the equation y = −x² + 6x.
In the equation, y represents the height of the ball in feet and x is
the time in seconds. At what time, x, is the ball at its highest point?
Answer:
At x = 3 sec, the ball is at its highest point.
Find x for 100
2x + 4 = -6 x = ____
Answer:
x = -5
Find x for 200
Is a TRUE or FALSE numerical sentence when x = -5?
x³ - 125) = 0
(
Answer:
This is a FALSE numerical sentence when x = -5.
-125 – 125 ‡ 0
Find x for 300
The average of 𝟕 and x is −𝟖 if x = _____.
Answer:
x = -23
Find x for 400
𝒙 + 𝟐² = −𝟗
Answer:
x = -13
Find x for 500
1___ = _1_
x–2
4
Answer:
x=6
Find x for 600
Consider the equation 𝟕+ x = 𝟏𝟐. Complete the table below:
THE NUMBER SENTENCE
TRUTH VALUE
Let x = 0
Let x = -7
Let x = 5
Let x = 1 + √9
THE NUMBER SENTENCE
TRUTH VALUE
Let x = 0
𝟕 + 0 = 𝟏𝟐
FALSE
Let x = -7
𝟕 + (-7) = 𝟏𝟐
FALSE
Let x = 5
𝟕 + 5 = 𝟏𝟐
TRUE
Let x = 1 + √9
𝟕 + 4 = 𝟏𝟐
FALSE
Find x for 700
Consider the algebraic equations 𝒙 +𝟏= 𝟒 and
a) Are these true numerical sentences if 𝒙 = 𝟑?
(𝒙+𝟏)² =𝟏𝟔.
b) Find another value for x besides 3 that would make the second a true
numerical sentence.
Answer: a)
Yes, x = 3 is a solution to both equations.
b) x = -5
Find x for 800
a) Determine whether the following number sentence is TRUE
or FALSE. 3² X 4² = 12²
b) Solve for x:
_x²_ = 4²
3²
Answer:
a) True sentence
b) x = 12
Find x for 900
Solve for x: -2 + x = 3.
Present the solution set in words, in set notation and
also graphically.
In words: -2 + x = 3 has the solution x = 5
In set notation: The solution set is { 5 }.
In a graphical Representation:
Find x for 1000
Determine the values for x that would make this
statement true and provide a graphical representation
on a number line.
x² = 𝟐𝟓
Answer:
x = -5 and x = 5
Definitions for 100
Coefficient
Answer: A Coefficient is a number used to multiply a variable (In the
example, 4x means 4 times x, so 4 is a coefficient).
Definitions for 200
Operator
Answer:
An Operator is a symbol (such as +, ×, -, etc) that represents an
operation.
Definitions for 300
Variable
A symbol for a number we do not know yet. It is usually a
letter like x or y. Example: in 4x - 7 = 5, x is the variable. If it is
not a variable it is called a Constant.
Answer:
Definitions for 400
Term
Answer:
A Term is either a single number or a variable,
or numbers and variables multiplied together.
Examples:
5
4x
-7
5
Definitions for 500
Like Terms
Answer:
Terms with the same variables (letters) and
Exponents (powers).
Definitions for 600
Constant
Answer: A Constant is a fixed value. In Algebra, a constant is a number on
its own, or sometimes a letter such as a, b or c to stand for a fixed
number. Example: in “4x - 7 = 5", 7 and 5 are constants.
Definitions for 700
Algebraic Expression
Answer: An algebraic expression is a mathematical phrase that can contain
ordinary numbers, variables (like x or y) and operators (like add, subtract,
multiply, and divide). Examples:
23
3p
4m²³
a+1
a² - b
-5m³ + 2 n³+ 1
Definitions for 800
Algebraic Equation
An equation is a math sentence that says that 2 things are equal. An
equation always has an equal (=) sign. The thing or things that are on the
left side of the equal sign are equal to the things on the right side of the
equal sign. Here are a few equations:
x = 5
m – 9 = 14
p² = 16
x + y = 12
a² + b² = c²
Answer:
Definitions for 900
Identify the expressions and the equations
(1) 14x³ + 19y² - 5z
(3) -2y² + 19y = 5
Answer:
(2) 14m + 19 = 2m + 10
(4) 5w
Expressions = 1 and 4 Equations = 2 and 3
Definitions for 1000
4x³y²z
Name the coefficient, variables and exponents
Answer:
Coefficient = 4
Variables = x, y, and z
Exponents = 3, 2, and 1