Modeling Expressions
Identifying Properties
Rate of Change
Factoring
Quadratic Formula
100
What is the degree of the polynomial
2x − x ^2+ 4x 3 ?
1) 1 2) 2 3) 3 4) 4
2) 2
100
When solving the equation 4x ^2− 16 = 0, Laura wrote 4x ^2= 16 as her first step. Which property justifies Laura's first step?
1) distributive property of multiplication over addition
2) multiplication property of equality
3) commutative property of addition
4) addition property of equality
4) addition property of equality
100
What is the formula for average rate of change?
y2-y1/x2-x1
100
When factored, the expression x ^3− 36x is equivalent to
3) x(x+6)(x-6)
100
What is the Quadratic Formula?
200
What is the constant term of the polynomial
2x^3 − x + 5 + 4x ^2?
1) 5 2) 2 3) 3 4) 4
1) 5
200
A teacher asked the class to solve the equation
3(x + 2) = 21. Robert wrote 3x +6 =21 as his first
step. Which property did he use?
1) associative property
3) distributive property
2) commutative property
4) zero property of addition
3) distributive property
200
The value of Tony's investment was $1140 on January 1st. On this date three years later, his investment was worth $1824. The average rate of change for this investment was $19 per
1) day 3) quarter 2) month 4) year
2) month
200
What is the correct factorization of x ^2+ 4x -12?
4) (x-2) (x+6)
200
What are the calculator steps to find the quadratic formula?
Menu+ Equation
F2
F2
Enter A,B,C
300
A student creates a fourth-degree trinomial with a leading coefficient of 2 and a constant value of 5. The trinomial could be
1) 2x^4 + 3x ^2+ 5
2) 2x ^2+ 5x + 3
3) 4x ^2− 3x + 5
4) 4x ^3− 5x ^2+ 3
1) 2x^4+3x^2+5
300
While solving the equation 4(x + 2)=28, Becca wrote 4x + 8 =28. Which property did she use?
1) distributive
3) commutative
2) associative
4) identity
1) distributive
300
An astronaut drops a rock off the edge of a cliff on the Moon. The distance, d(t), in meters, the rock travels after t seconds can be modeled by the function d(t) = 0.8t 2 .
What is the average speed, in meters per second, of the rock between 5 and 10 seconds after it was dropped?
1) 12 3) 60 2) 20 4) 80
1) 12
300
David correctly factored the expression
m ^2-12m - 64. Which expression did he write?
3) (m-16) (m+4)
300
If the quadratic formula is used to find the roots of the equation x^2 -6x -19 = 0, the correct roots are
1) 3+- 2 radical 7
400
Which statement is correct about the polynomial
3x ^2+ 5x - 2?
1) It is a third-degree polynomial with a constant term of -2.
2) It is a third-degree polynomial with a leading coefficient of 3.
3) It is a second-degree polynomial with a constant term of 2.
4) It is a second-degree polynomial with a leading coefficient of 3.
4) It is a second-degree polynomial with a leading coefficient of 3.
400
When solving for the value of x in the equation
4(x - 1) +3 =18, Aaron wrote the following lines on the board.
[line 1] 4(x - 1) + 3 =18
[line 2] 4(x - 1) = 15
[line 3] 4x - 1 =15
[line 4] 4x = 16
[line 5] x = 4
Which property was used incorrectly when going from line 2 to line 3? 1) distributive 3) associative 2) commutative 4) multiplicative inverse
1) Distributive
400
Consider the function given by f(x) = 9 - x^2. Find its average rate of change between the following points. Solve:
x=0
x=3
m=3
400
The trinomial x ^2- 14x + 49 can be expressed as
1) (x-7)^2
400
Use the quadratic formula to solve x^2 -4x + 1 = 0 for x. Round the solutions to the nearest hundredth
0.27,3.73
500
When (x)(x - 5)(2x + 3) is expressed as a polynomial in standard form, which statement about the resulting polynomial is true?
1) The constant term is 2.
2) The leading coefficient is 2.
3) The degree is 2.
4) The number of terms is 2.
2) The leading coefficient is 2.
500
A student is in the process of solving an equation. The original equation and the first step are shown below.
Original: 3a + 6 =2- 5a + 7
Step one: 3a +6 = 2 +7 -5a
Which property did the student use for the first step? Explain why this property is correct
Commutative
500
The graph below shows the distance in miles, m, hiked from a camp in h hours.
Which hourly interval had the greatest rate of change?
1) hour 0 to hour 1
3) hour 2 to hour 3
2) hour 1 to hour 2
4) hour 3 to hour 4
1) hour 0 to hour 1
500
The area of a rectangle is represented by
3x ^2- 10x -8. Which expression can also be used to represent the area of the same rectangle?
1) (3x+2) (x-4)
500
Do I have to memorize the quadratic formula?
Why?
No!!!!
Reference Sheet