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WorksheetsA Regents Review 175
Total questions: 175
Worksheet time: 10hrs 13mins
What is the vertex of this quadratic equation?
y = 2(x + 2)2 + 4
(-2,4)
(2,4)
(4,-2)
(-4,-2)
What do we call the graph of a quadratic function?
parabola
linear
cubic
sinusoidal
The axis of symmetry is a line that goes through the...
y-intercept
any random point
vertex
x-axis or y-axis
Does this graph have a maximum or a minimum?
maximum
minimum
What is the vertex and Axis of Symmetry for the parabola shown on the grid?
Vertex (3,8) A.O.S. x = 3
Vertex (3,8) A.O.S y = 3
Vertex (8,3) A.O.S x = 3
Vertex (8,3) A.O.S y = 3
Which coordinate point best represents the vertex of the parabola?
(-4, 0)
(-1, -9)
(0, -8)
(2, 0)
What are the x-intercept(s) of the parabola shown on the grid?
(-1,0) and (-3,0)
(1,0) and (3,0)
(0,-3)
(0,1) and (0,3)
What is the equation of the axis of symmetry?
y=0
y=3
x = 3
x = 0
What are the zero(s) of the function on the grid?
0 and 4
4
0
2 and 4
What is the significance of the ordered pair (2, -4) to the graph?
It is the vertex
It is an x-intercept
It is the y-intercept
It is the axis of symmetry
How many solutions/roots does this graph have?
Only one is true:
The vertex is (2,-4)
The y-intercept is 2
The axis of symmetry is y=2
The range is y≤−4
What are the roots?
0 and 4
2 and -4
y=2
x = 0
What is the axis of symmetry?
x=3
y=−3
x=−3
y=−2
f(x) = -x2 - 4x + 12
y=4x2-8x+9
What is the correct graph of the function?
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?
Is the point (2, -1) a solution to the systems of equations below?
y=5x+3
y=-2x-4
Yes
No
y = -x + 5
y = 2x - 7
A
B
C
D
Which class has the higher median?
1st period
2nd period
They have the same median
How many students have a shoe size bigger than 8?
2
3
4
9
What is the mode for this data set? Remember the mode is the most common or most frequent data.
55
60
70
75
Determine the IQR for this set of data. 12, 13, 14, 15, 17, 18, 19, 19, 22, 23
14
5
17.5
19
The median test score is 80.
The lower quartile is 65.
The upper quartile is 90.
The IQR is 30.
What is the median of this data?
40
90
100
140
150
What kind of slope would the graph of the model have?
Positive
Negative
There's no association
Jackson says the slope of this line is 0.01. He's not sure if it is positive or negative. What is it?
Positive
Negative
Which graph has a positive association?
A
B
C
D
A restaurant sells pizza for the prices in the data table. Calculate the linear regression equation of the data.
y = 1.5x + 12
y = 12x + 1.5
y = 0.67x - 8
y = -8x + 0.67
3.8, 4.2, 4.0, 4.2, 4.2
Dr. Dre is a dentist. He needs to report on the average (Mean) number of cavities that his patients have.
1, 0, 1, 5, 0, 3, 4. What is the average number of cavities?
14
2
7
1
Evaluate f(x)= -2x + 13 for f(10)
-7
1
-8
7
The graph of f(x)= x2 was transformed to create the graph of g(x) = (x - 7)2. Which of these describes the transformation?
A horizontal shift to the right 7 units
A horizontal shift to the left 7 units
A vertical shift down 7 units
A vertical shift up 7 units
The graph of a quadratic function is shown on the grid. Which equations best represents the axis of symmetry?
HINT: A.O.S. runs through vertex
y = 6
x = 2
y = 4
x = 0
-5 ≤ y ≤ -3
What is the Domain?
-10 < x < 3
-6 < x < 1
-10 < y < 1
-6 < x < 3
What is the Range?
-5 < y < 5
-5 < y < 7
-7 < x< 5
-5 < x < 7
Given f(x)=23x+5 what is f(12)?
243
20
23
5
Given f(x)=x−13x+2 , What is f(2) ?
8
5
0
undefined
f(3) =
-2
-1
0
1
2
Find
f(-2)
8
2.5
6
-3
If f(x)=20−1.5x
evaluate f(6)
(a)
Which of the tables represents a function?
Table A
Table B
Both Tables A & B represent functions
Neither table represents a function
Which value of w would allow these coordinates to represent a function?
{(4,-9), (6,0), (-3,2), (-5,7), (w,1)}
-3
-5
6
0
What value of m would result in this table representing a function?
3
6
2
Any value of m would make this a function.
What value of b would make this set of coordinates NOT a function?
{(-5,3), (-3,2), (0,4), (2,6), (-1,8), (b,-7)}
-7
-3
4
6
7x3 - 11x2 + 8x - 5
12 - 3x3 - 10x - x2
It is in Standard Form.
What is the degree of this polynomial?
2x4 - 3x5 + x
-3
2
4
5
What is the constant of this polynomial?
2x3 - 8x2 + 3x - 7
7
-8
3
-7
What is the leading term of this polynomial?
4x3 + 8x5 - 4x2 + 1x
1x
8x5
4x3
-4x2
What is the leading coefficient of the following?
2x3-8x5+3x-7
2
-8
3
-7
4x3 - 5x2 + 2x - 1
Classify by number of terms:
5x2 – 6x + 3
Monomial
Binomial
Trinomial
4-Term Polynomial
4x3 - 5x2 + 2x - 1
3x - 2
The largest exponent found in the polynomial
Term
Degree
Constant
Leading Coefficient
A polynomial that has two terms
Monomial
Binomial
Trinomial
Polynomial
Identify the degree of the polynomial
5x4 - 3x2 + 2x6 - x + 7
2nd degree
4th degree
5th degree
6th degree
Which of the following polynomials is written in standard form?
9 + 8x - 2x2
10x + x3 - 4x2 - 11
x4 + 5x3 - 6x +1
4x3 + 3x4 + 2x + 1
What is the leading coefficient in the polynomial 3x2 - 2x + 5?
3
2
5
0
Given the two polynomial expressions below select one which is in the standard form
x3−2x2+x−4 , −6+3x+x3
−6+3x+x3
x3−2x2+x−4
Arrange the polynomial expression 7x2+2x4−11 in standard form
2x4+7x−11
7x2+2x4−11
−11+7x2+2x4
7x3 - 11x2 + 8x - 5
12 - 3x3 - 10x - x2
It is in Standard Form.
What is the degree of this polynomial?
2x4 - 3x5 + x
-3
2
4
5
What is the constant of this polynomial?
2x3 - 8x2 + 3x - 7
7
-8
3
-7
What is the leading term of this polynomial?
4x3 + 8x5 - 4x2 + 1x
1x
8x5
4x3
-4x2
What is the leading coefficient of the following?
2x3-8x5+3x-7
2
-8
3
-7
4x3 - 5x2 + 2x - 1
Classify by number of terms:
5x2 – 6x + 3
Monomial
Binomial
Trinomial
4-Term Polynomial
4x3 - 5x2 + 2x - 1
3x - 2
The largest exponent found in the polynomial
Term
Degree
Constant
Leading Coefficient
A polynomial that has two terms
Monomial
Binomial
Trinomial
Polynomial
Identify the degree of the polynomial
5x4 - 3x2 + 2x6 - x + 7
2nd degree
4th degree
5th degree
6th degree
Which of the following polynomials is written in standard form?
9 + 8x - 2x2
10x + x3 - 4x2 - 11
x4 + 5x3 - 6x +1
4x3 + 3x4 + 2x + 1
What is the leading coefficient in the polynomial 3x2 - 2x + 5?
3
2
5
0
Given the two polynomial expressions below select one which is in the standard form
x3−2x2+x−4 , −6+3x+x3
−6+3x+x3
x3−2x2+x−4
Arrange the polynomial expression 7x2+2x4−11 in standard form
2x4+7x−11
7x2+2x4−11
−11+7x2+2x4
(2x + 7) - 3(5x - 4)
Factor completely
x2 - 3x - 10
2(x + 3)(x + 8)
(x - 5)(x + 2)
(x - 5)(x - 2)
2(x + 2)(x - 5)
Factor completely
4x2 + 16x - 84
4(x - 7)(x + 3)
(x - 7)(x + 3)
4(x + 7)(x - 3)
4(x - 7)(x - 3)
Factor completely
16v2 - 1
(4v + 1)(4v + 1)
(16v + 1)(16v + 1)
(4v + 1)(4v + 1)
(4v + 1)(4v - 1)
(4x+1)(5x−2)
-3x2( 7x2 - x + 4)
(2x³+6x²+4x-2)-(x³+4x²-x)
(x³-2x²+3)+(2x³+3x²-1)
(2x2 + 5x - 7) + (3 - 4x2 + 6x)
(3 - 2x + 2x2) - (4x - 5 + 3x2)
x2 + 9x - 36
Which of the following numbers is rational?
7
32
3.1456289...
π
Which of the following numbers is not rational?
−3
2.7
4
5
Determine which of the following examples is irrational.
A fraction whose denominator is larger than its numerator
A decimal that never ends but repeats
A perfect cube root
A decimal that never ends and never repeats
Which of the following number is rational?
127
π
2.5
8.98763...
Classify the following:
64
Rational
Irrational
Neither
Both
Classify the following:
43
Rational
Irrational
Neither
Both
Classify the following:
2
Rational
Irrational
Both
Um...
Which of the following numbers IS NOT rational?
−3
2.7
4
5
Which of the following is an irrational number?
0.333
8
49
225
Simplify:
62⋅514
327
607
372
2102
27+103
133
1030
136
193
Rationalize the denominator:
235
615
1815
653
1853
Rationalize the denominator:
4101
41
4010
41
40010
Fully Factor the Following
25x4-81
(5x2+9)(5x2-9)
Factor r2 - 9t2
(r + 3t) (r - 3t)
(r - 3t) (r - 3t)
(3r + t) (3r - t)
(r + 3t) (r + 3t)
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
Which sequence is NOT an arithmetic sequence?
-7, -13, -19, -25,...
-10, -6, -2, 2,..
6, 8, 10, 12,...
3, 15, 75, 375,...
What is the common difference of the following sequence?
7, 27, 47, 67,...
10
20
3
-20
Find the common ratio for the geometric sequence.
10, 40, 160, 640, ...
2
4
10
1/2
Which property was used to get to the second line?
Associative property
Commutative property
Distributive property
Zero property
Find the slope of a line that passes through the given points:
(6,3) and (1,4)
51
5−1
−5
1
A restaurant sells pizza for the prices in the data table. Calculate the linear regression equation of the data.
y = 1.5x + 12
y = 12x + 1.5
y = 0.67x - 8
y = -8x + 0.67
2x - 1 = ¾x + 9
5x - y = 16
Solve the following equation for the variable w:
V = lwh
w = V−lh
w = Vlh
w = Vlh
w = lhV
Two brothers went shopping at a back-to-school sale where all shirts and shorts were the same price. The younger brother spent $175 on 7 new shirts and 7 pairs of shorts. The older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. How much did one shirt cost?
$5
$10
$15
$20
2x + 4y = 450
2x + 4y = 315
3x + 4y = 450
