Regents Review

Properties of Algebra

100

Antonio started the question 2x+1=11 by writing 2x=10. The property that justifies this step is:

a. Commutative property of addition

b. Distributive Property

c. Addition Property of Equality

d. Multiplication Property of Equality

c. Addition Property of Equality

200

The property shown in the given equation:

4x+5=5+4x

Commutative Property

300

The property shown in the given equation

5+(6x-2)=(5+6x)-2

Associative Property

400

Equation 1: 2x=10

Equation 2: x=5

The property that justifies the step taken between Equation 1 and Equation 2

Multiplication Property of Equality

500

Jasmine wrote the equation 3(4x-1)=12x-3.

The property Jasmine used was

Distributive Property

Quadratic Functions

100

The vertex of

f(x)=(x-4)²  -4 

(4,-4)

200

The axis of symmetry for the function y=4x²+16x-3

(Hint: axis of symmetry formula is x= -b/2a)

x=-2

300

The solutions to a quadratic function are found in this location on a graph

The x-axis

400

The axis of symmetry for the function y=2x² -16x-3

(Hint: axis of symmetry formula is x= -b/2a)

x=4

500

The three other names for a zero are

Solution, x-intercept, root

Linear Functions

100

The equation of a line

y=mx+b

200

Given the equation y=-12x+16.5, the slope and y-intercept are

slope=-12

y-intercept=16.5

300

Given the points (-1,9) and (3, 17), the slope of the line through these points

(Hint: m= (y₂-y₁)/(x₂-x₁))

slope = 2

400

It costs $10 to go to the movies and $3 for each bag of popcorn. If y is the total cost and x is the number of bags of popcorn purchased, the equation that represents this situation is

y=3x+10

500

Dayna wants to buy an ice cream cone and add some toppings. The equation that relates the total cost for the ice cream cone and N toppings is P=1.50N+5. The number 5 in this equation represents

The cost of the ice cream cone

Sequences

100

2, 5, 8, 11, 14, ...

The given sequence is 

Arithmetic

200

5, 10, 20, 40, 80, ....

The common ratio of this sequence is

r=2

300

Given the sequence

a_n=3 - 6(n-1)

The first term is _______ and the common difference is ________

Hint: a_n=a₁+d(n-1)

3; -6

400

Find the 4th term of the sequence

a_n=5(3)^n-1

a₄=135

500

The sequence that represents this pattern 

5, 3, 1, -1, -3, ...      is

(Hint: a_n=a₁+d(n-1) or a_n=a₁(r)^n-1)

a_n=5-2(n-1)

Factoring

100

Factor: 2x-8

2(x-4)

200

Factor: x²-100

(x+10)(x-10)

300

Factor: x²+7x+10

(x+5)(x+2)

400

Factor: x³-x²-19x

x(x²-x-19)

500

Completely Factor: 3x²-27

3(x²-9) -->

3(x+3)(x-3)