Regents Review

Solving Equations

100

What is the value of m in the equation 2m− (m+ 1) = 0

m = 1

200

The solution to −2(1 − 4x) = 3x + 8 is

x = 2

300

What is the value of x in the equation 5(2x − 7) = 15x − 10?

x = -5

400

What is the value of x in the equation x/ 2 + x/ 6 = 2?

x = 3

500

3(x - 4) -2(3x + 4) = 4(3 - x) + 5x + 4

x = -9

Exponent Properties

100

What is (x³)³?

x⁹

200

What is the product of 10x⁴y² and 3xy³ ?

30x⁵ y⁵

300

The expression 24x⁶y³ / 6x³y is equivalent to

-4x³y²

400

The expression (2a²b³)(4ab⁵)(6a³b² ) is equivalent to

-48a⁶b¹⁰

500

The product of 4x^2/7y² and 21y³/20x⁴ , expressed in simplest form, is

3y/5x² 

Word Problems

100

Andy is 25 years younger than his father.  The sum of their ages is 53.  What is Andy’s age?

Andy is 14

200

The sum of two times a number and 4 is the product of 12 and 3. What is the number?

The number is 16

300

The sum of a number and twice the sum the number and 3 is 12. What is the number?

The number is 2. 

400

Find two consecutive integers such that ten more than twice the smaller is seven less than three times the larger.

The numbers are 14 and 15

500

FREE 200 POINTS

FREE 200 POINTS 

Polynomial Operations

100

The expression 15 – 3[2 + 6(–3)] simplifies to

63

200

Find the equivalent expression to 3x² - 5x + 26 -(2x² + 3x - 14)

x² - 8x + 40

300

Which expression is equivalent to 2(x² - 1) + 3x(x - 4)?

5x² - 12x -2

400

If y = 3x³ + x² - 5 and z = x² - 12, which polynomial is equivalent to 2(y + z)?

6x³ + 4x² - 34

500

The expression (2x + 1)² - 2(2x² - 1) is equivalent to

4x + 3

Properties

100

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?

distributive property

200

Give me an example of the multiplicative Identity Property

5(1) = 5

300

When solving p² + 5 = 8p + 7, Kate wrote              p² + 12 = 8p. The property she used is

the addition property of equality

400

Which property adds the opposite to get a value of zero?

Additive Inverse

500

Justify each step in the equation  2(x -4) + 3x = 9

Step 1: 2x - 8 + 3x = 9

Step 2: 2x - 3x - 8 = 9

Step 3: -x - 8 = 9 

Step 4: -x = 17

Step 5: x = -17

Step 1: Distributive 

Step 2: Commutative 

Step 3: Combine like terms

Step 4: Additive Property of equality 

Step 5: Multiplicative Property of equality