Keystone Module 1

Real Numbers

100

What is the GCF (greatest common factor) of 20x³y and 60x²? _{(20 sec)}

20x²

200

Simplify. _{(20 sec)}

|3^2-10|+1^3

2

300

Simplify. _{(30 sec)}

sqrt50

5sqrt2

400

Put the three real numbers in order from least to greatest. _{(30 sec)}

pi, 10/3, sqrt6, sqrt16

sqrt6, pi, 10/3, sqrt16

500

Compare the two irrational numbers with an inequality symbol. _____ (symbol) _____ _{(45 sec)}

2pi, sqrt36,sqrt48

2pi<sqrt48

or

sqrt48>2pi

Polynomials

100

Simplify. _{(30 sec)}

3k(2k^2-10k+1)

6k^3-30k²+3k

200

Simplify. _{(30 sec)}

(x+3)(x-7)

x^2-4x-21

300

What is the LCM of the two monomials shown? _{(30 sec)}

2m^2n, 5m^3n^4p

10m^3n^4p

400

Factor the trinomial. _{(30 sec)}

x^2-4x-24

(x+4)(x-6)

500

Factor the binomial. _{(30 sec)}

x^2-25

(x+5)(x-5)

Equations & Systems

100

 

_{(30 sec)}

A - Associative Property of Addition

(Since the order didn't change, just the grouping)

200

Most of the work to solve an equation is shown below. What is the solution to the equation shown? _{(30 sec)}

All real numbers (or infinite solutions)

300

What is the solution to the system of equations shown? _{(20 sec)}

(5,-2)

400

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. A system of equations representing the problem is given below. Explain what the solution (x, y) represents. Be specific. _{(90 sec)}

3x+y=38

3x+2y=52

x = price for a senior citizen ticket

y = price for a child ticket

500

Solve the system of equations. _{(90 sec)}

3x+y=38

3x+2y=52

(8,14)

Inequalities

100

Write the inequality for the graph shown. _{(30 sec)}

x>3 and x<=7

or

3<x<=7

200

Which number is a solution? _{(45 sec)}

2x+4>10

A) x = 1     B) x = 2     

C) x = 3     D) x = 4

D

300

Solve: -9 < -2x + 1 < 5

 _{(60 sec)}

-2 < x < 5

or

5 > x > -2

400

The senior class needs to raise at least $1000 for their end of year trip. They have $185 already and are selling pizzas for $11 each. What is the minimum number of pizzas they need to sell to reach their goal? _{(90 sec)}

They need to sell at least 75 pizzas.

(74.09 needs to round UP!)

500

Solve the inequality. _{(90 sec)}

|2x-4|<14

x> -5 and x<9

or

-5<x<9

Misc.

100

Is (2,2) a solution to the system of inequalities? Explain your thinking.

No, because it is not in the double-shaded region.

200

If 7(2x - 5) = 77, what is the value of 3x? _{(90 sec)}

24 

(x=8, so 3(8) = 24)

300

What is the greatest common factor? _{(30 sec)}

12x⁵yz⁴ , 60x²y⁶ , 24x³y⁴z⁶

12x²y

400

Solve: |x+2| - 3 = 5  

 _{(90 sec)}

x = 6, -10

1) Isolate the AV.

2) Branch (for two solutions)

500

If (x - 5)(2x² + 6x - 5) = 2x³ - mx² - 35x + 25, what is the value of m? 

_{(120 sec)}

m = 4

x * 6x = 6x² and -5 * 2x² = -10x²

6x² - 10x²