Alg Review Day 1

Factoring/ polynomials/exponents

100

Simplify: (2x²)(3x⁴)

6x⁶

200

Simplify: (2x²)(3x⁴)

6x⁶

300

Simplify √50

√25√2 = 5√2

400

Multiply (x+3)(x-4)

x² - x -12 

500

Find the value(s) of x:

x²−13x+36

x=4 and x=9

Solving Equations/Inequalities

100

5x - 8 = 2x + 10

x = 6

200

Solve and sketch a graph:

y>2x−1

• Dashed line for y=2x−1
• Shade above the line 

300

A number is decreased by 7 and then multiplied by 3. The result is 24. Find the number.

15

400

A gym charges a $25 sign-up fee plus $15 per month. Another gym charges $40 sign-up fee plus $12 per month. After how many months will the total cost be the same?

What is 5 months?

500

3(2x−5)−4(x+1)=2x+7

no solution 

Linear Relationships

100

Find the slope of the line passing through (2,3) and (4,7).

Slope = 2

200

Find the slope of the line represented by: 2y=6x−8

slope = 3

300

Is this relation a function?

(1,2),(2,3),(3,4),(4,5)

Yes

400

Evaluate: f(x)=2x+1  when x=4

9

500

A function is defined as:

f(x)=2x²−3x+1

Another function is:

g(x)=5x−4

Find the two values of x to make this equation true?

x=5/2,x=1

Systems of Equations

100

What does the solution represent in a system of equations? 

Where do the lines intersect?

200

Draw an example of each system of equations - one solution, no solution and infinitely many solutions. 

...

300

3 methods we learned to solve a system of equations? Circle your favorite 

graphing, substitution, and elimination 

400

Solve the system:

y=2x+1 and  y=x+5

(4,9)

500

Write a system and solve:

A school fundraiser sells T-shirts and hoodies.

• Each T-shirt costs $12
• Each hoodie costs $20

On a certain day, the school sells a total of 85 items and collects $1,420.

Let: x = number of T-shirts and y = number of hoodies

What does the solution mean in the context of this situation?

(35,50)

35+50 = 80 

12(35)+20(50)=1420

Error Analysis

100

A student simplified (x²)(x³) and wrote (x⁶)

When multiplying powers with the same base, you add exponents, not multiply them.

200

−2x > 10

x >-5

When you divide or multiply by a negative number, you must flip the inequality sign.

300

Maria claims that the set of coordinates below represents a function.

{(−2,3),(1,5),(3,7),(1,−1)}

• The repeated input is x=1x = 1x=1

• Two different outputs: 5 and -1

400

A student factored the trinomial x2+9x-10 as (x-10)(x+1)

The student  made an error with the signs when finding the two numbers to factor the trinomial.

500

A student solves the system:

2x+y=7 and y=x+5

Student starts by Substituting:

2x+(x+5)=7

 3x+5=7 

3x=2

x=2/3

Then the student finds y:

y=x+5

y=2/3 + 5

y=17/3

Student Answer: (2/3,17/3)

TRICKED YOU LOL 

The student was correct