End of Year Review Alg 1

Word Problems

100

You have two numbers. The sum of the two numbers is 14. The difference of the two numbers is 4. What are the two numbers.

5 and 9 

200

Over the Summer two students have been assigned to read a book. Ashley has read 500 pages of her reading assignment, and Genesis has read 460 pages. Ashley reads 20 pages per week for the remainder of the summer, and Genesis reads 30 pages per week for the remainder of the summer. How many weeks, M, will it take before the student read the same number of pages?

W = 4

300

Eder order 3 hamburgers and 2 orders of fries for a total of $29.50. Ada orders 2 burgers and 3 orders of fries for a total of $23. set up a system of equations to find the cost of a burger and the cost of an order of fries.

H = 8.5

F=2

400

Micah and Lorenzo are racing on a track. Micah runs 4 milers per hour and gets a .25 mile head start. Lorenzo runs 0.5 miles per hour faster than Micah. If Lorenzo and Micah run the same distance, how many hours, H, do they run? 

 H = 0.5

500

Braulio's Custom Kitchen Supplies sells handmade forks and spoons. It cost the store $2 to buy supplies to make a fork and $3 to buy the supplies to make a spoon. The store sells forks for $5 and spoons for $7. Last April Braulio's Custom Kitchen Supplies spent $12 on materials for forks and spoons. They sold the finished product for a total of $29. How many forks and how many spoons did they make last April?

S = 2

F = 3

System of Equations

100

y = 2

2y + x = 9

y = 2

x = 5   ( 5 , 2 )

200

y = -4x + 2

y = 6x - 8

( 1 , -2 ) 

X = 1    y = -2

300

y = -4x - 11

3x + 7y = -2 

( -3 , 1 )

x= -3      y = 1

400

6x + 5y = 4

6x - 7y = -20

( -1 , 2 )

X = -1     y = 2

500

4x + 5y = 6

6x - 7y = -20

( 29 , -22 ) 

x = 29     y = -22

Distributing

100

3 (2x + 3)

6x + 9

200

-(3x-5y+17)

-3x + 5y - 17

300

2(2y + 2x)

4x + 4y

400

3(3x + 5b) -5(3y - 4a)

-20a + 15b + 9x - 15y

500

-2(-3x + 11) + 10(4x - 10)

48x - 122

Factoring using GCF

100

-5y + 35x 

5(y + 7x)

200

35x³ + 15x²y²

5x²(7x + 3y) 

300

3x² + 18x + 9

3(x² + 6x +3)

400

6x²y + 14xy² - 42xy

2xy(3x + 7y - 21)

500

20x⁸y²z² + 15x⁵y³z + 35x³y³z

5x³y²z(4x⁵z + 3x² + 7y)

Combining Like-Terms

100

3x + 2x + 10 

5x + 10 

200

10x - 5y + 9x

19x - 5y

300

100x² - 37y + 15 - 100x + 36y

100x² - 100x - y + 15

400

20x² + 3² + 14 - 15x

20x² - 15x + 23

500

15x⁶ - 14x⁵ + 13x⁴ - 12x³ + 11x² - 10x + 9 - 8x⁶ + 7x⁵ - 6x⁴ + 5x³ - 4x² + 3x - 2

7x⁶ - 7x⁵ + 7x⁴ - 7x³ + 7x² - 7x + 7 

Equivalent Expressions

100

Write an equivalent expression for 

x + x + x + x + 20

4x + 20

or

4(x + 5)

200

Write an equivalent expression for

5x² - 4x + 9x²

x(5x - 4 + 9x)

300

Which of the following is an equivalent expression to

5(x + 4) -(2x + 1) 

A: 7x - 21 

B: 3x + 19

C: x + 20

B: 3x + 19

400

x + x + x + x + x + x + 5(x - 30) 

13x - 150

500

5x(20x + 4 + 7y) - 15y

100x² + 20x + 35xy - 15y