Algebra I Review!

Simplifying, Evaluating, and Factoring

100

Simplify the expression: (4x⁷)²

16x¹⁴

200

Evaluate the expression for x=5 and y=2:

y³-4x

-12

300

Factor out the GCF and rewrite in factored form:

35x²-14x

7x(5x-2)

400

Factor the trinomial completely:

x²+x-30

(x+6)(x-5)

500

Use the distributive property to multiply:

(3y+1)(2y²+4y-3)

6y³+14y²-5y-3

Equations

100

Solve for x: 7x+6=41

x=5

200

Solve for x: (y/2)-5=6

y=22

300

Solve for r: -5(r+4)=-96

r=76/5 OR r=15 and 1/5

400

Solve the following proportion:

(22/8)=(110/m)

m=40

500

A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 180 lb and each box of books weighs 60 lb. The maximum capacity of the elevator is 1440 lb. How many boxes of books can the delivery person bring up at one time?

21 boxes of books

Slope and Linear Equations

100

Find the slope of a line that passes through the points (-1, 4) and (3, -8).

Slope= -3

200

Name 3 points that lie on the line: y=3x+5

NO GRAPHING!

Answers may vary... :)

300

What is the slope of any vertical line?

Undefined!

400

Write the following in slope-intercept form:

3x+5y=-30

y=-3/5x-6

500

Write the equation of a line in slope-intercept form that passes through the following points: (-3, 7) and (2, -3)

y=-2x+1

Systems of Equations

100

Solve the system of equations by substitution:

x + y=4

y=3x

x=1, y=3

200

Solve the system using elimination:

3x+13y=12

4x-13y=16

x=4, y=0

300

There are three different amounts of solutions that a system of equations can have.  What are they?

No solution, one solution, infinity many solutions!

400

Does the system below have no solution, one solution, or infinite solutions?

10=7y+10x

10x+7y=17

NO solution!  You should've gotten an untrue equation (ex: 7=0)

500

Graphically, how do you know if a system of equations have infinitely many solutions?

If the equations are the same line!

Inequalities

100

Is the point (6, 0) a solution to the inequality below?

y < x-2

Yes! 0<4

200

How do you know when to have a closed circle or open circle when graphing an inequality on a number line?

Closed: greater than or equal, less than or equal

Open: greater than, less than

300

Graph the solution to the inequality on a number line:

3x+1 < 2x-4 

Open circle on -5, arrow going to the LEFT.

400

Yellow Cab Taxi charges a $1.75 flat rate in addition to $0.75 per mile. Katie has no more than $10 to spend on a ride.  How many miles can Katie travel without exceeding her budget?

Katie can travel at most 11 miles.

500

Solve the following inequality:

-2n-40 < 5(6+n)+7n

-5 < n OR n > -5