Math 12, Ch 2.5 Cumulative Review

Sets

100

List the elements in the set

{x|x in NN > 100}

{101, 102, 103, ...}

200

List the elements of the set that are whole numbers

{5,-2/3,8/2,sqrt9,1 5/8,-1,pi}

{5,8/2,sqrt9}

300

List the elements of the set that are integers

{5,-2/3,8/2,sqrt9,1 5/8,-1,pi}

{5,8/2,sqrt9,-1}

400

True or false

All rational numbers are integers

False

500

A={x|text(x is an even integer)}

B={x|text(x is an odd integer}

text(List the elements of ) A nn B

O/

Linear Equations

100

Solve 

4(x-5)=2x-14

3

200

Solve 

x+7=-2(x+8)

-23/3

300

Solve 

-4(2-3x)=2(3x-4)+6x

all real numbers

400

Solve 

6-3(2g+4)-4g=5(1-2g)

{ }

500

Solve 

(3a-3)/6=(4a+1)/15+2

11

Translate

100

and simplify: The sum of 3 consecutive integers if the first integer is x

3x+3

200

Write as an algebraic expression, then simplify: The perimeter of a triangle with sides 

x, 5x, 6x-3

12x-3

300

Find 3 numbers such that the second number is 3 more than twice the first number, and the third number is 4 times the first number. The sum of the numbers is 164.

23, 49, 92

400

Find two numbers such that the second number is 2 more than three times the first number, and the difference of the two numbers is 24.

11, 35

500

Twice the difference of a number and 3 is the same as 1 added to three times the number. Find the number.

-7

Inequalities

100

Solve and answer in interval notation

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

[5/2, oo)

200

Solve 

4(x+1)-3<4x+1

O/

300

Solve and answer in interval notation

2<4-x<7

(-3, 2)

400

Solve and write the solution in interval notation

x<=2 text( or ) xgt-5 

(-oo, oo)

500

Solve, write the solution in interval form

3(2x-7)-4xgt-(x+6)

(5,oo)

Word Problems

100

One-square-foot floor tiles come 24 to a package. How many packages are needed to cover a floor 18 feet by 21 feet?

16 packages

200

The length of a playing field is 5m less than twice its width. If 230m of fencing goes around the field, find the dimensions of the field.

40 m wide by 75 m long

300

In speed skating Hans scored times of 6.85, 7.04, and 6.92 minutes on his first three trials. Use an inequality to find the times he can score on his last trial so his average time is under 7 minutes. 

{x|x<7.19}

400

A plane's maximum takeoff weight is 2000 pounds or less. Four passengers and a two-person crew weigh an average of 160 pounds each. Use an inequality to find the weight of luggage and cargo the plane can carry.

{x|x<=1040}

500

A parking garage charges $1 for the first hour and 60 cents for each additional half-hour. Use an inequality to find how long you can park if you have only $4 for parking.

if x is number of half hours, 

{x|x<=5}text( 3.5 hours or less)