Level B2 Review Packet This packet briefly reviews the topics covered on the Level A Math Skills Assessment. If you need additional study resources and/or assistance with any of the topics below, please visit the Math Center (See our hours here: http://www.sjfc.edu/campusservices/mathcenter/) All questions and concerns about the assessment should be directed to mathcenter@sjfc.edu. Note: A calculator is not allowed on the Level B2 Math Skills Assessment. Decimal Addition and Subtraction ) 9.07 + 2.88 2) 4.3 + 2.2 3) 30.69-29.8 4) 2.02-6.069 Decimal Multiplication and Division ) 5.4 x 5.05 2) 0.6643 x 2 3) 20.8 x 6. 4) 9.4 x.3 5).2 00 6) 7.035 3
) Simplify the expression below. 2-6 (5 + 2 3 ) Order of Operations 2) Simplify the expression below. 2 6 4 2 2 + 2 3) Simplify the expression below. 2 7 + 3 3 4 2 4) Simplify the expression below. 4 + 2 3 (4 2-9) ) Fraction Addition and Subtraction 4 2) 7 2 3 2 5 3 3) 2 4) 5 9 4 6 5 5) 2 5 3 6) 3 8 2 3 5 7) 5 2 6 8) 8 3 7 5 5 8 6 2
) Fraction Multiplication and Division 4 2) 7 2 3 2 5 3 3) 2 4) 5 9 6 4 5 5) 2 5 3 6) 3 8 2 3 5 7) 5 2 6 8) 8 3 7 5 5 8 6 Converting Fractions to Decimals and Percents ) Convert 3 4 to a decimal and a percent. 2) Convert 4 5 to a decimal and a percent. 3) Convert 3 8 to a decimal and a percent. 4) Convert to a decimal and a percent. 8 3
Solving Equations ) Solve for x: 5 x 2 28 x 2) Solve for x: 3(3x 6) = 3(x 2) 3) Solve for x: -6x + = 3(2x +) 4) Solve for x: 3(2x 3) + 5 = 20 2x 5) Solve for x: 7x - 8 = 2(3 + 2x) + 4 3 6) Solve for x: x 8 4 4 7) Solve for x: 0 x 23 8) Solve for x: 3 6 0 2 x Determine value from linear equation. Let y 3.6 0.4x. If x has a value of 00, 2. Let y 90.5x. If x has a value of 200, what what would be the value of y? would be the value of y? 3. Let y 43x 00. If x has a value of 4, what is the value of y? 4. Let y 23x 22.6. If x has a value of 200, what would be the value of y? 4
) Evaluate x 3. a b a x 2 ( ) if, b 2 a and Evaluating Expressions 2 a b 2a 2c 2) Find the value of b a 3, b 4 and c 5. when 2 2 3) Find the value of 3a 2bc c when a 3, b 4 and c 5. 4) Find the value of x 3, y 2. x 3 2 4x 5ywhen ) Determine the slope of the line that passes through the points ( 2, 2) and (3,6) Determine Slope 2) Determine the slope of the line that passes through the points (,5) and ( 2,3) 3) What is the slope of the line whose equation is 7y 2 5x? 4) What is the slope of the line whose equation is 5 3x 2y? ) Find the percent increase or decrease from 2 ft to 24 ft. Percent Increase and Decrease 2) Find the percent increase or decrease from 200 miles to 60 miles. 3) Find the percent increase or decrease from 80 hours to 00 hours 4) Find the percent increase or decrease from 45 tons to 60 tons. 5
) Let s say you have 20 trading cards in your collection. If you lose 30 cards, what is the percent decrease in the number of cards? Word Problems Percent Increase/Decrease 2) You and your friend both have 60 baseball cards. Your friend agrees to give you 25% of his cards. How many cards will you then have? 3) During a job fair last week, 50 potential candidates were identified. This week 65 additional candidates were identified. What is the percentage increase in candidates this week? 4) Martha began a new exercise program and loses 20% of her body weight. If she weighs 28 lb now, how much did she weigh when she began the program? ) You know that a ¾ cup serving of your favorite cereal has 70 calories. How many cups of the same cereal will have 300 calories? Word Problems Proportions 2) Your lawnmower can run for 20 minutes on $0.50 worth of gas. How many minutes could it run on $.75 worth of gas? 3) Ginger runs in a 5 kilometer race and burns 500 calories. How many kilometers should she run in order to burn 450 calories? 4) If a medium size coffee (2 oz) costs $2.45, how much would a large size (20 oz) cost at that same rate? 6
) A 25 ft ladder is rested against a building that is 50 feet high. If the top of the ladder hits the wall at a height of 6 ft. and the bottom is 9 ft. from the wall, what is the slope of the ladder? Word problems slope 2) You are building a wheelchair ramp from the parking lot of a building up to the front door. The slope of the ramp can be no more than /7. If the height of the door is 3 ft above the parking lot, how long must the ramp extend into the parking lot? 3) The altitude at the top of the mountain is 3500 ft above sea level. If the altitude at the base of the mountain is 3000 ft, and the horizontal distance to directly under the top of the mountain is 2000 feet. What is the slope of the mountain? 4) You place a billiard cue against a billiard table. The foot of the billiard cue is 5 cm away from the table and the top of the billiard cue touches the table at a point 60 cm off the ground. What is the slope of the billiard cue?. A square tub is 2 feet on all four sides and 3 feet deep. If 0 cubic feet of water is put in the tub, how far is it from the surface of the water to the top of the tub? Word problems volume 2. A rectangular pool is 5 feet long, 0 feet wide, and 6 feet deep. If we put 200 cubic feet of water in the pool, how deep is the water? 3. Let s say you purchase a small container garden for your patio. The container is 5 feet wide, 6 feet long and 2 feet deep. If you fill the container with 50 cubic feet of soil, how far will it be from the top of the soil to the top of the container? 4. A frying oil vat is filled so that there is a distance of 6 inches (/2 foot) from the top of the oil to the top of the vat. If the vat is 3 feet deep, 2 feet wide, and 2 feet deep, how much oil is in the vat? 7
. Hannah s electricity company charges $0. per kwh (kilowatt hour) of electricity, plus a basic connection charge of $5.00 per month. Write a linear function that models her monthly electricity bill as a function of electricity usage (in kilowatt hours). Word problems linear relationships 2. A store sells chain by the foot. Regina purchases a 00 foot chain for $80. Scott needs a 50 foot chain. How much will he pay? 3. Warren can grow 2 plants with every seed packet. He already has 20 plants growing. If he purchases x additional seed packets, write an equation that determines how many plants he will have. 4. Shawn rides his bicycle at a constant rate of 5 feet per second. Let d be the distance (in feet) from the bicycle to a marking in the road. Determine a formula to determine d given the amount of time t (in seconds) since Shawn was 20 feet past the road marking. Determine Y-intercept. Determine the y-intercept for the line shown below: 2. Determine the y-intercept for the line shown in this graph: 3. Determine the y-intercept for the line shown in this graph: 4. Determine the y-intercept for the following line: 8
Function notation Let R(t) be the monthly revenue in dollars for a sales volume of t units. Determine the meaning of the following: ) R(t+0) 2) R(t)+0 3) 0*R(t) 4) R(00) You open a savings account that earns.002% interest each day with a deposit of $000. Let M(t) be the account balance in the account, measured in dollars, t days since it was opened. Determine the meaning of the following expressions: ) M(t+20) 2) M(20) 3) 2*M(0) 4) M(30)-M(0)) 9
Writing Expressions and Equations ) Cindy has four more than five times as many cousins as Kathy, k. Write an expression that represents how many cousins Cindy has compared with Kathy? 2) Dawn is 3 years older than her sister Sara. If Dawn s age is represented by x, which expression represents Sara s age? 3) Translate into a mathematical equation: when 7 is added to 4 times a number, n, the result is 35. 4) Write an algebraic equation that represents six less than half a number, x, is equal to 5. 0
. Bonita bought Problems Involving Fractions 2 kg of potatoes and kg of carrots. How much more potatoes than carrots did she buy? 5 2 2. A carpenter made shelves of length did he have left over? 3 4 ft. and 3 8 ft. If his board was 8 2 ft long, how many feet of board 3. From a piece of ribbon left? 2 2 inches long, a piece 3 5 4 inches long is cut. How many inches of ribbon are 4. Joan s room requires 7 20 square yards of carpeting and Sam s room requires 7 square yards of 4 8 carpeting. How many more yards of carpeting does Joan s room require? 5. To roast a turkey for Thanksgiving dinner, Juliette s recipe calls for 3 4 of an hour cooking time per pound. If her turkey weighs 2 2 pounds, how many hours should she cook her turkey? 6. About 3 of the land on the earth can be used for farming. Grain crops are grown on about 2 5 of this land. What part of the earth s land is used for growing grain crops?
7. Mrs. Meier had 3 5 kg of sugar. She used 4 of it to make cookies. How much sugar did she use to make the cookies? 8. Natalie cuts a raffia raffia? Give the answer in meters. 4 4 5 meters long into 8 pieces of equal length. What is the length of each piece of 9. Four friends evenly split 6 2 liters of soda. How many liters of soda does each one get? 0. If 4 of a container holds 6 cups of water, how many cups of water does 8 of the same container hold?. The length of a page in a particular book is 8 inches. The top and bottom margins are both 7 8 inch. How long is the page inside the margins, in inches? 2. Lauren spent 3 of her money on a refrigerator that cost $900. How much money did Lauren start with? 5 2
Problems Involving Percents. The Red Sox team played 60 games and won 65% of them. How many games did they win? 2. A basketball player took 400 shots during a season and scored on 40% of them. How many baskets did she score? 3. A gasoline tank holds 20 gallons. If the tank is already 25% full, how many gallons of gasoline are needed to fill the tank? 4. When the local department store put all of its shirts on sale for 20% off, Jason saved a total of $30 by purchasing four shirts. What was the total price of the four shirts before the sale? 5. Twelve students participated in a science competition to represent Montana State University. If they are 5% of the total number of science majors, how many students are majoring in science at MSU? 3
6. If 6 feet of a 30-foot pole are underground, what percent of the pole s length is above the ground? 7. Stacy won 8 of the 20 tennis games she played. What percent of the games did she win? 8. If 320 out of 500 families in a city have computers, what percentage of the families has computers? 9. Mr. Jenkins wants to distribute 40 fliers. He has distributed 30 fliers so far. What percent of the total number of fliers has Mr. Jenkins distributed? 0. If 3 of John s stamps are Canadian stamps, what percentage of his stamps are Canadian stamps? 5 4
Additional Problems. A certain recipe calls for 2 cups of milk for every 3 cups of flour. If 2 cups of flour are used, how many cups of milk should be used? 2. Carlos burns 75 calories for every 5 minutes he walks. How many calories will Carlos burn if he walks for 45 minutes? 3. Carlos burns 75 calories for every 5 minutes he walks. Carlos wants to burn 300 calories. How many minutes must Carlos walk in order to burn 300 calories? 4. On the city map, inch represents 2 mile. How many inches represent 3 4 miles? 5. Ellen buys 24 ounces of green beans at the grocery store. The green beans cost $.90 per pound. How much does she pay for the green beans, before tax? ( pound = 6 ounces) 6. An art teacher mixes 20 ounces of yellow paint with 8 ounces of red paint. How many ounces of yellow paint would she need to mix with 8 ounces of red paint to maintain the same proportion? 5