Cumulative MTE -9 Review This packet includes major developmental math concepts that students ma use to prepare for the VPT Math (Virginia Placement Test for Math or for students to use to review essential math skills. Please Note: This is a sample of topics covered in MTE -9, and it is not a comprehensive list. The VPT Math provides a calculator; no outside calculators are permitted. The calculators are not permitted for use in an of the BSK (Basic Math Skills and MTE courses and within portions of the MTE and MTE courses. Useful Conversions ma or ma not be provided for the student on the VPT Math. MTE Problems: Evaluate the following:. +. + 8. ( + (9 + + 9 + + 0 (8 + 9 Factor the following numbers into prime numbers: 6.. 99 8. Change to a mied number or improper fraction: 9. 6. 0... 9 Simplif 8 the following fractions: 6.. 69 Find the Least Common Multiple (LCM: 8., 9., 0.,,0 Perform the indicated operation:. 6 +. 6. 8 8 9 State whether the following statements are true or false: > 9. 9. 8 > 8. < 0. < 6. 9 Provided b Tutoring Services Cumulative Math Review Updated Jul 0
Convert the following:. tons = lbs.. 8 oz. = cups. 8 ft. = ds. Useful Conversions: ton = 000 lbs. 8 oz. = cup ft. = d. MTE Problems: Round the following numbers to the nearest tens and then to the nearest hundredths:.. 6.... Convert each fraction to a decimal and each decimal to a fraction: 6. 0. 0. 8 9 8. 000. 9.. 6 Perform the indicated operation. Round answers to thousandths where necessar: 0.. + 8..9.. 9... 0. Write each percent as a decimal and each decimal as a percent: 6. % 8. 0.6%.. 9. 0. 0. 68. % Convert the following units:. miles = km.. inches = cm.. 86 m. = feet Useful Conversions: inch =. cm. foot = 0. 0 m. mile =. 609 km. Evaluate the following: + [ (9 ] ( 8. What number is % of? 8. is what percent of? 9. Find 0 % of 0. 0. % of what is 8? 6. ( 69 (+. A new car costs $6,0 from the manufacturer. The dealership sells the car for $,000. What is the percent markup at the dealership? Provided b Tutoring Services Cumulative Math Review
MTE Problems: Evaluate the following:. ( 60 8(. ( ( +. 86 + 8 ( 9 + ( 8 0 6. 6 + 0 Solve the following:. + = 8. = 6 9. = 0. 6 ( = Solve the 8 following proportions: =. 9 =. 0. = 0 What is the area of the following object? cm. cm. 8 cm. A store sells rice at a rate of 9 cents per ounce. How much would pounds of rice cost ( pound = 6 ounces? 6. If the Thanksgiving turke takes6. hours to cook, and the instructions sa to cook the turke minutes for each pound, how much does the turke weigh?. Cat food is sold in three sizes: a 0 pound bag, a pound bag, and a 0 pound bag. The 0 pound bag costs $ 0., the pound bag costs $, and the 0 pound bag costs $ 6. 99. Which is the best value? 8. A rectangular field requires 00 feet of fence to enclose it. The length of the field is twice the width. What is the width of the field? 9. Two triangles are similar. Triangle A has sides measuring,, and. The shortest side on triangle B measures 6. What are the lengths of the other two sides? Translate the following in variable epressions: 0. Twent more than a number.. Ten times the difference between a number and fift.. The product of two-thirds and the sum of a number and seven.. Twice the sum of si times a number and seven. Solve and check: + = z + 9 = 6. =. = + Provided b Tutoring Services Cumulative Math Review
8. Write in decimal notation: 8. 0 9. Write in scientific notation: 9,000,000,000 Evaluate the following: 0.. 6. 6 MTE Problems: Solve and check the following. Write answer in interval notation where appropriate:. + > + = +. 8 <. = ( = (6 + 8 = 0 6. Check that the given value is a solution to the equation.,. 6 + = = 8. = 8 + 6, = 0 9., 9 0 = = 0 9 Solve for the given variable: A bh, h 0. =. D = rt, r b A = (,. h b + b. The sum of three consecutive odd integers is 9. What are the three integers? Three more than a number is si less than the sum of two times a number and seven. What is the number? Jack leaves home at 9 : 00 A.M. and drives to work arriving at 9 : A.M. If the distance between home and work is miles, what is Jack s average rate of speed? 6. Two runners, starting at the same time, run towards each other from opposite ends of an 8 -mile trail. One runner is running at a rate of mph., and the other is running at a rate of mph. How long after the start will the two runners meet?. Find the volume of a rectangular solid with a length of 6. ft., a width of ft., and a height of ft. 8. The height of a triangle is cm. The area of a triangle is 8 cm². Find the length of the base of the triangle. 9. The length of Sue s lawn is 6 ft. The width is 8 ft. How man feet of fencing will she need to create a pen for her dogs? 0. A small air conditioner can cool a room º in min. A larger air conditioner can cool the room º in 0 min. How long would it take to cool the room º with both air conditioners working together? Provided b Tutoring Services Cumulative Math Review
. Jane traveled 080 miles b jet and then an additional 80 miles b helicopter. The rate of the jet was four times the rate of the helicopter. The entire trip took a total of hours. Find the rate of the jet.. The distance (d a ball will roll down an inclined plane is directl proportional to the square of the time (t. If the ball rolls 6 ft. in sec., how far will it roll in sec.? MTE Problems: f ( =. Evaluate: 8 Plot the following points on a graph:. (0,. (,0 (, (, 6. Graph the inequalit: > 9. Is the ordered pair (,8 a solution?. Graph the line: = 8. Graph the line passing through the point (, with a slope of. 9. Are the lines = and + = 8 perpendicular? 0. Are the lines + = and + = parallel?. Find the equation of the line that contains the point = +. (, and is parallel to the line. Find the slope of the line that contains the ordered pairs (, and (,.. A rowboat team traveled with the current 6 miles in hours. Coming back against the current, it took hours to cover the same distance. Find the rate of the rowers in calm water and the rate of the current. A turboprop plane fling with the wind flew 800 miles in hours. Fling against the wind, the plane required hours to travel the same distance. Find the rate of the plane in calm air and the rate of the wind. Allen bus 6 ds. of nlon carpet and 0 ds. of wool carpet for $ 80. A second purchase, at the same prices, includes 8 ds. of nlon carpet and ds. of wool carpet for $ 00. Find the cost per ard of the wool carpet. Provided b Tutoring Services Cumulative Math Review
6. Sand has a total of $,000 deposited in three different accounts. The three accounts earn annual interest rates of 8 %, 6 %, and %. The amount she deposited in the 8 % account is twice the amount in the 6 % account. If she earns a total annual interest of $,0, how much mone is deposited in each account?. Solve b substitution: 6 = ; = + 8 8. Solve b graphing: + = ; = 6 9. Solve b elimination: 6 + = ; = 0. Solve b elimination: + z = ; + + z = ; + z = MTE 6 Problems: Simplif the following:. ( z ( 8 z.. (( z( z (. 0 (.9 0 (8. 0 ( z ( z ( z Perform the indicated operation: 6. ( + + (9 +. ( 8 + ( 8. 9. ( + ( ( + ( Completel factor the following: 0. 9 + 6. + 0 9 6. 9 +. 8 a b 0b + 6a Solve the following: 6. + = 0. ( + ( = ( + ( + MTE Problems: Simplif the following: +. +. Find all values restricted in the domain:. + + + 08 9 Provided b Tutoring Services 6 Cumulative Math Review
Preform the indicated operation: 6. + + + + +. 8 + 8. + 8 + 6 9. + + 6 + 0 0 90 0. 6 + + 8 +. Divide:. ( ( + 6 0. + Simplif the following comple rational epressions: n + n 6. + + + Solve the following:. + = 8 + 8. + = 9. Sarah can clean a kitchen in hours 0 minutes. Hannah and Sarah can clean the same kitchen in hour minutes. How long will it take Hannah to clean the kitchen b herself? Round to the nearest minute. MTE 8 Problems: Convert each fractional eponent to a radical and each radical to a fractional eponent: (.. ( z 6. Simplif the following: 9 6 6. 8 +. ( Solve the following:. + = + 8. 9. 6 0. ( 8 + + + =.. Perform the indicated operation: ( i + ( i 6. ( i( i MTE 9 Problems:. + 6 i 8. i 9. ( 6 i ( 6i 0. i Provided b Tutoring Services Cumulative Math Review
Solve b factoring:. = 0. = + 6 Solve b completing the square:. + = 0 = + Solve b using the quadratic formula: + = 0 6. Solve b taking the square root: ( + = 0 State the domain and range:. f ( = = f ( 8. = + Answer the following questions b completing the square for : 9. What are the domain and range of the function? 0. What is the equation in standard form?. What are the coordinates of the verte?. What is the ais of smmetr?. Does the graph open up or down? What are the and -intercepts? = + 6 Answer the following questions using the verte formula for : What are the domain and range of the function? 6. What is the equation in standard form?. What are the coordinates of the verte? 8. What is the ais of smmetr? 9. Does the graph open up or down? 0. What are the and -intercepts?. The perimeter of a rectangle is 00 m. What dimensions would give the maimum area?. The cost to produce biccle tires a da is given b value of minimizes production cost? C( = 0 + 6. What Provided b Tutoring Services 8 Cumulative Math Review
MTE Solutions:... 8 0 8 6.. 8. 9. 9 0... MTE Solutions:. 0,. 6. 0,.. 0,. 0. 8 6.. 0. 0 8. 0. 0 8 9. 0 MTE Solutions:. 880. 0. 0 8 0 6.. 8. 8 9. 8 0.... 9 6.. 8. 9. 96 0. 0.. 0.. 09. 9. 6... 6. 9 9. 8 0. 6 6. 0.. 0 % 8. 0. 006 9. 00 % 0. 68%.... 6. 86 cm. $ 0. 6 6. lb.. 0 lb. bag 8. 8. ft. 9. 8 and 0 0. + 0. 0( n 0. 8 8 6. 6. False 8. True 9. False 0. False. 00 lbs.. cups. 6 ds..... km.. 60. 96 cm. ft. 0. 6. 0... 8. 0 % 9. 0. 00..% (. +. (6 + 6.. 8. 0. 008 0 9..9 0 0.. 6 i. 8 Provided b Tutoring Services 9 Cumulative Math Review
MTE Solutions:. { > }.. =, = 9 { < } 6. 8. No MTE Solutions:. 9. See page. See page See page See page 6. See page, No. See page 8. See page 9. es MTE 6 Solutions: 8. 8.. 68 8 z 6 z. 0 0 z MTE Solutions:. +. +. None 6 6, + + + + 86 6.. 6. 8. Yes 9. Yes h = 0. b A r =. D t b = b. h A.,, 0. es =... Rowers: mph. Current: mph. Plane: 80 mph. Wind: 0 mph. $ /d. + 8 +. 8. 6 + 9. 8 + 0. 9( +. ( ( 0 8. 9. 0. 6+ 80+ ( + 8( ( 8 ( +. + +. +. 0 6 mph. 6. 0 min.. 9 ft.³ 8. 8 cm. 9. 08 ft. 0. 0 min.. 60 mph.. ft. 6. 8% : $0,00 6% : $,00 % : $9,00 (6,. 8. No solution 9. (, 0. (,, 6. ( +. ( + ( ( ( + 6 + 9 ( a b( + =, = 6. =, =. 8 n n 6+ 6. 8,. 8. 9. hour min Provided b Tutoring Services 0 Cumulative Math Review
MTE 8 Solutions:. 8.. 6. ( z ( 6 8 +. 6 + 9 + 8. 9. 0. + i... and 6i 6. 0i 0 i. 9 9 8. i 9. i 0. i MTE 9 Solutions:,.. 9. + i, i +, + i, i 6. + i, i. { } { 0} 8. { } { } 9. { < < } { } = ( 0.. (,.. Down : none : ( 0, { < < } { 8} = ( + 8 6.. (, 8 8. 9. Up 0. : (,0,( 6,0 : ( 0, 6. 0 m. b 0 m.. biccle tires MTE - #- MTE - #6... Provided b Tutoring Services Cumulative Math Review
MTE - #. MTE - #8. Provided b Tutoring Services Cumulative Math Review