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Systems of Equations
Work & Mixture Problems
Rational Expressions
Quadratic Equations
Area & Volume
100
Is (4, 1) a solution to this system of equations? 2x + 12y = 20 x + 6y = 10
What is "yes"?
100
It takes 1.5 hours for Tim to mow the lawn. Linda can mow the same lawn in 2 hours. How long will it take John and Linda, work together, to mow the lawn?
What is t = 6 / 7 hours = 51.5 minutes.
100
3 7 5 x y z ______ Simplify 2 9 x y z
What is 4 xz __ 2 y
100
Solve for r. (4r – 3)(7r + 9) = 0
What is r=3/4 or .75, or r=-9/7 or ~ -1.29?
100
The area of a triangle with base 16 cm and height 13 cm. (A=1/2bh, area equals half base times height)
What is 104?
200
Solve using substitution. -2x + y = 15 -7x + 10y = 20 ( , )
What is (-10, -5)
200
Hypatia has 20% and 15% solutions of saline (salt) solution. Find how much of each should she mix together to get 5 liters of 18% saline solution.
What is 3 liters of 20% Hypatia solution and 2 liters of the 15% solution in order to get 5 liters of an 18% solution?
200
Simplify: 2 n -9n+14 ________ 2 3n -12
What is n-7 _____ 3(n+2) ?
200
Solve. w2 + 32w + 31 = 0
What is w=-31, or w=-1?
200
The volume of a right triangular prism with hypotenuse 13, a leg of 5, and height 17. (V=Bh, volume equals base area times height)
What is 510?
300
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Dr. Ellison just got his PhD, and he wants to print copies of his thesis in hardcover book format. He could use Allenville Printing, paying a setup fee of $39 and $5 for every book printed. Alternately, he could go through Port Lanshine University, paying an up-front fee of $36 and $8 per book. It turns out that, given the number of books Dr. Ellison wants to print, the two options cost the same amount. How many books is that? What is the amount?
What is for 1 book, the cost is $44?
300
Amanda and Xander are weeding yards. It takes Amanda 10 minutes for her to weed 1 yard and Xander can weed 2 yards in 24 minutes. Find how long it would take them to weed 1 yard together.
What is 60/11, 5 5/11, or 5.45 minutes?
300
Add. 2 2 (t + 3t) + (2t + 6t + 4)
2 What is 3t+9t+4?
300
Find the discriminant. 2 3g – 7g + 8 = 0
What is -47?
300
The lateral area of a regular pentagonal pyramid with slant height 13 and side length 3. (L.A.=Pl, lateral area equals base perimeter times slant height)
What is 195 square units?
400
Solve using elimination. 5x + 6y = 4 5x + 7y = 8
What is (-4,4)?
400
You need 20 liters of 20% acid solution. You have jugs of 10% solution and 25% solution. How many liters of each should you combine to get the needed solution?
What is 6 2/3 liters of Solution 1 and 13 1/3 liters of Solution 2?
400
Simplify 2 (-4z + 4)
2 What is 16z-32z+16?
400
Solve by completing the square. 2 q – 30q – 37 = 0 Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
What is q=31.19 or q=-1.19?
400
Find the total area of a right rectangular prism with height 20 and the square bases' area of 289. (T.A.=L.A.+2B, total area equals lateral area (L.A.=Ph, base perimeter times height) plus the area of the two bases)
What is 1938(square units)?
500
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. At a community barbecue, Mrs. Ferguson and Mr. Avila are buying dinner for their families. Mrs. Ferguson purchases 3 hot dog meals and 3 hamburger meals, paying a total of $48. Mr. Avila buys 2 hot dog meals and 3 hamburger meals, spending $42 in all. How much do the meals cost?
What is hot dog meals for $6 each, and hamburger meals for $10 each?
500
A tank can be filled by pipe A in 5 hours and by pipe B in 8 hours, each pump working on its own. When the tank is full and a drainage hole is open, the water is drained in 20 hours. If initially the tank was empty and somenone started the two pumps together but left the drainage hole open, how long does it take for the tank to be filled?
What is t = 3.6 hours?
500
Factor. 10n3 – 8n2 + 15n – 12
2 What is (2n+3)(5n-4)?
500
Solve using the quadratic formula. 2 5g – 8g + 3 = 0 Write your answers as whole numbers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
What is g=1, or g=3/5?
500
The volume of a sphere with diameter 26. Keep in terms of pi. 3 (V=4/3pi r, volume equals 4/3 times pi times radius cubed)
What is 8788/3pi, 2929 1/3pi, or 2929.33pi?(cube units)