Mathematics

Donate | Algebra | College Algebra | Calculus I

Linear Equations

? What is an equation?
Solve for x ; 3x+1=7
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? Solve for x
(4/5)x+5=10
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? Solve for x
2(x+1)-3=5(x+1)-6
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? Solve for x
6x+15(x+18)+20=19(13x-9)+20(x+8)
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? Solve for x
x/2+x/3=2
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? Solve for t
(17+t)/t+(32+t)/t=100
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? Solve for t
t/(t+4)+4/(t+4)+2=0
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? Solve for x
(3x-2)/(3x+1)=(2x-4)/(2x-1)
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? Solve for x
.25x+.75(x-1)=.35x-1
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Applications I

? John's annual salary is $32,740 with a year end bonus of $500. If he is paid twice a month, what will be his gross pay for each paycheck?
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? You are currently being paid $7.50 an hour. The boss is promising to raise your rate to $9.00 an hour. What will be the percent raise?
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? Jill invested $10,000 in two ways. Part of the money was invested at 8.5 % simple interest and the remainder was invested at 10%. After one year, the combined interest was $900.00. How much did Jill invest in the first account?
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? Michael, made a profit of $100.00 at the farmers market selling tomatoes. He had a fixed cost of $10.00 and variable cost of 30 cents. He was selling his tomatoes for $1.00 each. How many tomatoes did he sell?
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? Zack needs to make a least a B in his math course. His three test grades are 79, 80, and 63. What score does he need to make on his fourth test for him to have an average of 80?
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? Coleen a popular barista at the Alpine coffee house is mixing two types of coffee beans. The first type cost $3.00 per pound and $2.75 per pound respectively, to make 30 pounds of a mixture costing $2.85 per pound. How many pounds of each were put into the mixture?
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? A 55-gallon barrel contains a mixture with a concentration of 35%. How much of this mixture must be withdrawn and replaced by 100% concentrate to bring the mixture up to 70% concentration?
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Quadratic Formula

? We will be deriving the Quadratic formula.
x=(1/(2a))(-b ± √(b²-4ac))
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? Find the solution(s) to the quadratic equation.
2x²-5x+5=0
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? Find the solution(s) to the quadratic equation.
2x²+x-1=0
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? Find the solution(s) to the quadratic equation.
x²-10x+22=0
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? Find the solution(s) to the quadratic equation.
28x-49x²=4
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? Find the solution(s) to the quadratic equation.
8t=5t+2t²
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? The area of a rectangle is 100 meters squared. The length is three more than twice the width. What are the dimensions of the rectangle?
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Complex Numbers

? Write in standard form:a+bi
2+√(-25)
5-√(-9)
1+√(-8)
√(-50)
-3i+i²
-4i²+3i
(√-4)²-3
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? Simplify :a+bi
(5+i)+(6+i)
(2-i)-(4-3i)
(-3+√(-8))+(5-√(-50))
12i-(2-7i)
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? Simplify :a+bi
(√(-3))(√(-2))
(√(-5))(√(-10))
(√(-10))²
(1+√(-1))(1-√(-1))
(1+i)(1-i)
(4+i)²
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? Simplify :a+bi
4/(1-5i)
(6-8i)/(1+i)
(1-3i)/(4i)
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? Solve for x
x²-2x+2=0
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? Solve for x
x²+6x+10=0
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? Simplify
i²
i³
i⁴
i⁵⁶⁷
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Other types of Equations

? Find the solution(s) to the equation.
4x⁴-18x²=0
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? Find the solution(s) to the equation.
x⁴-81=0
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? Find the solution(s) to the equation.
x⁶+7x³-8=0
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? Find the solution(s) to the equation.
2x+9√(x)-5=0
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? Find the solution(s) to the equation.
x=√(11x-30)
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? Find the solution(s) to the equation.
√(x)-√(x-5)=1
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? Find the solution(s) to the equation.
|2x-1|=5
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? The noon club chartered a bus for $520. When six more members joined the trip, the cost per member decreased by $6.00. How many members were there before the six joined?
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? Michael's tomato plants use 30 gallons of water per day. When ten more plants were added, volume per plant decreased by 1/10 of a gallon. How many plants were there before the ten were added?
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Linear Inequalities

? Find the solution set.
4x+2 ≤ 3x-4
1 < 3x+4 ≤ 10
-4 < (2x-5)/3 < 4
-3x+2 > 5
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? Find the solution set.
|x/3|>3
|x+18|+4 > 20
-2|3x+1| ≤ 5
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? Rental car Company A charges $250 per week. While, Company B charges $150 per week plus 25 cents per mile. How many miles will you have to drive so that Company B cost exceeds Company A cost?
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? The Grifasi coffee company is offering a sweet deal this week. If you purchase their signature cup for $10, refills will only cost 25 cents per cup, whereas a cup of coffee runs $1.95 per cup with no refills. How many refills will it take before the $10 cup will start saving money? How many refills will it take to save $100?
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Distance and Midpoint

? Find the distance between two points.
(0,0),(2,3)
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? Find the distance between two points.
(2,-2),(4,2)
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? Find the distance between two points.
(-1,3),(5,0)
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? Find the distance between two points.
(0,1),(5,10)
(-3,-10),(1,20)
Solve for x, given the distance is d=20, and (x,1),(10,20)
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? Find the midpoint.
(0,0),(5,6)
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? Find the midpoint.
(2,3),(10,100)
(-1,-1),(3,20)
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Graphs of Equations

Symmetry

Equation of a Circle

Lines in the Plane

Functions

Graphs of Functions

Inverse Functions

Quadratic Functions

Higher Degree Polynomial Functions

Polynomial Divison

Synthetic Division

Real Zeros of Polynomial Functions

Fundamental Theorem of Algebra

Approximating Zeros

Rational Functions

Partial Fractions

Conic Sections

Conic Sections and Translations

Exponential Functions

Logarithmic Functions

Properties of Logarithms

Logarithmic and Exponential Equations

Logarithmic and Exponential Applications

Systems of Equations

Systems of Inequalities

Linear Programming

Matrices and Systems of Linear Equations

Operations with Matrices

Inverse of a Square Matrix

Determinant of a Square Matrix

Properties of Determinants

Applications of Matrices

Test Questions

1) 16x+85-3x= 995 ; Find the solution.
2) -2x+191<187 ; Find the solution.
3) ax+by=c ; Solve for y
4) Convert 2 degrees Fahrenheit to Celsius ;Round to the nearest integer

Answers

1) 70
2) x>2
3) (c-ax)/b
4) -17 degrees Celsius