LESSONS

A Free Math Website

Finally!  A free math website that explains math in a simple way, and includes lots of examples, from Counting through Calculus!

Here are the topics that She Loves Math covers, as expanded below:  Basic Math, Pre-Algebra, Beginning Algebra, Intermediate Algebra, Advanced Algebra, Pre-Calculus, Trigonometry, and Calculus (to be completed). 

Basic Math

More Practice:

Mathway

Pre-Algebra

 Beginning Algebra

Introduction to Algebra 

Types of Numbers and Algebraic Properties

Solving Algebraic Equations

Linear Inequalities

Word Problems in Algebra

 Intermediate Algebra

 

Systems of Linear Equations and Word Problems

Algebraic Functions

Scatter Plots, Correlation, and Regression

Exponents and Radicals in Algebra

Introduction to Multiplying Polynomials

Introduction to Quadratics

Introduction to Quadratics (continued)

Solving Quadratics by Factoring and Completing the Square

Quadratic Inequalities

Quadratic Applications

Solving Radical Equations and Inequalities

Advanced Algebra

 

Advanced Functions: Compositions, Even and Odd, Increasing and Decreasing

Inverses of Functions

Parent Functions and Transformations

Piecewise Functions

The Matrix and Solving Systems with Matrices

Introduction to Linear Programming

Rational Functions and Equations

Graphing Rational Functions, including Asymptotes

Graphing and Finding Roots of Polynomial Functions

Exponential Functions

Logarithmic Functions

Pre-Calculus

Trigonometry

Right Triangle Trigonometry

Angles and the Unit Circle 

Graphs of Trig Functions

Transformations of Trig Functions

The Inverses of Trigonometric Functions

Solving Trigonometric Equations

Trigonometric Identities

Law of Sines and Cosines and Areas of Triangles

Polar Coordinates, Equations and Graphs

Trigonometry and the Complex Plane

Calculus

39 thoughts on “LESSONS

  1. This was VERY helpful! I had a test just tomorrow in Pre-Algebra and I was practically clueless. I am beginning to understand the areas of math we are going through, though I currently have a D in my class because the 13/20 on my unit test lowered it from a C+. I was about to give up, but I knew acing my next test would help my grade a lot. I recommend this site to any girls that are struggling with math or just need a little re-learning. Wish me good luck on tomorrows test! I hope I get this one, and I will be happier than ever…I’ve always wanted to show my mom a great math test score… :)

    • Thanks for the sweet comment, Emme! I’m thinking good math thoughts your way, and I know you can do it!! Thanks for visiting the site and let me know if you ever have any math questions!! Lisa :)

    • Renee,
      Congratulations for home-schooling your precious daughter. Thanks so much for kind words and let me know if there’s anything I can do to make the site better :)
      Lisa

  2. This site is exactly what I’ve been looking for to help my mathematically talented but easily bored son. The examples and explanations are thorough enough to educate but concise enough to hold interest.

  3. I’m having a really hard time when it comes to radicals :( Too bad, I can’t find something here that will help me. :( maybe you should add them to your site. :) Thank you! Your website is so cool

  4. I’m working on “Laplace Transform”…
    I need some real life examples which can be solve by L.T.
    can you help me ?
    please make it faster.

  5. I love the site and how much has gotten done since I last looked, but I also see that there isn’t a geometry section. Could you work on this after your other projects?

  6. A cubic polynomial function f(x) has leading coefficient -2 and intercepts the y-axis at 2.If f(1)=1, and f(-2) =-2, find f(-1) and write the complete
    function.

    • You can solve this using systems. let y = -2x^3 + ax^2 + bx +c. Plug in (0, 2) to see that c = 2. Then we have y = -2x^3 + ax^2 + bx +2. Plug in (1,1) to see that 1 = a + b. Then plug in (-2,-2) to see that -10 = 2a – b. Solve that system to see that a = -3, and b = 4. So we have y = -2x^3 – 3x^2 + 4x +2. So then f(-1) = -3. Hope that helps! Lisa

    • Thanks so much for writing, and please spread the word about She Loves Math. This makes me want to keep writing 😉 Thanks again, and let me know if I can make it better, Lisa

  7. Lisa
    I stuck on trying to figure out how to parametrize
    y=(-x^2/72)+x so as to get x=24 sqrt[2] t. Once I have the x
    I can figure the y which is -16t^2 +24Sqrt[2] t.
    (sqrt is abbreviation for square root)
    Thank you for your help
    Manuel

    • Thanks for writing, Manuel. I think when you go from an equation with x and y to parametric equations with t, t could basically be anything. But if they wanted the y in the form y = -16t^2 + something, we could set -x^2/72 to -16t^2 (the first term of the y), and solve for x to get 24sqrt(2)t. Does that make sense? Lisa

  8. Lisa
    As you said, I could have used any parameter for x.
    I was just wondering where the author chose
    24Sqrt[2] t, from the rectangular equation y=x-x^2/72 to get
    y=-16t^2 +24Sqrt[2] t. I tried all kinds of parameters for
    y=x^2/72 and sure enough, while I get different values for y,
    Thanks again. Basically, I didn’t understand what was meant by
    parametrization.
    Manuel

  9. Hello Lisa
    Please excuse if you received this comment before.
    I was wondering why you haven’t recommended the use of I believe the best calculator available, namely, Wolfram Alpha. It can be downloaded thru your app in your iPad or from the internet for free. It’s better on the iPad. I think it would help to take the drudgery out matrix`manipulations, vectors, quadratic equations, 3D graphing, et al.
    As far as I’m concerned you are the best Just thought you may be interested.
    You probably know this anyway.
    Manuel

    • Manuel,
      Thanks for writing! I don’t have a lot of experience with Wolfram Alpha and just downloaded the app on my ipad. It looks fantastic! I have used Mathematica in the past; I guess it was based on this.
      Thanks so much for the suggestion; that’s a great idea! They don’t use it at the high school, so I haven’t had to help any kids on it, but it’s definitely on my to-do list.

      Thanks again and spread the word about She Loves Math :)
      Lisa

  10. I am having trouble with this section, if you could get back to me asap it would be greatly appreciated.
    1)In the nineteenth century, the Austrian monk Gregor Mendel noticed while crossbreeding plants (peas in particular) that often a characteristic of the plants would disappear in the first-generation offspring but reappear in the second generation. He theorized that the first-generation plants
    contained a hidden factor (which we now call a gene) that was somehow transmitted to the
    second generation to enable the characteristic to reappear.
    As an example, suppose we denote the gene that produces the yellow seed by Y and the gene that
    produces the green seed by g. The uppercase Y indicates that yellow is the dominant gene and
    the lowercase g indicates that green is recessive. The table below shows the possible theoretical
    outcomes that can occur when we cross two first-generation plants.
    First Generation Plant
    Y g
    First Generation
    Plant
    Y YY Yg
    g gY gg
    Notice from the table that of the 4 possible outcomes, 3 of the plants will be yellow (since 3 have
    the dominant Y gene) while 1 of the plants (since only 1 has two recessive genes) will be green.
    From this we can say that the theoretical probability of the second-generation plant being green
    is ¼ or 0.25.
    There is of course a difference between theoretical and experimental. The following table lists
    some of the actual results that Mendel obtained in his experiments in crossbreeding peas.
    Experimental Results
    Characteristics That Were
    Crossbred First-Generation Plants Second-Generation Plants
    Tall versus Short All tall 787 tall
    277 short
    Smooth versus Wrinkled
    Seeds All smooth seeds 5,474 smooth
    1,850 wrinkled
    Yellow versus Green Seeds All yellow seeds 6,022 yellow
    2,001 green
    Notice from the results that tall, smooth, and yellow are all dominant genes. Also notice that based on the experimental results, the probability of a second-generation plant being green is 0.2494. This agrees fairly well with the theoretical probability.
    From the tables of possible theoretical outcomes and experimental results, answer the following questions.
    1) Assume that we are crossbreeding genetically pure tall plants with genetically pure short plants. Create a table (like the one for yellow and green plants) indicating the possible combinations of tall and short peas.
    2) What is the theoretical probability that a plant will be short?
    3) What is the experimental probability that a plant will be short?
    4) How do theoretical and experimental probabilities compare?
    5) Assume that we are crossbreeding genetically pure smooth-seed plants with genetically pure wrinkled-seed plants. Create a table (like the one for yellow and green plants) indicating the possible combinations of smooth-seed plants and wrinkle-seed plants.
    6) What is the theoretical probability that a plant will have smooth seeds?
    7) What is the experimental probability that a plant will have smooth seeds?
    8) How do theoretical and experimental probabilities compare?

    • Thanks for writing! I’m sorry – I’m having trouble making sense of the tables; let me see if I can find this problem online somewhere. Sorry about that. Lisa

  11. I THINK I understand the problem statement and questions. I have re-stated the problem and answered the questions in a file on my website. I hope it helps. The document is available on http://www.PaulkUSA.com. Click on the “Math Docs” tab and look for the Algebra 2 file named “Statistics Example 01.”

  12. How long will the calculus site in construction?? coz i hope it will help me in my calculus project assignment. i hope it will settle faster, pleaseeeee

    • Thanks for writing! I’m SO sorry about not completing the Calculus portion yet – I hope to by the fall! Keep checking back! Lisa

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