November 29th

Today, we are solving equations:
1. Biquadratic equations
A biquadratic equation is a quartic equation without odd degree terms; in general,
ax ⁴+bx²+c=0
where a, b and c are real numbers.
To solve it, we use the substitution y=x²; that leads to the quadratic equation ay²+by²+c=0.
Solve these exercises in your notebook and then check your answers on the web.

2. Radical equations
A radical equation is an equation that has at least one variable expression inside a radical, usually a square root. Here you have an explanation on how to solve these equations:

Now try some exercises.

3. Equations involving fractions
Solve these exercises.

4. Simultaneous equations
Do you remember how to solve simultaneous equations? Prove it.

November 8th

Polynomials
We´ve learned about the long and the synthetic division of polynomials, how to factor them and the Remainder and Factor Theorems. It´s time to put that knowledge to the test with some interactive quizzes:
Quiz 1: about synthetic division and the Remainder Theorem.
Quiz 2: factoring polynomials.
Quiz 3: Remainder and Factor Theorem Quiz.

Some extra practice (non-interactive).

Tuesday, October 18th

Last year we studied what scientific notation is. Here it´s the definition and some examples.
And now a TEST.

Adding and subtracting numbers in scientific notation
Watch the explanation.
So, when adding or subtracting in scientific notation, you must express the numbers as the same power of 10. This will often involve changing the decimal place of the coefficient.
For some exercises, try sections G and H on this page. The answers are at the end of that page.

Multiplying and dividing numbers in scientific notation
It´s so much easier. Just multiply or divide the coefficients and the powers of 10. Try the exercises at the end of these pages: multiplication, division.

Tuesday, October 11th

Today it´s about logarithms. We started last week with the definition; let´s remember it with this video.
At this point, you should already know what a common logarithm is or how to work out the value of log 0.001. More info about logs:

Rules of logarithms. Watch this video to learn how to use this rules or properties.

And here you have some examples and exercises.

Tuesday, October 4th

Today it´s about radicals (or surds, as you prefer). To be exact, "rationalising radicals". We are going to first check a presentation and then solve some exercises:

Rationalising radicals

View more presentations from susoigto

Here it´s a link to the video you just watched.

And now some exercises:
1. 4 very simple questions (solve them on your notebook).
2. Answer the questions on this page.
3. And now a game.

Tuesday, September 27th

This is what we are going to do today:

INTERVALS
We learned about intervals last week. Here there are some exercises:
- Go to the bottom of this page and click on "new problem". Try it at least 5 times.

Union and intersection of intervals

The union of two sets A and B, denoted AUB is the set that consists of all elements that are in A or in B (or in both A and B).

The intersection of two sets A and B, denoted A∩B is the set that consists of all elements that are in A and in B (the common elements to both sets).

Here it´s an example of the union and intersection of intervals. Study it and then solve the exercises:

- Go to this page, write your answers to questions 1 to 6 in your notebook and check them on the webpage.

- In the following exercises, click on the right answer: question 7, question 8, question 9, question 10.

- Work out the union and intersection of the following pairs of intervals:
a) A=(2,5), B=[3,7]
b) A=(-2,3], B=(3,4)
c) A=(-∞,0], B=[0,5)

RADICALS
Read the first lines from this Wikipedia page. Now you must know what a radical or surd is. Try some easy activities.