# Leaving Cert Maths Questions: Algebra 3 Quiz

As the Leaving Cert exams edge closer, it is an important time to test your math’s skills. What better way to do this than with a self-assesment quiz that I have created – all you have to do it answer the leaving cert maths questions and get the correct answer and solution as soon as you click “submit”.

## What are H1Maths Quizzes?

Every H1Maths course comes with an end-of-topic exam. So for the Higher Level  full bundle that’s 22 quick quizzes. It’s a great way to test your knowledge as well as helping you understand the areas you need to focus on to improve.

The quizzes are based on real leaving cert maths questions as well as a selection of the best questions from pre papers, maths books and revision handouts/ books, so you’re really getting a lot of variety and hopefully new questions than what you have seen before.

## What is Included in Algebra 3?

The inequality symbols $$>, \ge,<, \le$$ are needed when solving problems in which a range of possible values satisfy the given conditions. Inequalities can be solved using algebra, by graphing the inequalities or sometimes using a number line). Quadratic inequalities appear often in exam papers and are generally found by substituting = for the inequality sign, and finding the roots of the equation – then sketching a graph of these roots and then using the graph to find the set of values of $$x$$ that satisfy the inequality.

The modulus is represented like this, $$|x|$$, and the modulus of a number is a measure of its size or magnitude. No matter if the $$x$$ is – or + we are only interested in the size (so we take the positive value).

An example of a modulus inequality is shown below:

$$|x+3|<|3 x-7|$$

Proofs are a tricky topic on the exam. In algebra 3 we look at direct proofs, proofs by contradiction, proofs of abstract inequalities proofs by induction. That’s just paper 1, we of course have the 3 theorems in paper 2!

In mathematics a statement has to be proven to be always true and then becomes a theorem. Direct proofs use axioms, definitions and past theorems to construct a statement to prove something is always true. Proof by contradiction is when we set up a statement we know is false but claim it to be true, and by logically contradicting the statement we prove the statement must be false. Proofs by induction follows a specific procedure:

(i) The statement is proven true for some fixed value, usually $$n=1$$ or $$n=2$$.
(ii) The statement is then assumed true for $$n=k$$.
(iii) Based on this assumption, we must show that the statement is true for $$n=k+1$$.
(iv) In conclusion, a “rolling proof” is formed:
a. Since it was true for $$n=1$$,
b. it is now true for $$n=1+1=2$$.
c. Since it is true for $$n=2$$, it is true for $$n=2+1=3$$, etc.
d. It is therefore true for all values of $$n$$.

Indices: When a number is multiplied by itself a certain number of times, we use the index form to represent it: $$3^4 = 3\times3\times3\times3$$. 3 is known as the base and 4 is the index. We use the rules of indices to solve a variety of index questions in the exams (pg 21 of formulae and tables)

Exponentials: Exponentials are equations or expressions where the index is a variable $$x$$. When working with exponentials the most important thing  is to set all values to the same base number.

Logarithms: The logarithm of a number is the power to which the base number must be raised to get that number ($$a^x=y$$ is equivalent to $$\log_a{y}=x$$. Just like with the indices there are laws of logarithms that are on page 21 of the formulae and tables book.

If you require any assistance after the quiz or have any questions please reach out via the live-chat or email: [email protected]

You can always book a one-to-one grind here

Test your knowledge of indices, exponentials and logarithms with this short 5 question quiz. Best practice is to:

• Do the working-out on a sheet of paper
• Use the hint button if you require a little help to get you started
• Choose the right answer or fill in the blanks to answer the question
• Instantly be told if you are correct/ incorrect
• A pop-up will appear at the end of each question with a model solution to the question
• Do not get disheartened if you get a few incorrect answers, remember you can always review the on-demand videos or ask for help from the instructor!

Good luck! 😊