Chapter 3: Equations and Inequalities

Question 1

What is a line with a given equation?

Answer 1

The set of all points that satisfy such equation.

Question 2

If given a quadratic curve with a vertex and its roots on a diagram, how can we know the equation in a completed the square form.

Answer 2

-Find vertex (e.g. 15,10)
-Thus formulate the completed the square formula backwards
-Find the roots of the equation.
-Then, before solving this, ensure that a constant is placed before the brackets, if the vertex co-ordinate does not equal the completed the square eqn. (e.g. vertex 15,10 with roots 20)
-Then utilise one of the roots and find the scale factor, consult book if unsure how this worked.

Question 3

In set builder notation, what does the Q mean?

Answer 3

Rational numbers

Question 4

What does the Z mean?

Answer 4

Integers

Question 5

What does the N mean?

Answer 5

Natural numbers (positive numbers)

Question 6

What does the I mean?

Answer 6

Irrational numbers

Question 7

What does the r mean?

Answer 7

Real numbers, both rational and irrational numbers.

Question 8

What is a rational number?

Answer 8

A number that can be expressed as a simple fraction.

Question 9

For 6/x is greater than 2 Where x=0 how do we solve?

Answer 9

-Multiplying by a negative number flips the inequality, however multiplying by a positive number (ie. x) does not have this effect, as we are unaware what x is, we do not know if the inequality would flip or not.
-Thus we need to multiply by x^2, as then it is guaranteed that x is positive.

ETC.