Chapter 3 - Equations and Inequalities

Question 1

How can simultaneous equations be solved?

Answer 1

Using elimination or substitution.

Question 2

How many pairs of solutions are there with a simultaneous equation of one linear and one quadratic equation?

Answer 2

Two pairs of equations:

x= a x= c

y= b y= d

Question 3

What do the solutions of pairs of simultaneous equations represent?

Answer 3

The points of intersections between the two equations on their graphs.

Question 4

What is the formula for 2 real solutions of a function where a pair of simultaneous equations produced a quadratic equation?

Answer 4

b^2 - 4(ac) > 0

Question 5

What is the formula for 1 real solution of a function where a pair of simultaneous equations produced a quadratic equation?

Answer 5

b^2 - 4(ac) = 0

Question 6

What is the formula for no real solutions of a function where a pair of simultaneous equations produced a quadratic equation?

Answer 6

b^2 - 4(ac) < 0

Question 7

What is the solution of an inequality?

Answer 7

The set of all real numbers of x that make the inequality true.

Question 8

How do you solve a quadratic inequality?

Answer 8

Rearrange so that the right hand side of the inequality is 0.

Solve the quadratic equation to find the critical values.

Sketch the graph of the quadratic function.

Has the sketch to find the required set of values.

Question 9

If the curve y= f(x) is above the curve y= g(x) what is the inequality that satisfies this?

Answer 9

f(x) > g(x).

Question 10

If the curve y= f(x) is below the curve y= g(x) what is the inequality that satisfies this?

Answer 10

f(x) < g(x).

Question 11

What are the inequalities and type of line used when y= f(x) is not included in the region?

Answer 11

y > f(x) or y < f(x)

Represented by a dotted line.

Question 12

What are the inequalities and type of line used when y= f(x) is included in the region?

Answer 12

y>= f(x) or y <= f(x)

Represented by a solid line.