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 solutions: (x= a y= b) and (x = c, y= d)

Question 3

What do the solutions of pairs of simultaneous equations represent?

Answer 3

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

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

b² - 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

(b² - 4ac) = 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

(b² - 4ac) < 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.
• Use 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.