Pure- Equations and Inequalities (3)

Question 1

How can linear simultaneous equation be solved?

Answer 1

Elimination or substitution

Question 2

How many solutions do simultaneous equations with one quadratic and one linear have?

Answer 2

Two pairs of solutions

Question 3

What do the solutions to simultaneous equations represent?

Answer 3

The intersections of their graphs

Question 4

What is the solution of an inequality?

Answer 4

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

Question 5

What is the set notation for x>2 and x<=4?

Answer 5

{x:-2-2} ⋂ {x:x<=4}

Question 6

What does ⋂ mean?

Answer 6

Intersection ie. objects in set A and set B

Question 7

What is the set notation for x<=-1 or x>3?

Answer 7

{x:x<=-1} ⋃ {x:x>3}

Question 8

What does ⋃ mean?

Answer 8

Union ie.objects in set A or set B

Question 9

How do you solve a quadratic inequality?

Answer 9

• Rearrange so RHS=0
• Solve corresponding quadratic to find critical values
• Sketch graph of quadratic function
• Use sketch to find required set of values

Question 10

If y>f(x) or y

Answer 10

As a dotted line

Question 11

If y>=f(x) or y<=f(x) how is the curve drawn?

Answer 11

As a solid line

Question 12

If y=f(x) is below the curve y=g(x) which inequality is used?

Answer 12

f(x)

Question 13

If y=f(x) is above the curve y=g(x) which inequality is used?

Answer 13

f(x)>g(x)