IAL Edexcel P4 Parametric Equations

IAL Edexcel P4 Parametric Equations

Learning Objective:

Convert Parametric Equations into Cartesian form

Multiple Choice

What is the value of -2v + 2h - 8s if v = 9, h = 7, and s = -6?

• 44
• -44
• 54
• -54

Multiple Choice

What is the value of -6s - 5h if s = 9 and h = 5?

• -79
• 79
• 78
• -78

Multiple Choice

If a = 4 and b = 6, what is the value of 3a + 5b?

• 40
• 42
• 44
• 46

Multiple Choice

What is the equation of the circle, with center (4,2) and radius 5 units?

• (x + 4)² + (y + 2)² = 25
• (x + 4)² + (y + 2)² = 5
• (x - 4)² + (y - 2)² = 5
• (x - 4)² + (y - 2)² = 25

Multiple Choice

In the equation (x-3)²+(y+4)²=121, the radius of the circle is

• 242
• 11
• 121
• 22

Multiple Choice

What are the coordinates of the center and the radius of the circle with an equation:
(x + 7)² + (y - 6)² = 64 ?

• Centre (7,-6)
  Radius = 8 units
• Centre (-7,6)
  Radius = 64 units
• Centre (-7,6)
  Radius = 8 units
• Centre (7,-6)
  Radius = 64 units

Multiple Choice

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

• 4
• 2
• 3
• 16

Parametric Equations

Parametric equations are equations that are expressed in terms of a third letter, normally t.

t is the parameter

 

A normal equation tends to connect x and y, for example.

This is called a Cartesian equation.

Parametric Equations

Parametric Equations

Parametric Equations

There are 3 types of question:   

 -Eliminating the parameter to find the Cartesian Equation. 

-Sketching the graph of parametric equations

-Differentiating parametric equations to find gradients, tangents and normals. 
(Seen in chapter 5)

Multiple Choice

The variable "t" is called a

• parameter

• parallel

• paralegal

• paradise

Multiple Choice

Find the ordered pair based on the parametric equations.

t = -2

x = t² - 2

y = -t + 2

• (2, 4)

• (4, 2)

• (-6, 0)

• (0,-6)

Multiple Choice

Find the point based on the parametric equations. t = 3

x = 1 - 2t

y =4t + 1

• (-5, 13)

• (13, -5)

• (5, 13)

• (13, 5)

Trigonometric Identities

You can use Trig identities to convert trigonometric parametric equations into Cartesian form

Multiple Choice

sin²x + cos²x =

• 1

• 1/sinx

• sec²x

• csc²x

Multiple Choice

cos²x =

• 1 - sec²x

• 1 - sin²x

• sin²x

• 1

Multiple Choice

1/cosx =

• secx

• cosecx

• tanx

• sinx

Multiple Choice

1 - cos²x =

• sec²x

• cosec²x

• sin²x

• sec²x - 1

Multiple Choice

tan²x + 1 =

• csc²x

• sec²x

• sec²x - 1

• cosecx

Multiple Choice

1 - sin²x =

• cos²x

• cos²x+1

• cosec²x

• tan²x

Trigonometric Identities