PRINCIPLES OF MATHEMATICS 11

Section Assignment 4.1

Answer Key

Module 4

Principles of Mathematics 11 Section Assignment 4.1 45

General Instructions for Assignments

These instructions apply to all the Assignments, but will not be reprinted eachtime. Remember them for future sections.

(1) Treat this assignment as a test, so do not refer to your Module or notes orother materials. A graphing calculator is required.

(2) Where questions require computations or have several steps, show your work.

(3) Always read the question carefully to ensure you answer what is asked. Oftenunnecessary work is done because a question has not been read correctly.

(4) You may use a calculator (of course!)

46 Section Assignment 4.1 Principles of Mathematics 11

Module 4

7. On a number line, indicate the region corresponding to

a) x ≤ –1 or x > 3

b) x < 3 and not (x > 2)

8. Use appropriate quantifiers to write statements equivalentto the following:

a) Rectangles are parallelograms

All rectangles are parallelograms.

b) Rhombi can be squares

Some rhombi are squares

9. Write negations of the following:

a) Not all peppers are red.

All peppers are red.

b) All triangles are scalene.

No triangles are scalene.

−1 0 3

50 Section Assignment 4.1, Answer Key Principles of Mathematics 11

Module 4

(2)

(2 x 1 = 2)

(2 x 1 = 2)

0 2 3

13. and are tangent to a circle with centre O. Prove

that bisects ∠ A.

Given AB and AC are tangentsO is the centre

Prove AO bisects A

Join OB and OC OB = OC (radii) AB = A C

(tangents from an external point) and AO is a common side.So ABO ACO by SSS. Therefore 1 =

∠

≅ ∠ ∠2

since they are corresponding angles. AO is an angle bisectorby definition.

O

C

A

B

1

2

AOACAB

Principles of Mathematics 11 Section Assignment 4.1, Answer Key 53

Module 4

(3)

PRINCIPLES OF MATHEMATICS 11

Section Assignment 4.2

Answer Key

Module 4

Principles of Mathematics 11 Section Assignment 4.2 111

112 Section Assignment 4.2 Principles of Mathematics 11

Module 4

PRINCIPLES OF MATHEMATICS 11

Section Assignment 4.3 Answer Key

Principles of Mathematics 11 Section Assignment 4.3 159

Version 04 Module 1

160 Section Assignment 4.3 Principles of Mathematics 11

Module 4

b)

Identify, if they exist:

i) x-intercept(s) (0, 0)

ii) y-intercept(s) (0, 0)

iii) equationof horizontal asymptote y = 0

iv) equation of vertical asymptote(s) x = –2; x = 2

v) sketch

Y1 =

Y2 =

Y3 =

Y4 =x [ –7 , 7 ] y [ –5 , 5 ]

8. a) What are the restrictions on the graph of the followingfunction?

x ≠ –1, x ≠ 1

b) What occurs at each of these restricted values?

At x = –1 there is an asymptote

At x = 1 There is a hole in the graph

2

–1( )–1

xf xx

=

2( )– 4xf x

x=

164 Section Assignment 4.3, Answer Key Principles of Mathematics 11

Module 4

(7)

(2)

(Total 34)

( )X X ^ 2 4÷ −