1

x

y

x

y

MCR3U Review Unit A: Characteristics of Functions

1. For the following i. state the domain and range. ii. state whether or not the relation is a function.

a. {(1,2),(5,-1),(2,1),(1,0)}

Domain: {1, 5, 2, 0} Range: {2, -1, 1, 0} Function? Yes b.

.

Domain: Range: Function? No

2. Given 15)( 2 xxxf and 35)( xxg , determine ))0((gf

( ( ))

3. From the graph of )(xf shown, find

a. )3(f 1

b. x if 1)( xf

x = 9

4. For the following i. state the vertex and equation of the axis of symmetry ii. state the transformations iii. state the domain and range iv. graph

5)2(2

1)( 2 xxh

i) Vertex = (-2, 5) ; x = -2 ii) Left 2, up 5, reflection over x axis, compress-

ed by a factor of 1/2

iii) D = R =

2

5. Determine the inverse 2( ) 3 2f x x . State whether the inverse is also a function.

State the domain and range of the inverse function.

√

|

Algebraic Skills

1. Simplify 252252 xxx

2. Simplify 5024831082002

√ √

3. Factory fully.

a. 8179 2 xx ( )( )

b. 25132

x ( )( )

c. xxyxyx 32128 33

( )( )

4. Solve and graph the following inequality.

xx 92133

Graph on a number line

5. Simplify. State any restrictions.

.

6113

232

23

122

2

2

2

aa

aa

aa

aa

( )(( )

( )( )

( )( )

( )( )

( )( )

( )( )

3

Unit A: Quadratic Functions

1. Solve the following. 02045 2 xx

( √

( √ )

2. Solve the following inequality.

a. 01522 xx

( )( ) (Graph the parabola) So open circle at 5 on the number line, all numbers greater than 5, and open circle at -3, all numbers less than -3.

3. A rectangular field is to be enclosed by a fence. Two fences, parallel to one side of the

field, divide the field into 3 rectangular fields. If 2400 m of fence are available, find the dimensions of the field giving the maximum area.

Unit B: Exponential functions

1. Simplify. All exponents must be positive in the final answer.

a. 32

223

ab

ba b.

2

2

24

b

aab

2. Write in exponential form.

a. 34 x =

3. Write in radical form.

a. 2

3

x =

√

4

b.

= √

c. Fill in the table and sketch the function.

function 52 2 xy

y-intercept (0, 4.75)

horizontal asymptote

y=5

transformations Shift up 5, shift right 2, reflection over x

domain and range

d. Solve the following exponential equations.

a. xx 82 12 b. xx 21 279

x = 1

Unit C: Discrete Functions Other questions –

1. State whether the following are arithmetic, geometric or neither. a. 9, 15, 21, 27, …arithmetic b. 1, 8, 27, 64, …neither c. 64, -32, 16, -8, …geometric …

2. For the arithmetic sequence determine the general term, nt .

3, 1, -1, -3,… tn = -5

3. Determine 20S for the arithmetic series ...152127

20S = 600

4. Determine the sum of the arithmetic series.

a. 139...20136

n = 20

S = 1450

5

5. Use Pascal’s triangle to expand each power of a binomial.

a. 5)( ba

b. 62 yx ( ) ( ) ( ) ( ) ( )

Unit D– Trigonometric Functions Other questions –

1. Calculate each of the following. Use the special triangles and give exact answers only.

a. 45cos45sin b.

45sin

160sin

2

2

= √ =

2. The point Q(-9, 11) lies on the terminal arm. Calculate the exact values of the primary trigonometric ratios.

√

√

3. Angle is in the fourth quadrant and15

8tan . Find the exact values of the other

primary trigonometric ratios.

4. Angle is in the second quadrant and2

3cos . Determine sin , tan and show

that

tan

cos

sin .

√

√

5. In acute triangle DEF, d = 4.9 cm, e = 6.2 cm and E = 64° . Solve DEF. Round to the

nearest tenth of a centimeter. (3 marks)

6

7

6. Prove the identity 2cos (1 sin )(1 sin )x x x (2 marks)

RS=

RS = RS = LS

7. For the following

i. sketch for the interval 360360 x

ii. state the maximum and minimum values iii. state the amplitude and period iv. state the domain and range v. list the transformations

3452sin xy

ii) max = -2, min = -4

iii) A = 1 , P = iv) D =

R= v) Reflection over the x axis, left 45 down 3,

Period of 180

vi) Solve the following equations for the interval 3600 x (Round answers to 1

decimal place when necessary)

a. 2

3sin x

b. 011cos10sin8 2 xx