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