MHF4U – DIAGNOSTIC
NAME : _____________________
MCR3U REVIEW FOR MHF4U
ADVANCED FUNCTIONS PRE-REQ SKILLS
Only provide the answer in the space provided. Use Scrap paper to work out your solutions. Each
blank is worth one mark. Answer must be completely correct as indicated in each question.
½ marks may be assigned. CALCULATORS ARE NOT PERMITTED-UNLESS OTHEWISE STATED
TOPIC: Rational Expressions



Factoring (common, difference of squares, trinomial)
Simplifying Rational Expressions
 Multiplication/ Division
 Addition/ Subtraction
Restrictions
1. Expand and Simplify.
a)  3 x 2  4 x  1   x 2  2 x  2 
________________________________
b)  3z  1  2z 2  3z  4 
________________________________
c) (x + 2)2 (x – 1) – (x2 – 3x)(x + 2)
________________________________
2. Simplify ( in lowest terms ) and state any restrictions where indicated.
18 p 2q 2
a)
= _____________
12 p 1q 3
4 x 4 y 6 x 3 y 2
b)
= ________________

3x 2y 4
10 x 4
c)
2t  4
= ________________
t  6t  8
Restrictions : ________________
d)
t 2  6t  9 3t  9
= _________________

t 2  6t  9 2t  6
Restrictions : ________________
e)
a2  3a  10 a2  2a  15
= _______________

a2  a  12 a2  7a  12
Restrictions : ________________
f)
4
2
 2
= ________________
2m  m  1 m  2m  3
2
2
/ 12 MARKS
1
TOPIC: Quadratics

Solving quadratic equations


Simplifying Radicals
Types of solutions (Nature of the Roots)
 By factoring where possible
Using Quadratic Formula when factoring is not possible
1. Simplify as a radical in lowest terms.
a)
54 = __________
b) 2 12  4 20  3 27  5 45
c)
3
 6  21 = ____________
d) 2 3  3 2
e)
2  27 = ___________
f)

2 5
= _________
3 2
2. Solve the following inequality
a) x 2  3 x  3  2 x  x 2 ________________
g)
______________
 5  4 3  =___________________
2 3
= ___________________
2 3 3 2
b) 2  m  3   5  3  4  m   2 ___________________
/ 9 MARKS
TOPIC: Trigonometry


Evaluate Expressions
Solving Trigonometric Equations

Prove Identities
 Special Triangles
Exact Values
 Cast Rule
 Factoring
 Using Radians
1. Evaluate the following ( give 4 decimals where needed ): (CALCULATOR PERMITTED)
a) csc170.1o = ___________ b) cot 315o = _____________
2. If sec  135 , find the value of sin, cos  and tan as a fraction ( assume  is acute ).
sin = __________
cos = ___________
tan = ____________
3. Determine the exact value.( hint : leave as fraction where needed )
a) sin 1800 = _______ b) cos 210o = _______ c) sin45ocos135o + tan30o tan420o = ___________
4. Solve each of the following for 0o≤ x ≤ 180o.
a) sin x  2cos x  1  0 _________________ b) 2sin2 x tan x  tan x  0 _________________
/ 10 MARKS
2
NAME : __________________________
TOPIC: Transformations of Functions







Domain / Range
Amplitude, Period, Phase Shift, Vertical Translation, Reflection (Vertical and Horizontal)
Graphing Trigonometric Functions ( y  a sin b  x  d   c or y  a cos b  x  d   c )
1

Mapping Notation:  x, y    x  d, ay  c 
b

Function Notation
Inverse Function y -1 or f –1(x)
Explanation of a transformation / Write an equation under given transformation
1. State the domain, range, period, amplitude, vertical translation and phase shift ( horizontal
translation ) of each of the following:
a) y 
1
cos 2 x
2
b) y  3 sin x  1
Domain ________ Amplitude _______ Vertical Translation __________
Range _________ Period _________ Horizontal Translation __________
c) y = sin(x – 45o) – 3
Vertical Translation ___________ Horizontal Translation _____________
d) y = ½ cos (6x – 180o) – 5 Amplitude _______ Period ________
Horizontal Translation _________
2. If f  x   2x 2  5 x  1, find ( in simplified form ):
a) f  0  = ________
b) – f  3  = ________
c) f  x  3  = _________________
3. State the domain and range of each of the following:
a) y   3  4 x  6
b) y  2  x  3   5
Domain _______________
Domain _______________
3
4
7x  5
Domain _______________
Range ________________
Range ________________
Range ________________
2
c) y 
4. Given f  x   3 x  8 , determine:
a) x when f  x   14 ________________
b) f 1  6  _____________________
5. If f  x   2x 2  x and g  x   3  x , determine:
a) f  g  x   = _________________
b) g  f  4   = ___________________
/ 24 MARKS
3
TOPIC: Exponential Functions



Simplifying using exponent rules (in power form, radical form, and rational form)
Solving exponential equations
Exponential Growth and Decay
1. Evaluate. (No decimals – leave in simplified fraction form)
a)  4 
3
2

30  40
 125  3
= ______ b)
= __________ c) 27 3 = _______ d) 
 = __________
1
2
 8 
1
2. Simplify: (leave your answer in power form)
(ab)2 x y
a)
= __________
a xb y
b) a
x y
 a 2 x y  a 2 x7 = _____________
3. Simplify, and then evaluate for a = -1, b = 2:
4. Evaluate (without calculators):
a) 27
2
3
 16
5
0
4
30a 4b 2 (15a 2b5 )

= _____________
(5ab4 )2
45a3b6



3
7
3
7
1
   = ________________ b) 2 2  2 2 2 2  2 2 = ________________
7
5. Solve.
1
______________
36
b) 5 x 3  5 x 1  600 _______________
c) 32 x 9 x  243 ______________
d)  42  22 x 3   16 x 2 _______________
a) 62 x 1 
2
2x
e) 3
 6(3x )  27  0 ____________
/14 MARKS
4
MHF4U DIAGNOSTIC SUMMARY
MHF4U DIAGNOSTICS SUMMARY
Name :
Name :
Rational Expressions
/ 12
NSGE
Rational Expressions
/ 12
NSGE
Quadratics
/ 9
NSGE
Quadratics
/ 9
NSGE
Trigonometry
/ 10
NSGE
Trigonometry
/ 10
NSGE
Transformation of Functions
/ 24
NSGE
Transformation of Functions
/ 24
NSGE
Exponential Functions
/ 14
NSGE
Exponential Functions
/ 14
NSGE
MHF4U DIAGNOSTIC SUMMARY
MHF4U DIAGNOSTICS SUMMARY
Name :
Name :
Rational Expressions
/ 12
NSGE
Rational Expressions
/ 12
NSGE
Quadratics
/ 9
NSGE
Quadratics
/ 9
NSGE
Trigonometry
/ 10
NSGE
Trigonometry
/ 10
NSGE
Transformation of Functions
/ 24
NSGE
Transformation of Functions
/ 24
NSGE
Exponential Functions
/ 14
NSGE
Exponential Functions
/ 14
NSGE
MHF4U DIAGNOSTIC SUMMARY
MHF4U DIAGNOSTICS SUMMARY
Name :
Name :
Rational Expressions
/ 12
NSGE
Rational Expressions
/ 12
NSGE
Quadratics
/ 9
NSGE
Quadratics
/ 9
NSGE
Trigonometry
/ 10
NSGE
Trigonometry
/ 10
NSGE
Transformation of Functions
/ 24
NSGE
Transformation of Functions
/ 24
NSGE
Exponential Functions
/ 14
NSGE
Exponential Functions
/ 14
NSGE
5