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MCV 4U0 WELCOME BACK ASSIGNMENT!  

PRE-CALCULUS WARM-UPS - TIME TO PUMP UP YOUR BRAIN - ARE YOU READY? 

The following questions are intended to refresh your memory (I hope!) and prepare you for the world ofCalculus. These concepts will appear throughout the course and we must be proficient in these skills.

EQUATIONS OF LINES   (Concepts covered intercepts point"slope equation of a line)

(a) # line has slope $ and passes through the point  ) ,(    62 .

%ind its equation and y"intercept. &raw the graph of the line.

(b) # line has slope and passes through the point  ) ,(    03 . %ind its equation y"intercept and '"intercept.

(c) hat is the equation of the line which cuts the '"a'is at ' * and the y"a'is at y 1 +

(d) %ind the equation of the line which passes through the points  ) ,(    21  and  ) ,(    53 .

FACTORING   (Concepts covered common factoring difference of squares trinomial factoringgrouping sum and difference of cubes factor theorem e'tended factor theorem)

%actor the following polynomials as completely as possible.

(a) 22 2   r  pr  p   (b) 342  vv (c) 2157  2

  y y

(d) 2225   y x   (e) 6449   2 m (f) 9

2  )n x ( 

(g)  pyky px kx    (h) 2 )d  x ( d  x    (i) 624   2   x  x 

(,) 280248   mm  (k) 1201060  2

  y y (l)

22 225236   ) yu(  ) y x (  

(m) 12345   y y y y y (n) 22 21629   ) z  y x (  ) z  y x (   

(o) 222 212   z  yz  y p p 

(p) 33 278   y x   (q) 333 323   r  p )w x (   

(r) 6116   23   x  x  x  (s) 1096   23   x  x  x  (t) 122   23   x  x  x 

  (common factor these last three questions)

(u) 624 15273   x  x  x    (v) 352 14168    x  x  x    (w)32

11213 

 ) x (  ) x ( 

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Introduction to Calculus #ssignment page * of -

EQUATION SOLVING   (Concepts covered olving equations involving factoring and the quadraticformula)

 

olve each of the following equations forℜ x  (accurate to * decimal places where appropriate).

(a)   03522=

 x  x  (b)   013   2=

 x  x  (c)41

32 =

 x  x  x 

(d)   0252   23= x  x  x  (e)   x  x  x    423   (f)   278   3   x 

SOLVING POLYNOMIAL INEQUALITIES 

olve each inequality and sketch the solution on a number line.

(a)   042  

 x  x  x 

GRAPHING POLYNOMIAL FUNCTIONS 

A. /atch each graph with the appropriate polynomial function.

(a) (b)

(c) (d)

i. f(') (' 0 $)(' 1 *)*(' 0 2) ii. f(') (' 1 2)(' 1 -)(' 0 -)

iii. f(') "(' 1 2)*(' 0 $) iv. f(') (' 1 *)*(' 0 $)*

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Introduction to Calculus #ssignment page $ of -

B. ketch the graph of a polynomial function that satisfies each set of conditions.

(a) degree - positive lead coefficient $ 3eros $ turning points(b) degree - negative lead coefficient * 3eros 2 turning point(c) degree - positive lead coefficient 2 3ero $ turning points(d) degree $ negative lead coefficient 2 3ero no turning points(e) degree $ positive lead coefficient * 3eros * turning points

C. &etermine the equation of each polynomial function.

(a) (b)

(c) (d)

(e) (f)

The curve passes through the point (-3, -1.6). The curve passes through (-0.5, 1.5).

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Introduction to Calculus #ssignment page - of -

GRAPHING RATIONAL FUNCTIONS 

ketch the graphs of the following functions labelling the 3eros vertical hori3ontal and oblique (slant)asymptotes.

(a)1

2)( 2

−

=

 x

 x x f   (b) 52

182)(

2

+

−

= x

 x x g  (c)

 x

 x y

43

4

−

+

=

FUNCTION NOTATION   (Concepts covered function algebra)

4iven 432   x  x  ) x (   f     and 13  x  ) x (  g    find

(a)   )(   f     2 (b)   )h(   f   (c)   ) x (  g   2 (d)   ) x (   f  2

(e)   )h x (  f    (f)   ) x (  g   5 (g)   )h(  g   2 (h)h

 ) x (  f  )h x (  f   

RATIONALIZING RADICALS 

To rationali3e a radical we multiply by the conjugate. The con,ugate of is .%or e'ample the radical has the con,ugate . To rationali3e we multiply by.

 

2 x 

4 x 

2 x 

2 x 2 x 2 x 

 

=

 

. 5otice that2 x 

2 x 

 

and that we are really only

multiplying by 2 and thus we maintain equality. This idea of multiplying something by 2or adding 6 to it in a unique way is quite often done to simplify a mathematical e'pression. ewill use this technique of multiplying by the con,ugate in our discussion of limits. #t this point allwe want you to be able to do is work with the con,ugate.

7ationali3e by multiplying by the con,ugate (maintaining equality) and simplify where appropriate.

(a)   (b) 

(c) 

(d)