Math 11P Final Exam Prep

8/6/2019 Math 11P Final Exam Prep

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Math 11PFinal Exam Prep

SOLVING SYSTEMS OF EQUATIONS (CHAPTER 5)

1. Solve each system of equations by any means demonstrated in class.

a)152

934

yx

yxb)

34

1

3

1

52

13

yx

yxc)

xy

xy

23

5

d)13

4

xy

xye)

4

822

xy

xxyf)

322

122

142

zyx

zyx

yx

2. Pecans cost $22 per kg and walnuts cost $16 per kg. The two types of nuts are mixed together tocreate a 50 kg bag costing $18 per kg. How many kilograms of each type are there?

3. Sasha invests $15 000 at CIBC. He puts part in a GIC at 4% and the rest in a term deposit at 2.5%.At the end of the year, there is $472.50 in interest accumulated. How much did he put into eachinvestment?

4. 25 bolts and 25 washers have a mass of 475 g. 17 bolts and 34 washers have a mass of 442 g.Determine the mass of one bolt and one washer.

SOLVING QUADRATIC FUNCTIONS (CHAPTER 2)

5. Graph the following parabolas.

a) 12

1 2

xy b) 2)1(22

xy c)

2

)6(2

xy d) 2)2( xy e) 2)5( 2 xy f) 3)2( 2 xy

6. Graph the following functions andtheir inverses.a) 2 xy b) 3)2()( 2 xxf

7. Write the equations for the following reciprocals. Then, sketch the original graph andthe reciprocalgraph on the same grid.a) 5)( xxf b) 12)( 2 xxxf

8. Write a function with the following roots.

a) -2, -2 b)54,

32

9. Complete the square.a) 1522 xxy b) 1042 2 xxy


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POLYNOMIAL AND RATIONAL FUNCTIONS (CHAPTER 3, PART 1)

10. For the following parabolas,i) sketch the graphii) determine the domain and rangeiii) determine whether the function has a maximum or minimumiv) determine the value of the maximum or minimumv) calculate the zeros

a) 2)5(3 2 xy b) 14176 2 xxy c) 782 2 xxy

11. Sketch the graph of the following functions.a) )2()2()( 2 xxxf b) A quartic function with roots -4, 0, 2, 4 that has no minimum and is

congruent to 2)3)(4()( xxxxf

12. Determine the equation of the quadratic function from the following information.a) zeros at -5 and 4 and passes through (6, 11) b) roots at 4 and -4 and passes through (6, 3)

13. Determine the composition of function using the following.2)( xxf 23)( 2 xxxg 4)( xxh

xxp

1)(

1

2)(

x

xm 5)( xn

a) ))(( xfg b) ))(( xnh c) ))(( xng d) )())(( xmxfp

POLYNOMIAL AND RATIONAL FUNCTIONS (CHAPTER 3, PART 2)

14. Graph each of the following functions. Determine any critical points and asymptotes for each. Use atable of signs or table of values to determine the shape, size, and direction of each function.

a) 342)( xxf b) 312)( xxf

c) 23)( xxf d) 42)( xxf

e)1

2)(

x

xxf f)

3

6)(

2

x

xxxf

g)2

3)(

x

xf h)82

1)(

2

xxxf

SOLVING POLYNOMIAL EQUALITIES AND INEQUALITIES (CHAPTER 4)

15. Describe the purpose for the following theorems.a) Remainder Theorem b) Factor Theorem

16. Calculate the remains for the following systems. Indicate if the divisor is a factor of the polynomial.

a) )1(f when 252)( 24 xxxf b) )2(g when xxxxg 232)(

c) )4(h when 3)( 23 xxxh d) )3()132( 24 www

e) )1()1252( 23 qqqq f) )1()324( 23 gggg

g) )52()3732( 23 xxxx h) )32()3232( 23 xxxx


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17. When the polynomial 73)( 23 nxmxxxg is divided by 2x , the remainder is 3 ; however,

when the polynomial is divided by 1x , the remainder is 18 . Determine the values of m and n.

18. Solve the following using the quadratic formula.

a) 11123)( 2 xxxf b) 1710 2 xx

19. Determine the nature of the roots for the following.

a) 16 2 xxy b) 168 2 xx c) 0125 2 xx

20. Determine the values of k so that the function has:

a) two equal real roots; 0122 xkx b) no real roots; 0202 2 kxx

c) one real root; 082 kxx

21. Factor each of the following by any of the methods demonstrated in class.

a) 2543)( 23 xxxxf b) 3434)( 23 xxxxf

c) 0234 23 xxx d) 08292 234 xxxx

22. Solve for x for the following equalities and inequalities.a) 0)2)(6)(4( xxx b) 0)2)(6)(4( xxx

c) 01072 xx d) 01072 xx

e) 0245 23 xxx f) xxx 245 23 0

COORDINATE GEOMETRY (CHAPTER 9)

23. Determine the shortest distance between )5,4( and 5 xy

24. Write the equations of the circles using the following information.a) centre )1,8( and radius 6 b) centre )5,5( ; passes through )1,1(

25. Determine the vertical, horizontal, and shortest distance between the following lines:01223 xy and 0623 xy .

26. Determine the equation of a tangent at point A )6,8( to circle 10022 yx .

27. Determine the points of interception between 2 xy and 9)2()1( 22 yx .

28. Prove algebraically that quadrilateral ABCD is a parallelogram. A )1,3( , B )8,5( , C )9,10( , D )2,8( .

29. Determine the equation of the tangent to the circle with equation 25)3()2( 22 yx and the P

)6,6( .


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CIRCLE GEOMETRY (CHAPTERS 7/8)

30. Find the measure of each indicated angle or segment. Write a reason for each answer.

1 = _________ _____________________________________

2 = _________ _____________________________________

3 = _________ _____________________________________

HEF = _________ _____________________________________

HG = _________ _____________________________________

EF = _________ _____________________________________

HF = _________ _____________________________________

4 = _________ _____________________________________

5 = _________ _____________________________________

6 = _________ _____________________________________

7 = _________ _____________________________________

8 = _________ _____________________________________

9 = _________ _____________________________________

SU = _________ _____________________________________


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1 = _________ _________________________________

2 = _________ _________________________________

3 = _________ _________________________________

4 = _________ _________________________________

5 = _________ _________________________________

6 = _________ _________________________________

7 = _________ _________________________________

8 = _________ _________________________________

ABE = _________ _________________________________

1 = ______________________________________________

2 = ______________________________________________

GH = ______________________________________________

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Math 11P Final Exam Prep