Unit 0 – Miscellaneous Topics Big idea Feedback ... · expressions that have variables in the...

1 PreCalculus AP U0 – Miscellaneous Topics from gr9+10+MCR+AP Name: __________________________

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Unit 0 – Miscellaneous Topics

Big idea

In this unit you will review grade 9 – 10 topics as well as learn how to work with algebra of more complex nature than you’ve seen so far. You’ll learn about new types of factoring techniques, about how to simplify and solve roots, you will learn about a new exponent law that involves fractions in the exponent and finally how to simplify expressions that have variables in the numerators and the denominators.

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Date Pages Topics Questions to ask the teacher:

2-5

Linear Relations (gr9) Journal #1, 2

6-7

Radicals (MCR) Solve Root (AP) Journal #3

2days 8-11

Exponent Laws (one new law MCR) Journal #4

2days 12-17

Factoring (some new methods AP)

Journal #5

18-19

Quadratic Basics Journal #6

2days 20-24

Quadratics Word Problems Journal #7-8

25-26

Non Linear Systems (MCR) Journal #9

27-29

Trigonometry Journal #10

30-31 Simplify/Multiply/Divide Rational Expressions (MCR) Journal #11-12

32-33 Add/Subtract Rational Expressions (MCR) Journal #13

Common Errors Journal #14


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ASSIGNMENT Linear Relations (gr9)

Solve the following equations, leave answers as exact fractions

1.

2.

3.

4.

5.

6.


3

Solve by elimination

7.

8.


4

Write a system of equations to represent the situation. Do let statements to identify variables, then solve the system by

using substitution method and answer the question.

9.

10.


5

Sketch the graph of each line

11.

12.

13.

14.


6

ASSIGNMENT Radicals (MCR)

1.

2.

3.

4.

5.

6.

7.

8.


7

9.

10.

11.

12.

13.

14.


8

ASSIGNMENT Exponent Laws

Exponent Laws (gr9-10) Simplify, record answers with positive exponents

1.

2.

3.

4.

5.

6.

7.

8.


9

Rational Exponent Law (MCR) Rewrite roots with rational exponents or vise versa, then evaluate without using calculator

9.

10.

11.

12.

Simplify, record answers with positive exponents. At the end, ask yourself if absolute value should be inserted.

13.

14.

15.

16.

hint: record everything as a base of 3 before simplifying


10

Simplify, record answers with positive exponents. At the end, ask yourself if absolute value should be inserted.

17.

18.

19.

20.

21.

22.

23.

24.


11

Solve Root Equations (AP) 25.

26.

27.

28.


12

ASSIGNMENT Factoring

Common Factoring and Factoring by Grouping (gr10) 1.

2.

3.

4.

5.

6.

Difference of Squares Factoring (gr10) careful! some are impossible 7.

8.

9.

10.


13

Trinomial - Criss Cross Factoring (gr10) 11.

12.

13.

14.

15. don’t forget to check for common factor first

16.

17.

18. check if you can do diff of sq at the end

19.

20.


14

Mix of Factoring (gr10) 21.

22.

23.

24.

25.

26.

27.

28.

29.

30.


15

31.

since this doesn’t factor over the integers use quadratic formula but then record

in factored form since instructions are to factor not solve

32.

33.

34.

35.

36.

37.

38.

39.

40.


16

New types of Factoring (AP) 41.

42.

43. 2 616 8 1 9x x x− + − go back over #26 and #30 to verify those

44.

45. Difference of Cubes

46. Sum of Cubes

47.

48.


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Factor without expanding first – think what is in common that you should divide

hint: smallest exponent on the common thing is the one to divide by, also remember if you divide same bases, exponents subtract

49.

50.

51.

52.

53.

54.


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ASSIGNMENT Quadratic Basics (gr10) Complete the square, leave answers as exact fractions.

1. 22

4 183

y x x= − −

2. 23 4 2y x x= − + −

Solve by factoring

3.

4.

5.

6.


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7. Find the equation of the following parabolas. Use the most convenient form. a.

b.

c. The parabola is vertically compressed by 2, opens down, goes through the point (-6, 10) and has a y-intercept of 4.

d. The parabola has the axis of symmetry at 3 and x-intercept at 7 and y-intercept at -2.

8. Sketch the following parabolas FACTORED form

e. (4 2 )( 8)y x x= − +

VERTEX form

f. 21.5( 2) 1y x= + +

STANDARD form

g. 210 5y x x= + −


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ASSIGNMENT Quadratic Word Problems (gr10)

1. Revenue problem The circus sells 1000 tickets for $6 each. The circus owners want to increase their revenues, so they increase prices. They have noticed that ticket sales decrease by 45 tickets every time the price increases by $0.50. a) What is the revenue equation? b) What price will maximize the revenue? c) What is the quantity at maximum? d) What is the maximum revenue?

2. Falling object problem A water balloon is catapulted into the air so that its height, in meters after t seconds is given by a quadratic function. The balloon’s initial speed is 27 meters/second and it was released from the height of 3 meters. When does the balloon reach the height of 35m?


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3. Profit problem If the total costs are $600 flat and $90 per item, and

the revenue is given by 2( ) 150R x x x= − , where x

is the number of items sold. a) What is the profit equation? b) Determine the items sold that would produce

the maximum profit. c) Find the number of items to sell to have the

profit of $100. d) What is the initial profit?

4. Fence (or rope) off an area problem For a park swimming area, 4500 m of line is used to mark off the permissible area. One side not roped off is next to the beach. Find the dimensions of the swimming area that will make it a maximum


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5. The hypotenuse of a right triangle is 6 cm more than the shorter leg. The longer leg is three more than the shorter leg. Find the lengths of all three sides.

6. Find three consecutive integers such that four times the sum of all three is 2 times the product of the larger two


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7. This is a diagram of a practice field. The track and field coach wants two laps around the field to be 1000m. But the Phys. Ed. department wants the rectangular field to be as large as possible. What dimensions would satisfy both conditions?


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8. Dan and Sue set off at the same time on a 42 km go-cart race. Dan, drives 0.4 km/min faster than Sue, but has to stop en route and fix his go-cart for one-half hour. This stop costs Dan to arrive 15 min after Sue. How fast was each person driving?


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ASSIGNMENT Non Linear Systems (MCR)

1. Find the point(s) of intersection of the parabola and the line.

2 264

2 3

y x

y x

+ =

− = −

2. Explain the solution to question 1 using pictures.

3. Find k so that the system has only one solution. 2

3 1y x x

y x k

= − + −

= − +

4. Predict the number of solutions the following system will have. Explain your reasoning.

22 3

2

y x x

y x

= − + −

= − −


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Find the point(s) of intersection

5.

6.

7. A toy rocket’s flight path is given by 2( ) 5 3 2h t t t= − + + and a bird’s flight path is ( ) 5 4h t t= − + where t is time

in seconds. What time did the bird and the toy rocket collide?


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ASSIGNMENT Trigonometry (gr10) Solve for x, the triangles are similar

1.

2.

Find the missing measure

3.

4.

5.


28

6.

Solve each triangle (find all angles and all sides). Round to nearest tenth

7.

8.


29

9.

10.


30

ASSIGNMENT Simplify/Multiply/Divide Rational Expressions (MCR)

1.

2

3

3 6

xy

x x=

− simplify, then sketch.

2. Note that there are two values of x that make the

original expression undefined. Show how these

affect the graph you drew. This is why it is very

important to state restrictions.

Simplify the rational expressions and state the restrictions

3.

4. 2 4

2 2

21 15

6 14

x y ab

a b x

−×

5. 2 2

2

9 4

12 2 6

x x x

x x x

− −×

− − − simplify, then sketch.

6. 5

2 2 5

5 15

12 18

a a

yz y z÷

Find the domain of each function

7. ( )

3

3

49

xf x

x x

+=

−

8.

9.


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10.

11. ( )

225 6

10 243 12

x xx x

x

+ +÷ − −

+

12.

13.

14.

15.

simplify, then sketch.


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ASSIGNMENT Add/Subtract Rational Expressions (MCR)


1.

2.

3.

2 2

3 1 4

5 5

x x

x x x x

+ ++

− −

4.

2 2

2 5

2 24 7 12x x x x−

− − + +


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5.

6.

7. 2 2

2 2

3 1 4

2 3 5 2

x x x x

x x x x

+ −−

− − +

−

+

8.

2( ) 5( ) 6 3 ( ) 3

x y y

x y x y x x y x

++

+ − + − + +

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