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Please answer the following multiple choice questions. Click on your answer. Please feel free to use paper or graphing calculators to find the correct.

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Presentation on theme: "Please answer the following multiple choice questions. Click on your answer. Please feel free to use paper or graphing calculators to find the correct."— Presentation transcript:

1 Please answer the following multiple choice questions. Click on your answer. Please feel free to use paper or graphing calculators to find the correct answer. Click here to go to question #1

2 When finding solutions to equations, you are finding the A) x-intercepts A) x-intercepts A) x-intercepts A) x-intercepts B) y-intercepts B) y-interceptsB) y-interceptsB) y-intercepts C) vertex points C) vertex pointsC) vertex pointsC) vertex points D) line of symmetry D) line of symmetryD) line of symmetryD) line of symmetry

3 Correct! Great job! Click here to go to the next question Click here to go to the next question Click here to go to the next question Click here to go to the next question

4 OOPS Please try again. Click here to return to Question #1 Click here to return to Question #1 Click here to return to Question #1 Click here to return to Question #1

5 How many solutions does the equation have? 10x x 2 + x + 2 = 0 A) 6 A) 6 B) 5 B) 5 C) 3 C) 3 D) 2 D) 2

6 Right! You knew to look for the highest degree of exponent. Click here to go to question #3 Click here to go to question #3 Click here to go to question #3 Click here to go to question #3

7 Sorry, thats incorrect. Dont add the exponents, but the answer does deal with exponents Click here to go back to #2 Click here to go back to #2 Click here to go back to #2 Click here to go back to #2

8 OOPS Try again, but think about what the exponents tell us. Click here to go back to #2 Click here to go back to #2 Click here to go back to #2 Click here to go back to #2

9 Do all of the solutions to these problems have to be real number solutions? A) Yes A) Yes B) No B) No

10 Correct! They can have a combination of real and imaginary solutions! Click here to go to the next question Click here to go to the next question Click here to go to the next question Click here to go to the next question

11 Thats incorrect. Remember they can have a combination of real and imaginary solutions. Click here to go to the next question Click here to go to the next question Click here to go to the next question Click here to go to the next question

12 If factoring by grouping, which terms would you group together to factor x 3 + x 2 + x + 1 A) (x 3 + x 2 ) + (x + 1) A) (x 3 + x 2 ) + (x + 1) B) (x 3 + x) + (x 2 + 1) B) (x 3 + x) + (x 2 + 1) C) (x 3 + 1) + (x 2 + x) C) (x 3 + 1) + (x 2 + x) D) A, B, & C work D) A, B, & C work

13 Super! Although they all work, choices A and B make this problem much easier to solve. Click here to go to question #5 Click here to go to question #5 Click here to go to question #5 Click here to go to question #5

14 This is a correct way to group, but they actually all work. Choices A) (x 3 + x 2 ) + (x + 1) B) (x 3 + x) + (x 2 + 1) make this problem much easier to solve than choice C) (x 3 + 1) + (x 2 + x) Click here to go to question #5 Click here to go to question #5 Click here to go to question #5 Click here to go to question #5

15 If you chose to group like this (x 3 + x 2 ) + (x + 1) What would be the next steps? A) x(x 2 + x) + (1 + x)A) x(x 2 + x) + (1 + x) B) x 2 (x + 1) + 1(x + 1) B) x 2 (x + 1) + 1(x + 1) A) x(x 2 + x) + (1 + x)B) x 2 (x + 1) + 1(x + 1) (x)(x 2 + x)(2) (x 2 + 1)(x + 1) (x)(x 2 + x)(2) (x 2 + 1)(x + 1)(x)(x 2 + x)(2)(x 2 + 1)(x + 1)(x)(x 2 + x)(2)(x 2 + 1)(x + 1) C) x 3 (1 + x) + 1(x + 1)C) x 3 (1 + x) + 1(x + 1) D) x 2 (x) + (x + 1) D) x 2 (x) + (x + 1) C) x 3 (1 + x) + 1(x + 1)D) x 2 (x) + (x + 1) (x 3 + 1)(x + 1) x(x 2 + 1) (x 3 + 1)(x + 1) x(x 2 + 1)(x 3 + 1)(x + 1)x(x 2 + 1)(x 3 + 1)(x + 1)x(x 2 + 1)

16 Correct Great job! Click here to go to question #6 Click here to go to question #6 Click here to go to question #6 Click here to go to question #6

17 OOPS Please look at all the choices and try again. Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem

18 Now we have the factored form (x 2 + 1)(x + 1) Are all of the solutions real numbers? A) Yes A) Yes B) No B) No

19 Thats correct. (x 2 + 1) gives imaginary solutions & (x + 1) gives a real solution Click here to go on Click here to go on Click here to go on Click here to go on

20 Thats incorrect. (x 2 + 1) gives imaginary solutions & (x + 1) gives a real solution Click here to go on Click here to go on Click here to go on Click here to go on

21 What are the real solutions to (x 2 + 1)(x + 1) = 0 ? __ __ __ A) 1, B) 1, A) 1, B) 1, __ __ __ C) ±1D) C) ±1D)

22 Thats correct! -1 is the only real solution Click here to go to the next question Click here to go to the next question Click here to go to the next question Click here to go to the next question

23 Sorry, thats not right. Remember to find solutions set each factor equal to zero and solve. Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem

24 Which is the correct graph for x 3 + x 2 + x + 1 A)A) B) B) A)B) C)D) C)D)

25 Great job! You must have remembered what graphs with a 3 rd degree polynomial look like, then you only had to remember the real solution to figure it out. Or You used your graphing calculator. Click here to go to question #9 Click here to go to question #9 Click here to go to question #9 Click here to go to question #9

26 Youre close but remember what the real solution was to this problem. We solved it in the last question. Click here to go back to graphs Click here to go back to graphs Click here to go back to graphs Click here to go back to graphs

27 Thats incorrect. Think about what shape the graph of a 3 rd degree polynomial should look like. Click here to go back to graphs Click here to go back to graphs Click here to go back to graphs Click here to go back to graphs

28 How many solutions does the equation have? 4x 6 – 20x 4 = -24x 2 A) 12 A) 12 B) 6 B) 6 C) 4 C) 4 D) 1 D) 1

29 Great! Youre thinking now. Click here to go to the next question Click here to go to the next question Click here to go to the next question Click here to go to the next question

30 No, remember you dont add the exponents. What do the exponents tell us? Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem

31 Sorry thats incorrect. What do the exponents tell us? Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem

32 Factor the following x Click here when you have an answer Click here when you have an answer Click here when you have an answer Click here when you have an answer

33 Select the answer that you found. If your answer is not below, click below to return to the problem A) (x 2 + 4)(x – 2) B) (x – 2)(x 2 + 2x + 4) C) (x + 2)(x 2 + 2x + 4) D) (x – 2)(x 2 – 2x – 4) A) (x 2 + 4)(x – 2) B) (x – 2)(x 2 + 2x + 4) C) (x + 2)(x 2 + 2x + 4) D) (x – 2)(x 2 – 2x – 4) A) (x 2 + 4)(x – 2) B) (x – 2)(x 2 + 2x + 4) C) (x + 2)(x 2 + 2x + 4) D) (x – 2)(x 2 – 2x – 4) Go back to problem Go back to problem Go back to problem Go back to problem

34 Super! Youre doing great and youre half way finished. Click here to go to question #11 Click here to go to question #11 Click here to go to question #11 Click here to go to question #11

35 No, think about the rules for factoring the difference of cubes. Click here to go back to choices Click here to go back to choices Click here to go back to choices Click here to go back to choices Click here to see the problem again

36 Not quite, but youre close. Think about the signs that you need when factoring the difference of cubes. Click here to go back to the choices Click here to go back to the choices Click here to go back to the choices Click here to go back to the choices Click here to go back to the problem

37 Which of the following are possible solutions to the function x 3 + 3x x = -30 A) 3 A) 3 B) -3 B) -3 C) 10 C) 10 D) 5 D) 5

38 Great job! Did you remember that there are several ways to get this solution. If you factored and then set them equal to zero, you could have checked your answer by graphing the equation, and finding the x-intercepts. (If you havent graphed it try now.) Click here to go to the next problem Click here to go to the next problem Click here to go to the next problem Click here to go to the next problem

39 No, please try again. Hint 1: set the equation equal to zero Hint 2: factor, set each equal to zero and solve Hint 3: graph and look at the x-intercepts Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem

40 Find one possible solution to the equation below -2x 3 – 4x 2 – 3x – 6 = 0 A) 3/2 A) 3/2 B) -3 B) -3 C) -2 C) -2 D) No real solutions D) No real solutions

41 Super job! Youre doing great! Click here to go to the next question Click here to go to the next question Click here to go to the next question Click here to go to the next question

42 No, please try again. Hint 1: factor, set each equal to zero and solve Hint 2: graph and look at the x-intercepts Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem

43 Which could be the graphical representation of 32x A)B) A)B) C)C) D) D) C)D)

44 Correct! Great job! Click here to go to the next question Click here to go to the next question Click here to go to the next question Click here to go to the next question

45 No, think about what shape the graph of a cubic should look like. Click here to go back to the graphs Click here to go back to the graphs Click here to go back to the graphs Click here to go back to the graphs

46 No, but you have the right shape. Click here to go back to the graphs Click here to go back to the graphs Click here to go back to the graphs Click here to go back to the graphs

47 Factor 27x Click here when you have an answer Click here when you have an answer Click here when you have an answer Click here when you have an answer

48 Select your answer, if it is not here click here to go back to the problem so you may try again click hereclick here A) (3x – 2)(9x 2 – 2x + 4) A) (3x – 2)(9x 2 – 2x + 4) B) 27(x + 2)(x 2 – 2x + 4) B) 27(x + 2)(x 2 – 2x + 4) C) 27(x – 2)(x 2 + 2x – 4) C) 27(x – 2)(x 2 + 2x – 4) D) (3x 2 – 6)(3x +6) D) (3x 2 – 6)(3x +6)

49 Super job! You remembered everything, you must be thinking. Click here to go on Click here to go on Click here to go on Click here to go on

50 No, please try again. Taking out the GCF might be a good start. Click here to go back to answers Click here to go back to answers Click here to go back to answers Click here to go back to answers Click here to go back to the problem

51 You remembered to take out the GCF, but check your signs. Click here to go back to answers Click here to go back to answers Click here to go back to answers Click here to go back to answers Click here to go back to the problem

52 Which of the following is a solution to the function 2x = 0 A) -3 A) -3 B) 2 B) 2 C) 3 C) 3 D) 9 D) 9

53 Correct, great job. There were several ways to come up with this answer. Here are a few of the ways: - graph, look for x-intercepts - solve algebraically - because its multiple choice you could have used substitution and tried all possible answers. Click here to go on Click here to go on Click here to go on Click here to go on

54 OOPS, thats wrong. Think about possible ways to solve this equation: Here are a few of the ways: - graph, look for x-intercepts - solve algebraically - because its multiple choice you could have used substitution and tried all possible answers. Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem

55 Youre very close, go back and check your work. You may also want to try it another way, such as: - graph, look for x-intercepts - solve algebraically - because its multiple choice you could have used substitution and tried all possible answers. Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem

56 How many solutions does the following equation have? 2x x = 14x 3 A) 9 A) 9 B) 5 B) 5 C) 3 C) 3 D) 2 D) 2

57 Great job! You knew it was the largest exponent. Did you also remember that not all solutions have to be real solutions? Click to see part 2 of this problem Click to see part 2 of this problem Click to see part 2 of this problem Click to see part 2 of this problem

58 Sorry, thats incorrect. Dont add the exponents, but the answer does deal with exponents Click here to go back to the equation Click here to go back to the equation Click here to go back to the equation Click here to go back to the equation

59 OOPS Try again, but think about what the exponents tell us. Click here to go back to the equation Click here to go back to the equation Click here to go back to the equation Click here to go back to the equation

60 What are possible solutions to 2x x = 14x 3 A) 0, 2, -2, 3, -3 A) 0, 2, -2, 3, -3 B) 0, 3, 4 B) 0, 3, 4 __ __ __ __ __ C) 0, -2, 2, 3, -3 C) 0, -2, 2, 3, -3 D) -2, 2 D) -2, 2

61 Click here to go to the last question Click here to go to the last question Click here to go to the last question Click here to go to the last question Click here to go back and see the original equation Super! Did you solve this algebraically, graphically, or by using the solutions that were given? If you only tried one method, try another before you move on.

62 No, please try again. Hint: Check your math or try to solve the problem another way (graphically). Click here to go back to the equation Click here to go back to the equation Click here to go back to the equation Click here to go back to the equation

63 What are possible solutions to 2x 3 – 5x x = 45 A) 2.5 A) 2.5 B) 2.5, 3, -3 B) 2.5, 3, -3 C) 2.5, -9 C) 2.5, -9 D) No real solutions D) No real solutions

64 Super job! There is only 1 real solution, the other 2 are imaginary. Click here, please Click here, please Click here, please Click here, please

65 No, think about all the ways that we can find the solution. Then try again, remember not all solutions must be real. If you havent tried graphing click this link to try that method or go back to the problem and try another method. graphing Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem Click here to go back to the problem

66 Were all through, I hope you have a better understanding of solving equations.


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