Name: Final Mixed ReviewPeriod:

13-5 Units 1-12 mixed ReviewDirections: Now that we’ve reviewed all units, let’s put all topics together. This packet will help you review a mix of questions from each unit. Remember to check the answer key and ask questions!

1. In the research department of a university, 300 mice were timed as they each ran through a maze. The results are shown in the cumulative frequency diagram opposite.(a) How many mice complete the maze in less than 10 seconds?

(b) Estimate the median time.

2.

(c) Another way of showing the results is the frequency table below.

Time t (seconds) Number of mice

t 7 0

7 t 8 16

8 t 9 22

9 t 10 p

10 t 11 q

11 t 12 70

12 t 13 44

13 t 14 31

14 t 15 23

(i) Find the value of p and the value of q.

(ii) Calculate an estimate of the mean time.

2. Let A and B be events such that P(A) = 21

, P(B) = 43

and P(A B) = 87

.

(a) Calculate P(A B).

(b) Calculate P(AB).

(c) Are the events A and B independent? Give a reason for your answer.

3. Let P (A )=0.6, P (B )=0.5, and P (A ∩B )=0.2.

a) Draw a Venn diagram to represent the information.

Find each of the following probabilities.

b) P(A∪B)

c) P(A∪B)'

d) P (A|B )

No calc

4. Write 4 log3 x+13

log3 y−5 log3 z as a single logarithm.

NO CALC

5. Solve each equation.

a. log3 (4 x−1 )=3

b. log x−1 ( x+1 )=2

c. log3 (2 log x )=4

d. log2(x−2)+ log 12(x−1)=3

NO CALC

6. If m=logx 4 and n=log x8, find expressions in terms of m and n for

a. log 4 8

b. log x2

c. log x16

d. log 832

NO CALC

7. . Solve the equation 2 cos2 x−5 cos x−3=0 ,0≤x ≤2 π.

NO CALC

8. Solve the equation 4 sin2θ−1=0 ,0° ≤θ≤360 °.

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