Pure Math 30 Cumulative 2 Review

Pure Math 30 Cumulative 2 Review

1.  If 2log(5x3) + 1 = log(nx6), then n =

2.  Solve, finding the smallest solution to

2log2(x - 3) + 1 = log2(x2 – 2)

3.  Solve 4(31-x) = 5x+1

4.  If 500 bacteria grow exponentially to 15 000 in 20 h, the time, in hours, it will take for the bacteria to grow to 100 000 is

5.  The number of two or three digit odd numbers with no repeating digits is

6.  The exponent of x in the 4th term in the expansion of (5x3 – x-1)12 is

7.  The number of arrangements of the letters in CANADIAN is

8.  The number of pathways from point A to point B is

A

B

9.  The number of committees with 5 members with at least two females that can be selected from 5 males and 5 females is

10.  The probability of getting exactly 1 Ace in a 5 card hand from a standard deck of 52 cards is

11.  The probability of getting exactly 5 heads on 8 tosses of a coin is

12.  If 20% of people smoke, the probability of at least 3 smokers being part of a group of 10 people chosen at random is

13.  If the probability of winning is 0.4 in any one game, then the probability of winning at most 40 games out of 100 played is

14.  If the heights of students is normally distributed with a mean of 1.28 m and a standard deviation of 0.35 m, then the probability of a person selected at random being between 1.00 m and 1.50 m is

15.  If 40% of results in a normal distribution are greater than 72 when the mean is 68, then the standard deviation is

16.  If 76% of the results in a standard normal distribution are between z = -1.5 and z = m, then m is

17.  The point (5, 2) is on the function y = f(x). The y coordinate of the transformed point on the function y = -2f(x + 3) + 7 is

18.  If the point (-2, 4) is stretched vertically about the line y = -2 by a factor of 3, then the y coordinate of the transformed point is

19.  The horizontal stretch factor of a transformation is 5. The transformed function could be written as y = f(bx). The value of b is

20. If the point (-4, 5) is on the terminal arm of angle q, then csc q equals

21.  The largest solution to the equation 4sin2x – 3 = 0, 0 < x < 2p is

22. The length of an arc that subtends an angle of 145° when the radius of the circle is 5 cm is

Answers: 1. 250 2. 10 3. –2.59 4. 31.2 5. 360 6. 24 7. 3360 8. 33 9. 226 10. 0.30 11. 0.22 12. 0.32 13. 0.54 14. 0.52 15. 15.8 16. 0.94 17. 3 18. 16 19. 0.2 20. 1.28 21. 5.24 22. 12.7