1. El primero examen trimestal

2.  For the function, find a. b. Your answer is a

3.  Which is the correct recursive formula for the sequence? {-2, 1, 4, 7, … }  A recursive function has two parts  The first term  The function, doing something to the previous term  The first term, u 1 = -2  The function adds 3 to each term, so u n = u n-1 + 3  The answer is b

4.  Select the correct description of the sequence {-12, -17, -22, -27, -32, …}  The sequence is arithmetic, because we’re adding a -5 to each term (arithmetic = add)  The answer is b

5.  Find the sum of  Use the calculator – that’s why I got them  sum seq(function, variable, start, end, increment)  sum seq(4x + 3, x, 1, 32, 1) = 2208  The answer is a

6.  Use the partial sum formula because you’re stubborn  Find u 1 and u k u 1 = 4(1) + 3 = 7 u 32 = 4(32) + 3 = 131  Use the first formula   The answer is still a

7.  Find the k th partial sum of the arithmetic sequence {u n } with a common difference d k = 14, u 1 = -1, d=6  To use the calculator, we need a function  That’s achieved by using the explicit form  u n = u 1 + (n-1)(d) = -1 + (n-1)(6) = -1 + 6n – 6 = 6n – 7  Use the calculator  sum seq(6x – 7, x, 1, 14, 1) = 532  The answer is d

8.  Use the partial sum formula, particularly the 2 nd partial sum formula. Remember your order of operation…   The answer is still d

9.  Which best describes the relationship between the line through E and F and the line through G and H? E = (-8, -5), F = (-5, -1) and G = (-1, 2), H = (-5, 5)  Find the slope of each line  Because the slopes are inverse reciprocals (flip the fraction, flip the sign), the two lines are perpendicular.  The answer is b

10.  Find an equation for the line satisfying the given conditions. y-intercept 6 and slope  You’ve got slope intercept form, so plug in the slope and the intercept   Your answer is d

11.  Find the common ratio for geometric sequence 10(5) n-1  The common ratio is the number that is multiplying the function again and again  That number is 5, and I don’t know how to explain that any more simply.  Your answer is d

12.  Solve by completing the square:  x 2 + 3x – 10 = 0  Use the quadratic formula. It always works.  a = 1, b = 3, c = -10  The answer is c

13.  Solve by completing the square:  x 2 + 3x – 10 = 0  Turns out this one can be factored  Find two numbers that multiply to get ac: -10  That add together to get b: 3 Those numbers are -2 and 5  Factor  (x 2 – 2x) + (5x – 10) = 0  x(x – 2) + 5(x – 2) = 0  (x + 5)(x – 2) = 0  x + 5 = 0or x – 2 = 0  x = -5or x = 2  The answer is b

14.  Solve by completing the square:  x 2 + 3x – 10 = 0  Sure, complete the square The answer is still c

15.  Plug in for x  If both answers equal 0, you’ve got a solution  (2) 2 + 3(2) – 10 = 0  4 + 6 – 10 = 0  So, 2 is an answer  (-2) 2 + 3(-2) – 10 = 0  4 – 6 – 10 ≠ 0  So -2 isn’t an answer  Check, 2 and -5 both work  For the last time, the answer is c

16.  Solve by taking the square root of both sides 4(x-2) 2 - 252 = 0  Get the squared term by itself The answer is d

17.  Determine the nature of the roots: 4x 2 + 32x + 64 = 0  Use the discriminate to determine the number of real roots  Because the discriminate equals 0, there is one real root, and the answer is b

18.  Solve the equation 5x = 3x 2 + 1  Get everything to equal 0 and use the Quadratic Equation  The answer is d

19.  If {u n } is an arithmetic sequence with u 1 =4 and u 2 =5.6 a. Find the common difference Subtract u 1 from u 2 to find d d = 5.6 – 4 = 1.6 b. Write the system as a recursive function Recursive functions have two parts, starting point and a function that uses the previous term (Just like problem #2) u 1 = 4 and u n = u n-1 + 1.6 c. Give the first eight terms of the sequence Put ‘4’ into the calculator, hit enter Put ‘Ans + 1.6’, and keep hitting enter to get the rest of the terms 4, 5.6, 7.2, 8.8, 10.4, 12, 13.6, 15.2 d. Graph the sequence See the answer sheet, but in short. The first term (4) has an x value of 1 and a y value of 4; the second term (5.6) has an x value of 2 and a y value of 5.6, etc.

20.  For the geometric sequence with u 1 =3 and u 2 =12 a. Find the common ratio Divide u 2 by u 1 to find r r = 12/3=4 b. Write the system as a recursive function Recursive functions have two parts, starting point and a function that uses the previous term (Just like problem #2) u 1 = 3 and u n = u n-1 (4) c. List the first four terms of the sequence Put ‘3’ into the calculator, hit enter Put ‘Ans 4’, and keep hitting enter to get the rest of the terms 3, 12, 48, 192 d. Graph the sequence See the answer sheet, but in short. The first term (3) has an x value of 1 and a y value of 3; the second term (12) has an x value of 2 and a y value of 12, etc.

21.  Solve the equation x 2 – 6x + 7 = 0  Use the Quadratic Equation

22.  Find the mean, median, and mode for the set of numbers: 1, 21, 21, 21, 18, 23, 13, 10  We break out the O NE V AR function  Store the data as a list [2 nd, subtract key]  {1, 21, 21, 21, 18, 23, 13, 10}  D Receive our data back as confirmation  O NE V AR [A LPHA ] D is the mean (16) Push down to get the median (19.5)  The answer is d (The mode is 21)

23.  1, 21, 21, 21, 18, 23, 13, 10  Rearrange the data in numerical order. The middle term(s) is/are the median  1, 10, 13, 18, 21, 21, 21, 23  (18 + 21)/2 = 39/2 = 19.5  The mode is obviously 21  The answer is still d

24.  Describe the shape  Recap:  Skewed left graphs have a short left side (the left is screwed)  Skewed right graphs have a short right side (the right is screwed)  Uniform graphs all have the same data (uniforms are all the same)  Symmetric graphs look like a mirror (symmetry, reflection)  The answer is a

25.  Find the population standard deviation of the data set 70, 58, 70, 43, 58, 55, 58, 68  Use the ONEVAR function again  Store the data as a list [2 nd, subtract key]  {70, 58, 70, 43, 58, 55, 58, 68}  D Receive our data back as confirmation  ONEVAR [ALPHA] D Push down to get the population standard deviation ( σ x) ≈ 8.58778 ≈ 8.59  The answer is b

26.  Data set: 70, 58, 70, 43, 58, 55, 58, 68  Find the mean of the data set  (70 + 58 + 70 + 43 + 58 + 55 + 58 + 68) / 8 = 60  Find the distances from the mean  Square them and add them together  10 2 + 2 2 + 10 2 + 17 2 + 2 2 + 5 2 + 2 2 + 8 2 = 590  For population standard distribution, take the average of the distance  590 / 8 = 73.75  Take the square root of that value   The answer, again, is b

27.  In a clinical trial, a drug used to as caused side effects in 6% of patients who took it. Three patients were selected at random. Find the probability that all had side effects.  0.06 probability for each having side effects  P(all three having SE) = 0.06 3 = 0.000216  The answer is b

28.  5 yellow, 7 red, and 6 green marbles.  Two marbles are drawn.  Replacement occurs.  A random variable assigned to number of green marbles.  What is the probability that the random variable has an output of 2?  The only time you’d get a random variable of 2 is when you get 2 green marbles.  The probability of drawing a green marble is 6/18  P(2 green) = (6/18)(6/18) = 1/9  The answer is c

29.  2 yellow, 6 red, and 5 green marbles.  Two marbles are drawn.  Replacement occurs.  Random variable assigned to number of red marbles.  Calculate the expected value of the random variable.  We need to figure out all possibilities of red marbles (2 red, 1 red & 1 non-red, 0 red)  2 red = (6/13)(6/13) = 36/169  0 red = (7/13)(7/13) = 49/169  1 red = everything else = 1 - 36/169 - 49/169 = 84/169  Expected value = sum of each random variable multiplied by its probability  (2)(36/169) + (1)(84/169) + (0)(49/169) = 0.92  The answer is b

30.  18 students. How many ways can the students who go first, second, and third be chosen?  Order matters, so we’re using Permutations  18 P 3 = 4896  The answer is b

31.  What’s not right about this picture…  Each of the lines/boxes represents 25% of the data A is true as it spans both boxes B is true, as the range is the max value – min value C is liar. Only half the data is greater than 65: 1 box and the right whisker D is true, as the left side of the box represents Q 1, the median of the lower half  The answer is c

32.  Spin a spinner 5 times  Red = 17%; Blue = 22%; Green = 17%; Yellow = 44%  What is the probability all five will be red? Take red probability and multiply by itself five times (0.17) 5 ≈ 0.000141 ≈ 0.01%  What is the probability that none of the outcomes will be yellow? The probability of not yellow is 1 – P(yellow) 1 – 0.44 = 0.56 Take that probability and multiply by itself five times (0.56) 5 ≈ 0.0550 ≈ 5.5%

33.  Find the expected value of the random variable with the given probability distribution.  Multiply each outcome by its probability and add them all together  (47)(0.05) + (23)(0.06) + (79)(0.29) + (58)(0.23) + (82)(0.37)  70.32 Outcome4723795882 Probability0.050.060.290.230.37