El primero examen trimestal

For the function , finda.

b.

Your answer is a

( ) 8f x x

1

(11)

(11)

( ) 3

1 8

11

f

f

f

( )

( ) 8

f a

f a a

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, u1 = -2

The function adds 3 to each term, so un = un-1 + 3

The answer is b

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

Find the sum of

Use the calculator – that’s why I got themsum seq(function, variable, start, end,

increment)sum seq(4x + 3, x, 1, 32, 1) = 2208

The answer is a

32

1

4 3k

k

Use the partial sum formula because you’re stubborn Find u1 and uk

u1 = 4(1) + 3 = 7 u32 = 4(32) + 3 = 131

Use the first formula

The answer is still a

11

32

1

( )2

324 3 (7 131)

2

16(138)

2208

k

n kn

n

ku u u

k

Find the kth partial sum of the arithmetic sequence {un} with a common difference dk = 14, u1 = -1, d=6

To use the calculator, we need a function That’s achieved by using the explicit form

un = u1 + (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

Use the partial sum formula, particularly the 2nd partial sum formula. Remember your order of operation…

The answer is still d

11

( 1)

2

(14(14 1

6)2

(6)2

14 91(6)

14 5

1

46

532

4( 1)

1

)

24

18

k

nn

k ku ku d

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

2 1

2 1

2 1

2 1

1 ( 5) 4

5 ( 8) 3

5 2 3

5 ( 1) 4

EF

GH

y ym

x x

y ym

x x

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

9

2

96

2

y mx b

y x

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

Solve by completing the square:x2 + 3x – 10 = 0

Use the quadratic formula. It always works.a = 1, b = 3, c = -10

The answer is c

22 3 3 4(1)( 10)4

2 2(1)

3 9 40 3 49 3 7

2 2 24 10

or 2 or 52 2

b b ac

a

Solve by completing the square: x2 + 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

(x2 – 2x) + (5x – 10) = 0 x(x – 2) + 5(x – 2) = 0 (x + 5)(x – 2) = 0 x + 5 = 0 or x – 2 = 0 x = -5 or x = 2

The answer is b

Solve by completing the square:x2 + 3x – 10 = 0

Sure, complete the square

The answer is still c

2

2

2

2 2

3 10 0

3 10

3 49

2 4

3 49

2 43 7

2 24 10

o

3 3

2

r 2 or 52

1 1

2

0 0

2

x x

x x

x

x

x

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

Solve by taking the square root of both sides4(x-2)2 - 252 = 0

Get the squared term by itself

The answer is d

2

2

2

252 252

4 4

4( 2) 252 0

4( 2) 252

( 2) 63

2 63

2 63 2 9 7 2 3 7

x

x

x

x

x

Determine the nature of the roots:4x2 + 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

2

2

4

32 4(4)(64)

1024 1024 0 0

b ac

Solve the equation5x = 3x2 + 1

Get everything to equal 0 and use the Quadratic Equation

The answer is d

2

2

22

5 3 1

0 3 5 1 (a = 3, b = 5, c = 1)

( 5) ( 5) 4(3)(1)4

2 2(3)

5 25 12 5 13

6 6

x x

x x

b b ac

a

If {un} is an arithmetic sequence with u1=4 and u2=5.6a. Find the common difference

Subtract u1 from u2 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) u1 = 4 and un = un-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.

For the geometric sequence with u1=3 and u2=12a. Find the common ratio

Divide u2 by u1 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) u1 = 3 and un = un-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.

Solve the equationx2 – 6x + 7 = 0

Use the Quadratic Equation2

22

6 7 0 (a = 1, b = 6, c = 7)

( 6) ( 6) 4(1)(7)4

2 2(1)

6 36 28 6 8 6 4 2 6 2 23 2

2 2 2 2

x x

b b ac

a

Find the mean, median, and mode for the set of numbers:1, 21, 21, 21, 18, 23, 13, 10

We break out the ONEVAR functionStore the data as a list [2nd, subtract key]{1, 21, 21, 21, 18, 23, 13, 10} D

Receive our data back as confirmationONEVAR [ALPHA] D

is the mean (16) Push down to get the median (19.5)

The answer is d (The mode is 21)

x

1, 21, 21, 21, 18, 23, 13, 10 Rearrange the data in numerical order.

The middle term(s) is/are the median1, 10, 13, 18, 21, 21, 21, 23 (18 + 21)/2 = 39/2 = 19.5

The mode is obviously 21 The answer is still d

Describe the shapeRecap: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

Find the population standard deviation of the data set70, 58, 70, 43, 58, 55, 58, 68

Use the ONEVAR function againStore the data as a list [2nd, subtract key]{70, 58, 70, 43, 58, 55, 58, 68} D

Receive our data back as confirmationONEVAR [ALPHA] D

Push down to get the population standard deviation (σx) ≈ 8.58778 ≈ 8.59

The answer is b

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 102 + 22 + 102 + 172 + 22 + 52 + 22 + 82 = 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

73.75 8.58778 8.59

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) = 0.063 = 0.000216

The answer is b

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

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

18 students. How many ways can the students who go first, second, and third be chosen?

Order matters, so we’re using Permutations

18P3 = 4896

The answer is b

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

Q1, the median of the lower half

The answer is c

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%

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

Outcome 47 23 79 58 82

Probability

0.05 0.06 0.29 0.23 0.37