Essential Question: Does this help my marking period grade?

(Answer: No)

For the function , finda.

b.

Your answer is b

( ) 2f x x

4

(4)

(4) 2

(4) 2

f

f

f

( )

( ) 2

f a

f a a

Find the sum of

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

increment)sum seq(2x – 7, x, 1, 15, 1) = 135

The answer is b

15

1

2 7k

k

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

u1 = 2(1) – 7 = -5 u15 = 2(15) – 7 = 23

Use the first formula

The answer is still b

11

15

1

( )2

152 7 ( 5 23)

2

7.5(18)

135

k

n kn

n

ku u u

k

Which best describes the relationship between the line through E and F and the line through G and H?E = (2, -5), F = (-1, -1) and G = (-4, -7), H = (0, -10)

Find the slope of each line

If the slopes are the same, the lines are parallel. If the slopes are inverse reciprocals (flip the fraction, flip the sign), the two lines are perpendicular. This is neither of the above.

The answer is c

2 1

2 1

2 1

2 1

1 ( 5) 4

1 2 3

10 ( 7) 3

0 ( 4) 4

EF

GH

y ym

x x

y ym

x x

Find the common ratio for geometric sequence

The common ratio is the number that is multiplying the function again and again

That number is 1/6, and I don’t know how to explain that any more simply.

Your answer is b

11

46

n

Determine the nature of the roots:2x2 – 12x + 18 = 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

( 12) 4(2)(18)

144 144 0 0

b ac

Find all solutions:

The answer is d

2 13 72 6x x

2

22

2

2

13 72

13 72 36

9

13 36 0

( 9)( 4

or 4

6

3 6

)

3

0

6

x x

x x

x x

x x

x x

Solve the inequality and express your answer in interval notation: -15<-3x+3<-3

[2, 6] The answer is a

3 3 3

3

15 3 3 3

18 3 6

6 2

2 6

3 3

x

x

x

x

Determine the domain of the function

The rule about domains are that they’re all real number except when taking square roots (not applicable) or dividing by 0.

To check the denominator, set it equal to 0.x(x2 – 81) = 0x = 0 or x2 – 81 = 0x = 0 or x2 = 81x = 0 or x = +9

The answer is a

2

2( )

( 81)

xh x

x x

9) Use the vertical line test Yeah… use the vertical line test All of the graphs fail the vertical line test, except

for a, which is your answer

10) Which function is in quadratic x-intercept form?

x-intercept form: a(x – s)(x – t) The only one that fits that mold is b, which is your

answer Remember:

Transformation form: a(x – h)2 + k Polynomial form: ax2 + bx + c

Your midterm will ask you to identify one of the three

Find the rule… translated 2 units left and 3 units up on the parent function f(x) = x2

The only graph that resembles x2 is c, but just to confirm… Is it shifted 2 units left? Yup Is it shifted 3 units up? Yup Is it the answer? You betcha.

f(x) = x4 & g(x) = 3 – 2x. Find (f o g)(x)Take x, plug it into the closest function

g(x) = 3 – 2xTake that answer, plug it into the next

closest function f(3 – 2x) = (3 – 2x)4

At no point are we dealing with square roots or fractions, so the domain is all real numbers.

The answer is a

If {un} is an arithmetic sequence with u1=3 and u2=5.9a. Find the common difference

Subtract u1 from u2 to find d d = 5.9 – 3 = 2.9

b. Write the system as a recursive function Recursive functions have two parts, starting point and a

function that uses the previous term u1 = 3 and un = un-1 + 2.9

c. Give the first eight terms of the sequence Put ‘3’ into the calculator, hit enter Put ‘Ans + 2.9’, and keep hitting enter to get the rest of the

terms (remember, 3 is the 1st term) 3, 5.9, 8.8, 11.7, 14.6, 17.5, 20.4, 23.3

d. Graph the sequence 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. Like the quarterly, I’m going to tell you to skip the graph

Solve the equationx2 – 10x + 20 = 0

Use the Quadratic Equation2

22

10 20 0 (a = 1, b = 10, c = 20)

( 10) ( 10) 4(1)(20)4

2 2(1)

10 100 80 10 20 10 4 5 10 2 5

2 2 25

25

x x

b b ac

a

Find all real solutions:

Real solutions? When numerator = 0 x2 + x - 42 = 0 (x - 6)(x + 7) = 0 x = 6 or x = -7

I’m only asking for real solutions, so just test your real solutions in the denominator to make sure they’re not extraneous (denominator = 0). (6)2 + 16(6) + 63 = 195 (works) (-7)2 + 16(-7) + 63 = 0 (extraneous)

Real solution: 6

2

2

420

16 63

x x

x x

Solve the inequality and express your answer in interval notation:

Critical Points Real solutions: 5 & -9 Extraneous solution: 4

Test the intervals (-∞, -9] use x = -10, get -15/14 > 0FAIL [-9, 4) use x = 0, get 11.25 > 0 PASS (4, 5] use x = 4.5, get -13.5 > 0 FAIL [5, ∞) use x = 6, get 7.5 > 0

PASS Interval solutions are [-9, 4) and [5, ∞)

( 5)( 9)0

( 4)

x x

x

Find the selected values of the function

Check each input to decide which function it should be plugged into (top or bottom)a) f(-1) [bottom function], -8 + 7(-1)2 = -1b) f(0) [top function], ⅓(0) = 0c) f(1) [top function], ⅓(1) = ⅓d) f(-1.9) [bottom function], -8 + 7(-1.9)2 =

17.27

13

2

if x > -1( )

8 7 if x -1

xf x

x

f(x) = 16 – x2, g(x) = 4 – x.Find (f – g)(x) and its domain

Subtract the second function from the first. Make sure to use parenthesis around the function. [16 – x2] – [4 – x] (distribute the negative

sign)16 - x2 – 4 + x (combine like terms, put in

order) -x2 + x + 12Domain of f is all real numbers. Domain of g is

also all real numbers. The domain of the added function is all real numbers.

Find the difference quotient: 2x2 – 3x – 8Function using (x+h) – function

using x

2 2

2 2 2

22

2

2

( ) ( )

2( ) 3( ) 8 2 3 8

2( 2

4

) 3 3 8 2 3 8

4 2 3

4 2

3 3

2 33

82 2 8

f x h f x

h

x h x h x x

h

x xh h x h x x

h

xh h h

h

xh h h

hh

x x xx

x

Determine the x-intercepts and vertex of the functionf(x) = x2 + 12x + 36

x-intercepts are found using the quadratic equation, or factoring (x + 6)(x + 6). There is only one x-intercept: -

6 The vertex is at

1st coordinate: (-12)/2(1) = -6 2nd coordinate, plug in: (-6)2 + 12(-6) + 36 =

0 Vertex is at (-6, 0)

,2 2

b bf

a a

Find the mean, median, and mode for the set of numbers:5, 25, 25, 25, 11, 20, 25, 16

We break out the ONEVAR functionStore the data as a list [2nd, subtract key]{5, 25, 25, 25, 11, 20, 25, 16} D

Receive our data back as confirmationONEVAR [ALPHA] D

is the mean (19) Push down to get the median (22.5)

The answer is a (The mode is 25)

x

5, 25, 25, 25, 11, 20, 25, 16 Rearrange the data in numerical order.

The middle term(s) is/are the median5, 11, 16, 20, 25, 25, 25, 25 (20 + 25)/2 = 45/2 = 22.5

The mode is obviously 25 The answer is still a

Find the population standard deviation of the data set68, 56, 58, 60, 70, 75, 72, 53

Use the ONEVAR function againStore the data as a list [2nd, subtract key]{68, 56, 58, 60, 70, 75, 72, 53} D

Receive our data back as confirmationONEVAR [ALPHA] D

Push down to get the population standard deviation (σx) ≈ 7.69740216 ≈ 7.7

The answer is c

Data set: 68, 56, 58, 60, 70, 75, 72, 53

Find the mean of the data set (68 + 56 + 58 + 60 + 70 + 75 + 72 + 53) / 8 =

64 Find the distances from the mean

Square them and add them together 42 + 82 + 62 + 42 + 62 + 92 + 82 + 112 = 474

For population standard distribution, take the average of the distance 474 / 8 = 59.25

Take the square root of that value

The answer, again, is c

59.25 7.6974 7.7

In a clinical trial, a drug used to as caused side effects in 9% of patients who took it. Two patients were selected at random. Find the probability that neither of the patients had side effects.

Make sure to read the problem (it alternates between all and none)

0.09 probability for each having side effects 0.91 probability for each not having side

effects P(both having SE) = 0.912 = 0.8281

The answer is a

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

Order matters, so we’re using Permutations

13P4 = 17,160

The answer is a

Find the expected value of the random variable with the given probability distribution.

Multiply each outcome by its probability and add them all together (25)(0.24) + (9)(0.22) + (33)(0.11) + (51)(0.09) +

(81)(0.34)43.74

Outcome 25 9 33 51 81

Probability

0.24 0.22 0.11 0.09 0.34