Name: CP1 Math 1 Final Exam June 19, 2018

Class (please circle): Hadden/A Hadden/E Tracy/C Tracy/F Kelly/H page 1

Right now, please write your name at the top of pages 1, 3, 5, and 7.

As always in this course, show any needed work leading to your answers.

1. A high school is predicting how many students it will have in future years. It creates the

following recursive formula, where x is the number of years from now, and f(x) is the number

of students in the school.

0 if2.1)1(

0 if625)(

xxf

xxf

a. Complete this table for function f(x).

x f(x)

0 625

1 750

2 900

3 1080

4 1296

b. Write a closed-form function formula for f(x).

c. Using a percentage, describe how the number of students at the high school is predicted

to grow each year. Write your answer as a complete sentence.

The number of students at the high school is predicted to grow by 20% each year.

OR

The number of students each year is predicted to be 120% of the number in the previous year.

CP1 Math 1 Final Exam June 19, 2018 page 2

2. Mistakes grow your brain, but they’re also important to fix. Fix the mistakes these students

made, by writing your own correct version of the work.

a. Tony: Look how I solved the equation 5 – 4x = 13 + 9x.

Tony’s incorrect work:

5 – 4x = 13 + 9x

4x = 8 + 9x

5x = 8

x = 5/8

x = 0.625

Your correct work:

5- 4x = 13 + 9x

-4x = 8 +9x

-13x = 8

x =

b. Sasha: I simplified the exponential expression 73

5)(

1x

x

.

Sasha’s incorrect work:

73

5)(x

x

1

=

10

5

x

x

11

10

5x

x

1

5

10

x

x

5x

Your correct work:

73

5)(x

x

1

=

11

x5

×x21 =

x5 ×x21 =

x26

Name: CP1 Math 1 Final Exam June 19, 2018

Class (please circle): Hadden/A Hadden/E Tracy/C Tracy/F Kelly/H page 3

2. (continued) Fix the mistakes by writing your own correct version of the work.

c. Derman: I had to write an equation for the line with slope –2 through the point (–3, 4),

so I wrote it and then simplified.

Derman’s incorrect work:

y = –2 (x - 3) - 4

y = –2x - 6 - 4

y = –2x - 10

Your correct work:

y = –2 (x + 3) + 4

y = –2x - 6 + 4

y = –2x - 2

CP1 Math 1 Final Exam June 19, 2018 page 4

3. The questions on this page are about line segment AB where A = (10, –2) and B = (–6, –4).

a. Find the coordinates of the midpoint of AB. Show or explain how you get your answer.

Midpoint of AB

b. The diagram shows this line segment divided into four equal parts. Find the coordinates

of points C, D, and E.

D = (–2, 3) from part a

c. If line l is perpendicular to AB, what is the slope of line l ?

slope of AB

slope of l

Name: CP1 Math 1 Final Exam June 19, 2018

Class (please circle): Hadden/A Hadden/E Tracy/C Tracy/F Kelly/H page 5

4. For each part of this problem, write an equation that could be entered into a graphing

program such as Desmos to achieve each goal.

a. Make a line that goes exactly through these two points.

b. Make a graph that goes exactly through these four points.

c. Make a line that has a close fit to this set of points.

CP1 Math 1 Final Exam June 19, 2018 page 6

5. A math teacher has been collecting data about whether students complete their homework

and whether they remember to bring a calculator to class. Here is a segmented bar graph

showing how these two variables are related.

a. Fill in the missing values in this two-way table.

Completed homework? Yes No Total

Brought calculator?

Yes 64 28 92

No 16 12 28

Total 80 40 120

b. What percentage of students who brought a calculator to class also did their homework?

c. If a student brought a calculator, are they more likely to have done their homework than a

student who did not bring a calculator? Give evidence for your answer.

Percent who didn’t bring a calculator and did do their homework:

Yes, 70% of students who brought a calculator also did their homework while only 57% of

students who didn’t bring a calculator did their homework .

Name: CP1 Math 1 Final Exam June 19, 2018

Class (please circle): Hadden/A Hadden/E Tracy/C Tracy/F Kelly/H page 7

6. a. For the triangles shown in the first picture, identify an additional pair of equal parts

that would guarantee ABC DEF.

or any other pair of corresponding sides

b. Using the given coordinates, show that

the pair of parts you chose in part a

is equal.

c. Again using the coordinate picture, fill in the following mapping notation for the

transformation from ABC to DEF.

(x, y) a (x+5, y-2)

CP1 Math 1 Final Exam June 19, 2018 page 8

7. The beginning of a sequence of figures is shown below.

a. Continue the pattern by drawing Figure 5.

b. Find a function formula for f(n), the number of black squares in Figure n.

Show or explain how you get your answer.

Each figure increases by 3. Working backwards you can determine that “Figure 0” would have

2 squares.

Thanks for a great year. Happy summer!