Download 2017 Placement Test Cover Letter

ST. MARK’S MATH PLACEMENT
Dear new St. Marker,
Welcome! In order to find the most appropriate math placement for you, I need you to take the
enclosed placement test. This test is meant to be taken by students coming from a variety of
backgrounds, so answer the questions that you can, and show your work on everything, so that I can
see your reasoning.
Please mail your completed placement test to the Admissions Office by May 19, 2016.
The course usual course progression through Precalculus is as diagrammed below. Usually after
Precalculus, students select from Calculus and other theoretical mathematical courses, or applied
mathematics courses such as Mathematical Modeling and Advanced Statistics.
Precalculus
Algebra II
Geometry
Algebra I
Directions
The attached placement test will be used as one factor in helping us to judge your appropriate math placement.
•
•
•
•
Please take the test without help from anyone.
Show your answers and your work on the test paper or on attached paper.
Be sure your name is on all sheets of paper that you return.
Please take your time – there is no time limit!
If you have completed
(or are currently taking)…
…then complete the following sections.
Pre-Algebra
Pre-Algebra Section
Algebra I
Algebra I Section
Geometry
Algebra I and Geometry Sections
Algebra II and beyond
Algebra I, Geometry and Algebra II Sections
There may be problems on the placement test that touch on unfamiliar material. Do your best to solve the
problems correctly, take your time, and show all your work clearly.
If your work on this test and your previous work in mathematics indicate that you are a candidate
for an Honors class in the fall, I will notify you about taking an additional Honors Placement Test,
which will be given during orientation.
Thank you,
Allyson Brown, Mathematics Dept. Chair
[email protected]
ST. MARK’S MATH PLACEMENT
PRE-ALGEBRA SECTION
Complete this section only if you have not taken Algebra I.
Name _________________________________
Form you will enter at St. Mark’s _________
For questions 1-17, perform the indicated operations without using a calculator and simplify your
answers.
1.
7 5
−
12 12
2.
1 3
+
6 4
3.
5 3
×
6 20
4.
2+3× 4
5.
7 12 × 3 23
6.
7 12 ÷ 56
7.
−5 + 10
8.
−5 − 10
9.
−5 + −10
10. −5 − −10
11.
13.
2 35
+
3 23
62.5
× 1.2
⎛ 38 ⎞
15. ⎜ ÷ 5⎟ ÷ 1 43
⎝ 5
⎠
12.
7 12
− 3 23
5 2
+
14. 6 3
3
8
16. 6 × ( −2 ) ÷ ( −3) + ( −4 )
Pre-Algebra Section, Page 1 of 2
Name _________________________________
⎛ 1⎞
17. ⎡⎣6 − ( −3) ⎤⎦ × ( −2 ) × ⎜ − ⎟
⎝ 18 ⎠
18. 40 is 25% of what number?
19. 40 is what percent of 25?
20. 30 is what percent of 2500?
For questions 21-23, solve for x.
21.
5 15
=
2 x
22.
150 − x
= 12
11
23. 9x = 84 + 2x
For questions 24 and 25, find the value if x = 3 and y = 2
24. xy 2
25.
(x + y )
2
26. A tower casts a shadow 270 ft. long and, at the same instant, a boy 5 12 ft. tall casts a shadow
11 ft. long. How high is the tower?
27. A board 33 ft. long and weighting 18 pounds is cut into two pieces. One piece weighs 6
pounds. How long is the other piece?
28. Mr. Bemis had $2500 in his savings account and Ms. Elkins had $4500 in hers. The interest
rate for both accounts was the same. If Mr. Bemis received $125 in interest last year, how
much did Ms. Elkins receive?
Pre-Algebra Section, Page 2 of 2
ST. MARK’S MATH PLACEMENT
ALGEBRA I SECTION
Complete this section if you have completed (or are currently taking) Algebra I.
Name _________________________________
I.
II.
Form you will enter at St. Mark’s _________
If a = 2 and b = −3 evaluate the following. Please simplify your answers.
a + 2b
1. 3a 2 − b
2.
a − b2
Solve for x.
3.
3x − 7 = x − 11
4.
5x + 3 ( x − 2 ) = 15 − ( 7 − x )
5.
4x 2 = 12x
6.
( x + 3)
7.
30
5
+2=
x −3
x −9
8.
2=3 x −x
9.
2x 2 − 5x + 1 = 0
2
2
= 16
Algebra I Section, Page 1 of 3
Name _________________________________
III.
Simplify.
10.
(x + y )
3x − 2 y
⋅ 2
11.
4x + 4 y 3x + xy − 2 y 2
2x x − 1
−
3
2
12. Expand ( 2x − 5 y )
2
2
IV.
13. Find an equation for the line through the point (1, -6) with slope -2.
V.
Simplify without a calculator. Leave your answer in simple radical form. You may use a calculator
to check.
14. 2 5 ⋅3 5
15.
18 + 2
VI.
16. Solve the system of equations for (x, y).
2x + 3 y = 12
x −4 y =5
VII.
17. The difference between two numbers is 8. Five times the smaller number is 4 more than
three times the greater. What are the numbers?
18. Given the rectangular box with dimensions 5 cm by 5 cm by 4 cm, as
shown, find its total surface area. Include units in your answer.
4
5
5
Algebra I Section, Page 2 of 3
Name _________________________________
VIII.
Graph. Please include a scale or label significant points.
19. y = 2x − 4
21. y = x 2 − 2x − 8
20. x + 2 y = 4
IX.22. Write an equation that would produce
this graph:
4
1
-4
4
-4
X.
23. Given the sequence of patterns as
drawn,
a. Sketch and count F5
b. Give a rule for Fn, the nth
pattern in the sequence.
F1 = 3
F2 = 5
F3 = 7
F4 = 9
F5 =
Algebra I Section, Page 3 of 3
ST. MARK’S MATH PLACEMENT
GEOMETRY SECTION
Complete this section if you have completed (or are currently taking) Geometry.
Name _________________________________
Form you will enter at St. Mark’s _________
1. Find the exact volume and surface area of a right regular hexagonal pyramid whose base edge
is 6 and lateral edge is 10.
2. Two perfume bottles are similar. The volume of the large one is 27oz and the small one is
8oz.
a. If the smaller one is 4 inches tall, how tall is the larger one?
b. The label for the large one is 6 square inches, how large is the label for the smaller
one?
Geometry Section, Page 1 of 3
Name _________________________________
3. Algebraically, determine what kind of quadrilateral has vertices A ( 2,6) , B ( 9,7) , C ( 4, 2 )
and D ( 3,1) .
Geometry Section, Page 2 of 3
Name _________________________________
4. Explain or write a proof for the following: Area△ABD = Area△DBC where D is the
midpoint of AC .
B
A
D
C
Geometry Section, Page 3 of 3
ST. MARK’S MATH PLACEMENT
ALGEBRA II SECTION
Complete this section if you have completed (or are currently taking) Algebra II.
Name _________________________________
Form you will enter at St. Mark’s _________
A. Without a calculator, solve the following for x.
1.
3
(
(
)
5− x +1 − 7 = 5− x + 6
x −2
2.
2 64
3.
x −2−
)
⎛ 1⎞
= 8⎜ ⎟
⎝ 4⎠
x +1
4 − x2
= 3x + 7
x +2
B. Simplify the following. Your answer should have no negative exponents.
−5
−1
−3
4.
−2a −2 + a 2 a + a 2 ⋅a 2
5.
⎛ 3x 2 y 7z −2 ⎞
⎜⎝ 12xy 8z 5 ⎟⎠
−2
Algebra II Section, Page 1 of 2
Name _________________________________
C. Without a calculator, write the following as one logarithm or as a number.
6.
log 50 − log 5 + log 1
7.
2 log 12 6 + log 12 32 − log 12 8
8.
log a 3
log a 2
D.
9. A is an angle of a right triangle.
5
If sin A = , find cos A
13
E.
10. A population of bacteria is doubling every 6 hours. If there are currently 400 grams of the
bacteria, how much will there be in two days?
Algebra II Section, Page 2 of 2