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PATI Math Placement Test
1. What is the definition of complementary angles?
2. Solve the equation for x:
If y = 7x-1, then x=___________.
3. If side = 15 and ÐC = 38, what is the length of AC?
4. How would you best describe the transformation between the two graphs below?
5. Find the mean average, median, mode, and range for the following set of numbers:
15, 27, 10, 18, 13, 13, 16, 20, 12, 11, 15
Mean average=___________________
Median=________________________
Mode=__________________________
Range=_________________________
6. Factor the expression:
9 + 2x + 16
PATI Math Placement Test
7.
If = , what can you conclude?
8.
What is the value of y in the system of equations:
x – 2y = 3 and –x + y=7 ?
9.
Branson opens a bank account with a starting balance of $40. Each month he adds an additional $10.
How much money will Branson have in his account at the end of one year?
10. What angle is complementary to 92?
11. The third, fourth, and fifth numbers of a sequence are 16, 22, and 28. Which of the following
functions describes the sequence?
a.
b.
c.
d.
12.
f(n) – 6n + 16
f(n) = 6n – 2
f(x) = 3x + 12
f(x) = 12x + 6
c
3
+ =
a
4
13. What is the slope and y-intercept of the equation y = 6x + 8? Provide two answers.
14. A survey was done at school to see how many students struggled the most with each category of
math. The results were as follows:
Algebra: 67
Functions: 12
Geometry: 6
Trigonometry: 58
What is the population proportion for the easiest category of math?
PATI Math Placement Test
15. A cube has a surface area of 216, what is its volume?
16. If the sixth root is equal to -5, then y = ?
17. Solve:
(− 23)
2
18. Multiply the numerator and denominator by y-x2
Then simplify. y+ x2+y2
x2+y2
19. The parallelogram shown below has a perimeter of 44 cm and an area of 64 cm2.
Find angle T in degrees.
5x+4
3x+2
T
20. The probability of flipping a head on a coin is 0.5. What is
the probability you will flip 12 heads in a row?
a.
b.
c.
d.
2.4 x 104
6.0
1.6 x 107
0.5 x 1012
PATI Math Placement Test Answer Key
1. What is the definition of complementary angles?
Complementary angles are either of two angles whose sum is 900.
2. Solve the equation for x:
If y = 7x-1, then x=___________.
x = or x = y/7 + 1/7 7
This is a single equation with two variables, and thus you cannot
determine unique real number solutions for x and y. However,
you can rearrange the equation to express x in terms of y by
adding one to both sides of the equation and then dividing each
term by seven.
3. If side = 15 and ÐC = 38, what is the length of AC?
AC = 19.2
This is a basic trigonometry question, and in order to solve it properly, you will need a scientific or
graphing calculator. The first thing you must do is determine which formula to use based on the
information that is provided. Begin by finding the names of the two sides we are working on. These two
sides are the side we know and the side we are trying to find. In our question, the side we know is
called the opposite. The side we are trying to find is the adjacent. Using the acronym SOHCAHTOA, we
can determine which formula we need to complete our problem. We know have an opposite side, and
we are searching for an adjacent side. Therefore, the formula we need is as follows:
tan38° = Opposite/Adjacent=15/x, where x is the length of AC
Crossmultiplying, x tan38 • o = 15.
Dividing both sides by tan38o gives x = 15/tan38o = 19.2.
AC =19.2
PATI Math Placement Test Answer Key
4. How would you best describe the transformation between the two graphs below?
This is a reflection in the yaxis. You can check this by choosing several points on the first graph and
reflecting them in the yaxis. For example, (1, 1) on the first graph would become (1, 1) when
reflected, (2, 2) would become (2, 2) and so on, producing the second graph. (Note: The same result
could be obtained by rotating the first graph 180o, that is, 180o clockwise.)
5. Find the mean average, median, mode, and range for the following set of numbers:
15, 27, 10, 18, 13, 13, 16, 20, 12, 11, 15
Mean average=___________________ 15.45
Add all values together and divide the total by 11, which is the total number of data points.
Median=________________________ 15
Arrange values from smallest to largest and choose the middle value.
Mode=__________________________ 13 and 15
These are the most commonly occurring numbers in the data set.
Range=_________________________ 17
This is the difference between the largest value, 27, and the smallest value, 10.
6. Factor the expression:
9 + 2x + 16
This expression is not factorable.
7. If = , what can you conclude?
3m = 2p
The crossproducts of equivalent fractions are equal, thus 3m =
2p. It is not possible to find a single, unique solution for m and p.
For example, m = 4 and p = 6 is one possible solution, as is m = 20 and p = 30.
PATI Math Placement Test Answer Key
8.
What is the value of y in the system of equations:
x – 2y = 3 and –x + y=7 ?
y = 10
Notice the coefficients of x in the two equations. This system is most easily solved by elimination.
Adding the two equations leaves us with y = 10, thus, y = 10. You could also solve this system by
substitution. The first equation may be rearranged to give x = 2y + 3. When this expression is
substituted for x in the second equation, we get 2y 3 + y = 7, which gives y = 10 or y = 10.
9.
Branson opens a bank account with a starting balance of $40. Each month he adds an additional
$10. How much money will Branson have in his account at the end of one year
Branson will have $160 in his bank account at the end of one year.
$10 per month x 12 months = $120
$120 plus the original balance of $40 = $160
10. What angle is complementary to 92?
2°
The student must remember that a pair of complementary angles
MUST add up to 90o. Hence:
92 ° + 2° = 90 ° If a student has difficulty comprehending the concept of a negative angle, point out
that the negative sign generally suggests clockwise rotation.
11. The third, fourth, and fifth numbers of a sequence are 16, 22, and 28. Which of the following
functions describes the sequence?
a.
b.
c.
d.
f(n) – 6n + 16
f(n) = 6n – 2
f(x) = 3x + 12
f(x) = 12x + 6
b. f(n) = 6n – 2
Evaluating f(n) = 6n – 2 at n = 3, 4 and 5 gives 16, 22, and 28 respectively. It may be helpful to the
student to clarify that the independent variable in a function may be position of a number in a
sequence. Comprehension may be further assessed by having the student generate other terms in the
sequence (e.g. 1st term is f(1) = 4, etc.)
12.
c
3
+ =
a
4
ac + 12
4a
The easiest common denominator to use in adding these fractions is 4a. Multiplying the first fraction
by unit fraction 4/4 and the second by unit fraction a/a gives both fractions a denominator of 4a, and
+ 12
a total of ac 4a
when the two fractions are added.13. What is the slope and y-intercept of the
equation y = 6x + 8? Provide two answers.
PATI Math Placement Test Answer Key
13. What is the slope and y-intercept of the equation y = 6x + 8? Provide two answers.
m = 6, y-intercept at (0, 8)
The slope of the line is the coefficient of x, which is 6. The yintercept is the
point at which x = 0. So, y = 6(0) + 8 = 8 at the yintercept. There are no other answers for the slope
and yintercept of this line.
14. A survey was done at school to see how many students struggled the most with each category of
math. The results were as follows:
Algebra: 67
Functions: 12
Geometry: 6
Trigonometry: 58
What is the population proportion for the easiest category of math?
6/143 (approximately 0.045 or 4.5%)
Geometry is the easiest category of math for students in this population, as fewer students struggle
with geometry as compared to the other categories. The population proportion of students struggling
with geometry is 6 out of a total of 143 students, and 6/143 = 0.045 or 4.5%.
15. A cube has a surface area of 216, what is its volume?
216 cm3
The volume of a cube is a product of its length, width and height. As all three of these dimensions are
equal for a cube, one must find the length of an edge. A cube has six faces, each of equal area. Thus,
the area of each face is 216 cm2/6 = 36 cm2. A square face with an area of 36 cm2 has a side
length of √36 cm or 6 cm. So, the length of each edge of the cube is 6 cm.
Then, V = lwh = 6 cm x 6 cm x 6 cm = 216 cm3
16. If the sixth root is equal to 5, then y = ?
y = 15 625
If = 6√y = -5, then y = (-5)6= 15 625.
17. Solve:
(− 23)
2
-23
By definition, the square root of 23 is a number that, when multiplied by itself, gives 23.
Thus the square root of 23, when squared, gives 23. This is true regardless of the fact that no real
number, when squared gives a negative quantity. The square root of 23 can be
defined using imaginary numbers.
18. Multiply the numerator and denominator by y-x2
Then simplify. y+ x2+y2
x2+y2
PATI Math Placement Test Answer Key
19. The parallelogram shown below has a perimeter of 44 cm and an area of 64 cm2.
Find angle T in degrees.
5x+4
3x+2
T
T = 34.8o
The unknown quantity x can be found using the perimeter of 44cm. 2(3x + 2) + 2(5x + 4) = 44
simplifies to 16x + 12 = 44, giving a value of x = 2. This gives a length of 5(2) + 4 = 14 cm for the
base. For a parallelogram A = bh, so h = A/b. Thus we can solve for the height, h, as h = 64 cm2/14
cm = 4.57 cm. Now, consider a right triangle constructed by dropping a line from the top left vertex
of the parallelogram perpendicular to the base. That triangle has a height of 4.57 cm which is
opposite angle T and a hypotenuse of length 3(2) + 2 = 8 cm. Thus, sinT = opposite/hypotenuse
= 4.57/8 = 0.571. Using an inverse sine function to find the angle T,
we find that sin1(0.571) = 34.8o.
20. The probability of flipping a head on a coin is 0.5. What is
the probability you will flip 12 heads in a row?
a. 2.4 x 104
b. 6.0
c. 1.6 x 107
d. 0.5 x 1012
a. 2.4 x 104
Each coin flip is independent, meaning that the outcome of the one coin flip does not affect the
probability of the others. The probability of a series of independent events occurring is the product of
the probabilities of the individual events. Thus the probability of 12 heads in a row is
0.512 = 2.4 x 104.