Download Sample Questions - Jones County Junior College

Jones County Junior College
Bobcat Math League
Pre-Season Practice Session
Sample Questions
Directions: Answer each of the following 10 multiple choice questions without the use of a calculator.
You will have 60 minutes to complete this quiz.
1. A basketball team shoots at the basket 50 times during a game and makes 23 baskets. What is their
shooting percentage for the game?
A. 23%
B. 46%
C. 73%
D. 100%
2. If a child has 6 shirts, 7 pairs of pants and 4 pairs of socks to wear to school, and you were told to list
every possible combination on a piece of paper, you would probably draw a __?__ .
A. stem-and-leaf plot
B. bar graph
C. box-and-whisker plot
D. tree diagram
3. Which of these satisfies the equation | x + 4 | = 8 ?
A. -12
B. -4
C. 2
D. 12
4. What is the volume of a box 4 inches by 5 inches by 6 inches?
A. 15 in3
B. 29 in3
C. 34 in3
D. 120 in3
5. Find the velocity at t = 2 seconds of a particle whose equation of motion is y = 5t2 + 7t – 10.
A. 24 units/sec
B. 27 units/sec
C. 82 units/sec
D. 526 units/sec
6. 35 = ?
A. 35
B. 81
C. 125
D. 243
7. In which quadrant of the x-y plane are both x and y always less than zero?
A. first
B. second
C. third
D. fourth
8. (4x2yz) (5xy3z2) = ?
A. 9x3y4z3
B. 20xy2z
C. 20x3y4z3
D. 45x2y3z2
9. – ln (28) = ln ?
A. 1/28
B. -1/28
C. 28
D. -28
10. An employee at a clothing store gets a 25% discount on everything he buys there. What was the
original price of his purchase if his discounted total is $45?
A. $33.75
B. $56.25
C. $60.00
D. $70.00
Pre-Season Practice Session
Sample Question Answers
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Jones County Junior College
Bobcat Math League
Regular Season Match
Sample Questions
Directions: Answer each of the following 20 multiple choice questions without the use of a calculator.
You will have 60 minutes to complete this quiz.
1. You have a quarter, a dime, a nickel and a penny in your pocket. What is the probability that the first
two coins you pull out will add up to exactly 15 cents?
A. 1/2
B. ¼
C. 1/6
D. 1/12
2. In 2011, the world’s population reached 7 billion people. The Earth has a land surface of about 1.4 x
108 square kilometers. If all of the Earth’s land surface were evenly divided among the world’s
population, how many square kilometers would each person get?
A. 5
B. 50
C. 500
D. 5,000
3. For an angle X°, sine X = 0.4 and cosine X = 0.9. What is cosine 2X° ?
A. 0.44
B. 0.65
C. 0.72
D. 1.8
4. A triangle has a perimeter of 87. Its longest side is 15 greater than its second-longest side and 6 more
than twice its shortest side. How long is the longest side?
A. 18
B. 27
C. 42
D. 66
5. The polynomial expression (x2 – x – 20) / (x2 + 14x + 45) is undefined at x = ?
A. -5 and -9
B. -4 and -5
C. 1 and 5
D. 5 and 9
6. A sphere has a radius of 9 units. The ratio of the sphere’s volume to its surface area is:
A. 1 to 3
B. 1 to 12
C. 12 to 1
D. 3 to 1
7. What is the acceleration of a particle at time t = 2 seconds if the particle is on the path
x = 5t3 – 9t2 + 14t – 12 ?
A. -34
B. 20
C. 30
D. 42
8. (85) / (162) = ?
A. 128
B. 64
C. 32
D. 2
9. The base of a parallelogram has two corners at (2, 8) and (6, 14). If the height of the parallelogram
is 12 , what is the area of the parallelogram?
A. 2 13
B. 2 39
C. 4 13
D. 4 39
10. What is the radius of the circle with equation x2 – 8x + y2 + 6y = 24 ?
A. 3
B. 4
C. 7
D. 14
11. A 3-by-3 matrix has a first row of 1, 2, 3, a second row of 4, 5, 6 and a third row of 7, 8, 9. You try to
find the determinant by expanding across the top row. What number should be multiplied by the 1?
A. -3
B. -6
C. 3
D. 6
12. 8.50 is the third-largest of a sequence of 6 decimal numbers, where the difference between a number
and its next largest number is always the same and the 6 numbers sum to 57.87. Give the interval between
each number.
A. 2.29
B. 5.21
C. 6.87
D. 11.09
13. Which pair of binomials does NOT multiply together to give 12y2 + 30y + 12 ?
A. (12y + 6) (y + 2)
B. (6y + 3) (2y + 4)
C. (4y + 2) (3y + 6)
D. (2y + 1) (6y + 6)
14. For a 7-24-25 right triangle where angle X is opposite from the height of 24, what is secant X ?
A. 25/7
B. 7/25
C. 25/24
D. 7/24
15. The circumference of a circle in inches is 4 times the circle's area in square inches. What is the
diameter of the circle ?
A. ¼ in.
B. ½ in.
C. 1 in.
D. 2 in.
16. If g (x) = 3x2 - 8x + 9, then g (g (4) ) =
A. -41
B. 25
C. 625
D. 1,684
17. If y2 = 4x, then dy/dx =
A. 4x
B. 2/y
C. 2
D. 4
18. The Cartesian point (3, 4) has the polar coordinates:
A. (5, 36.9°)
B. (5, 53.1°)
C. (25, 36.9°)
D. (25, 53.1°)
19. Line Z contains the points (3, 7) and (5, 21). The line perpendicular to line Z that contains (7, -2) has
the equation:
A. y = 7x - 51
B. y = 7x - 14
C. y = - 1/7x + 1
D. y = - 1/7 x - 1
20. In 1974, 90,000 foreigners immigrated to California. By 2002, that number had risen to 286,000. If
the straight line between 1974 and 2002 were extended, how many foreigners would immigrate to
California in 2012?
A. 196,000
B. 356,000
C. 376,000
D. 482,000
Regular Season Match
Sample Question Answers
1. You have a quarter, a dime, a nickel and a penny in your pocket. What is the probability that the first
two coins you pull out will add up to exactly 15 cents?
A. 1/2
B. ¼
C. 1/6
D. 1/12
[2 x (1/4 x 1/3) = 2/12]
2. In 2011, the world’s population reached 7 billion people. The Earth has a land surface of about 1.4 x
108 square kilometers. If all of the Earth’s land surface were evenly divided among the world’s
population, how many square kilometers would each person get?
A. 5
B. 50
C. 500
D. 5,000
(7 x 109 / 1.4 x 108)
3. For an angle X°, sine X = 0.4 and cosine X = 0.9. What is cosine 2X° ?
A. 0.44
B. 0.65
C. 0.72
D. 1.8
[(0.9)2 - (0.4) 2]
4. A triangle has a perimeter of 87. Its longest side is 15 greater than its second-longest side and 6 more
than twice its shortest side. How long is the longest side?
A. 18
B. 27
C. 42
D. 66
[x + x – 15 + ½ (x – 6) = 87, so 2.5x = 105]
5. The polynomial expression (x2 – x – 20) / (x2 + 14x + 45) is undefined at x = ?
A. -5 and -9
B. -4 and -5
C. 1 and 5
D. 5 and 9
(where denominator = 0)
6. A sphere has a radius of 9 units. The ratio of the sphere’s volume to its surface area is:
A. 1 to 3
B. 1 to 12
C. 12 to 1
D. 3 to 1
[4/3 π r3 / 4π r2 = 1/3 r, so 1/3 x 9]
7. What is the acceleration of a particle at time t = 2 seconds if the particle is on the path
x = 5t3 – 9t2 + 14t – 12 ?
A. -34
B. 20
C. 30
D. 42
(second derivative gives 30t – 18)
8. (85) / (162) = ?
A. 128
B. 64
C. 32
D. 2
(512/4)
9. The base of a parallelogram has two corners at (2, 8) and (6, 14). If the height of the parallelogram
is 12 , what is the area of the parallelogram?
A. 2 13
B. 2 39
C. 4 13
D. 4 39
(base x height)
10. What is the radius of the circle with equation x2 – 8x + y2 + 6y = 24 ?
A. 3
B. 4
C. 7
D. 14
( 49 )
11. A 3-by-3 matrix has a first row of 1, 2, 3, a second row of 4, 5, 6 and a third row of 7, 8, 9. You try to
find the determinant by expanding across the top row. What number should be multiplied by the 1?
A. -3
B. -6
C. 3
D. 6
(45 – 48)
12. 8.50 is the third-largest of a sequence of 6 decimal numbers, where the difference between a number
and its next largest number is always the same and the 6 numbers sum to 57.87. Give the interval between
each number.
A. 2.29
B. 5.21
C. 6.87
D. 11.09
[x + 2A = 8.50 and 6x + 15A = 57.87]
13. Which pair of binomials does NOT multiply together to give 12y2 + 30y + 12 ?
A. (12y + 6) (y + 2)
B. (6y + 3) (2y + 4)
C. (4y + 2) (3y + 6)
D. (2y + 1) (6y + 6)
14. For a 7-24-25 right triangle where angle X is opposite from the height of 24, what is secant X ?
A. 25/7
B. 7/25
C. 25/24
D. 7/24
(cos X = 7/25)
15. The circumference of a circle in inches is 4 times the circle's area in square inches. What is the
diameter of the circle ?
A. ¼ in.
B. ½ in.
C. 1 in.
D. 2 in.
(πd = 4πr2, so 2r = 4r2 and 1 = 2r, so r = ½ and d = 1)
16. If g (x) = 3x2 - 8x + 9, then g (g (4) ) =
A. -41
B. 25
C. 625
D. 1,684
[g(25)]
17. If y2 = 4x, then dy/dx =
A. 4x
B. 2/y
C. 2
D. 4
(2y dy/dx = 4)
18. The Cartesian point (3, 4) has the polar coordinates:
A. (5, 36.9°)
B. (5, 53.1°)
C. (25, 36.9°)
D. (25, 53.1°)
(sin-1 0.8 = 53.1° and is findable even without a calculator because it must be > 45°)
19. Line Z contains the points (3, 7) and (5, 21). The line perpendicular to line Z that contains (7, -2) has
the equation:
A. y = 7x - 51
B. y = 7x - 14
C. y = - 1/7x + 1
D. y = - 1/7 x - 1
(slope is negative reciprocal of 7; plug in (7, -2))
20. In 1974, 90,000 foreigners immigrated to California. By 2002, that number had risen to 286,000. If
the straight line between 1974 and 2002 were extended, how many foreigners would immigrate to
California in 2012?
A. 196,000
B. 356,000
C. 376,000
D. 482,000
[90,000 + (7,000 x 38)]
Jones County Junior College
Bobcat Math League
Post Season
Sample Questions
The following is a sample of questions used during past Jones County Junior College math
competitions. Feel free to use these questions as a guide in preparing for this year’s post season
competitions. However, keep in mind that these are a sample of previous year’s questions — the
questions for this year’s math competition have been updated. Questions for the competition are
based upon topics ranging from percents, fractions, probability, statistics, algebra, geometry,
trigonometry, pre-calculus, to calculus.
How many faces does a decahedron have?
answer: 10
In the spring of 2009, the total number of reported swine flu cases in the U.S. was doubling every 2
weeks. If the country reported 5,000 total cases on May 14, how many total cases had been reported after
6 more weeks?
answer: 40,000 cases (doubled 3 times in a 6-week period)
What is the least number of x-intercepts that the function f x   6 x 4  5x 2  9 can have?
answer: zero or none
You decide to put away money to buy a $30,000 car 8 years from now when your current car stops
working. Calculate how much money you must invest at 9% annual return to be able to buy the car at that
point by using the rule of 72.
answer: $15,000 (rule of 72 means money doubles in 8 years at 9%, so half of $30,000)
What mathematical representation uses circles to signify sets, with the position and overlap of the circles
showing set intersections?
answer: Venn diagram
What is the degree of the monomial 6a 7bc4 ?
answer: 12
If f of x = 3x2 + 20, calculate the inverse of f.
answer: y =
( x  20)
3
What is the perimeter of a 9 foot by 8 foot rectangle?
answer: 34 feet
What famous scientist and mathematician was the author of the book “Elements?”
answer: Euclid
What is the domain of f x   2 x  3 ?
answer: all real numbers
Give the contrapositive of this conditional: “If a coach has won the Super Bowl, he is a good football
coach.”
answer: “If a man is not a good football coach, he has not won the Super Bowl.”
(accept clearly equivalent answers)
Find the exact value of sin 270 .
answer: -1
If a parallelogram has one angle that is 38°, give the value of that angle’s consecutive angle, which is the
same as its supplementary angle.
answer: 142° (180 – 38)
A car is traveling 60 miles per hour. How many miles will it travel in 4 hours?
answer: 240 miles
According to the Rational Roots Test, what integer should be factored to obtain the possible x-intercepts
for the equation y = 2x3 + 4x2 – 38x – 40 ?
answer: -20 (-40 / 2; last coefficient, divided by the first)
3
, determine sec  .
4
5
answer:
4
Given tan 
When finding the inverse of a 2-by-2 matrix, specify the two elements of the matrix that can change
places with each other without changing signs.
answer: top left and bottom right (accept clearly equivalent answers)
Find the values of x and y that satisfy these two equations: 3x – 2y = -23 and -9x + 5y = 65.
answer: x = -5, y = 4 (multiply first equation by 3 and add)
If Emily has $20, and she wants to buy a whole number of watermelons that cost $3.50 each, how many
whole melons can she buy?
answer: 5
Find the limit of the function x 2  5x  3 as x approaches 1.
answer: -1
In a standard deck of 52 playing cards, what is the probability (in lowest terms) that the top card is either
a five or a spade?
answer: 4 /13 [13 spades plus 4 fives minus the five of spades = 16/52 or 4/13]
Factor x 4  16 completely in the real numbers.
answer: x 2  4 x  2x  2


Federal income tax of someone with an income of $40,000 is "$1,500, plus 15% of the amount over
$15,000". How much federal income tax does someone with that income pay?
answer: $5,250 (1500 + [15% of 25,000])
Solve for x :
3x  1  2 .
answer: no solution
Give the median of the set of odd, single-digit whole numbers?
answer: 5
Which trigonometric function equals 1 over the sine?
answer: cosecant
A spinner has equal chances of landing on each number from 1 to 6. How many times would the spinner
be expected to land on 5 in a series of 900 spins?
answer: 150 (1/6 of 900)
The Cartesian Coordinate Plane is divided into quarters. What are these quarters called?
answer: quadrants
Calculate the area of a triangle whose three vertices are at the points (12, 6), (6, 0) and (12, 0).
answer: 18 (1/2 x 6 x 6)
The number of degrees in each interior angle of a regular polygon with n sides can be expressed as 1/n,
times the quantity (180n - 360). In the limit, what is the measure of each interior angle of a polygon with
an infinite number of sides?
answer: 180° (180 - 360/n as n approaches infinity)
A car drives north for 6 miles and then turns east and drives 8 miles. How far in miles is the car from the
starting point?
answer: 10 miles
Divide the polynomial (6x3 + 23x2 - 83x - 30) by the term (2x - 5).
answer: 3x2 + 19x + 6
Give the two vertices of the hyperbola whose equation is x2/25 - y2/9 = 1.
answer: (-5, 0) and (5, 0)
Is
2 less than or greater than
answer: greater than
Simplify the expression
answer: 3xy
3
3
4
?
3
27 x5 y 3 .
x2
What is the vertical asymptote of the function f ( x) 
answer: x  3
1
?
x3
A 14 by 12 matrix has how many elements?
answer: 168
Let  be an angle in standard position. Give the quadrants in which the terminal side of  may lie if
cos  0 .
answer: quadrants I and IV
How many two-digit numbers are evenly divisible by 5?
answer: 18
A 2-by-2 determinant has a top row of 6 and 5 and a bottom row of 4 and 7. In the inverse of the matrix,
what integer goes in the bottom-left corner and is divided by the matrix's determinant of 22?
answer: -4 (opposite of 4)
If Rob can finish a job in 3 hours, and John can finish the same job in 6 hours, how fast can they finish it
working together?
answer: 2 hours
Calculate the polar coordinates for the rectangular-coordinate point (1, √3).
answer: (2, π/3) (length of hypotenuse is 2, angle is 60°)
Change 0.31 % to a decimal number.
answer: 0.0031
What is the conjugate of the denominator of the expression
3
?
x 2
answer: x  2
A group of 5 students takes a test and receives a mean score of 70. The students scored 2x + 6, x + 19,
2x - 2, x + 24 and 2x - 17, respectively. Give the value of x.
answer: 40 [sum of all 5 = 350]
Steve has a bag with 20 jelly beans – 8 red, 5 yellow and the rest green. If he removes two jelly beans
from the bag without looking, what is the total probability, in lowest terms, that he will end up with a red
one and a yellow one?
answer: 4/19 [(8/20 x 5/19) + (5/20 x 8/19)]
Which algebraic quantity used to determine the number of distinct roots for a quadratic polynomial equals
b 2  4ac ?
answer: discriminant
In how many ways can the four students in Ms. Carson’s piano class be arranged for an upcoming recital?
answer: 24
A bacteria colony doubles its number of bacteria every hour. At 4:00 PM, the bacteria colony has 128,000
bacteria. At 8:00 AM that morning, how many bacteria did the colony have ?
answer: 500
Give the result when the quantity (a - b) is divided into the quantity (a cubed minus b cubed).
answer: a squared plus ab plus b squared (a2 + ab + b2)