LTP Math Jeopardy - D (650+ difficulty)

Linear & Non-linear Functions

100

The function f is defined by f(cx)=4x+10 for all values of x, and c is a positive constant.

If f(5)=71, what is the value of  c ?

 \frac{20}{61} 

200

The functions f and g are defined by the given equations, where x\ge0. Which of the following equations displays, as a constant or coefficient, the maximum value of the function it defines, where  x\ge0?

I.  f(x)=15(0.216)(0.6)^{x-3} 

II.  g(x)=15(0.6)^{x+1} 

A. I only
B. II only
C. I and II
D. Neither I nor II

A. I only

300

The function f is defined by f(x)=\frac{3}{(x-1)(x+1)} for all values of x such that x!=+-1.

The graph of y=f(x) in the xy-plane is reflected over the line y=x.

Which of the following points must the reflection of the graph of y=f(x) pass through?

A. (0,-3)
B. (2,1)
C. (-3,1)
D. (1,-2)

D. (1,-2)

400

The function g is defined by g(x)=\frac{\abs{2x}}{b}-1, where b<0.

What is the product of g(4b) and g(7b) for b<0?

135

500

 f(x)=\frac{x^2-x-a}{x^3-x-b} 

The function f is defined by the given equation, where a and b are constants. In the xy-plane, the graph of  y=f(x) passes through the point (0,9), and f(-9)=0.

What is the value of b?

A. 10

B. 9

C. -9

D. -10

A. 10

Geometry

100

The length of a rectangle's diagonal is 3\sqrt{26}, and the length of the shorter side of the rectangle is 3. What is the perimeter of the rectangle?

A.  18 

B. 6+6\sqrt{26} 

C. 36 

D.  45\sqrt3 

C. 36

200

A line intersects two parallel lines, forming four acute angles and four obtuse angles. The measure of one of these eight angles is 6x-120°. The sum of the measures of four of these eight angles is k°.

Which of the following could not be equivalent to k, for all values of x?

A. -12x + 1020

B. 12x - 60

C. -24x + 1200

D. 360

A. -12x + 1020

300

In the figure below, AC=CD. The measure of angle \angle EBC is 38°, and the measure of angle \angle ACD is 98°. What is the value of x?

79

400

The area of the triangle below is at least 66 but no more than 72 square units. If y is an integer, what is the sum of all possible values of x?

 \frac{115}{12]  or 9.58\overline3 

500

A circle has center G, and points M and N lie on the circle. Line segments MH and NH are tangent to the circle at points M and N, respectively.

If the radius of the circle is 175 millimeters and the perimeter of quadrilateral GMHN is 6470 millimeters, what is the distance, in millimeters, between points G and H?

3065

Algebra

100

If \frac{2x-5}{7}=\frac{2x-5}{11}, the value of x is between which of the following pairs of values?

A.  -7 and -1 

B.  -1 and 1 

C.  1 and 5 

D.  5 and 11 

B.  -1 and 1 

200

The three sides of a triangle must satisfy the property that the sum of any two must exceed the third. If two sides of a triangle are 5 and 9, which inequality correctly represents the possible lengths for the third side of the triangle?

A.  x<14 

B.  5<x<9 

C.  4<x<14 

D.  x<5 or x>9 

C.  4<x<14 

300

A certain monthly WMATA (Washington Metro) pass costs $216 and allows for an unlimited rides of any length. Tickets for individual trips cost $2.75, $4.70, or $6.75, depending on the length of the trip.

What is the minimum number of trips per month for which a monthly pass could cost strictly less than purchasing individual tickets for trips?

33

400

The coordinates of three points on a line in the xy-plane are shown by the table below. What is the value of k?

11

500

A salesperson earns an annual base salary of b dollars per year, plus 15% commission on their total sales during the year. This year, the sales person plans to make enough sales to have their total earnings be at least 4 times and at most 5 times the base salary. Which inequality represents the possible values of total sales s, in dollars, the salesperson can make this year to meet their goal?

A.  3b\les\le4b 

B.  \frac{3b}{0.15}\les\le\frac{4b}{0.15}

C.  4b\les\le5b 

D.  \frac{4b}{0.15}\les\le\frac{5b}{0.15} 

B.  \frac{3b}{0.15}\les\le\frac{4b}{0.15} 

Data Analysis

100

A grove has 8 rows of birch trees and 5 rows of maple trees. Each row of birch trees has 8 trees that are 20 feet or taller and 6 trees that are shorter than 20 feet. Each row of maple trees has 10 trees that are 20 feet or taller and 4 trees that are shorter than 20 feet. What is the probability of selecting a maple tree, given that the tree must be at least 20 feet?

A.  \frac{25}{57} 

B.  \frac{1}{2} 

C.  \frac{10}{18} 

D.  \frac{5}{7} 

A.  \frac{25}{57} 

200

In 2010, the number of crows in a certain murder (group of crows) was found to be 1.47 times the number of crows in that murder in 2005.

If the number of crows in 2005 in this murder is p% of the number of crows in 2010, what is the value of p, rounded to the nearest whole number?

68

300

A distributor buys holiday-themed candles at a wholesale price of $4.00 each. They are then sold at a retail price that is 215% greater than the wholesale price. After the holiday is over, remaining candles are put on sale for 85% off the retail price.

What is the post-holiday sale price of each remaining candle, in dollars?

$1.89

400

Object R and S each travel at a constant speed, and the speed of Object R is half the speed of Object S. Object R covers a distance of 4x inches in y seconds. Which expression represents the time, in seconds, it takes for object S to travel a distance of 24x inches?

A. 16y

B. 12y

C. 6y

D. 3y

D. 3y

500

The table below summarizes a set of data, where a is a positive integer. How much greater is the median than the mean of this data?

 frac{1}{7} 

Miscellaneous

100

How many solutions does the equation (3678x-1000)^2=1 have?

A. None

B. Exactly one

C. Exactly two

D. Infinitely many

C. Exactly two

200

 \frac{8}{d}=\frac{8}{a}-\frac{8}{b}-frac{8}{c} 

The given equation relates the positive variables a,b,c and d. Which of the following is equivalent to a?

A. b+c+d 

B.  8(b+c+d) 

C.  \frac{bcd}{bc+bd+cd}

D.  \frac{bcd}{8b+8c+8d} 

C.  frac{bcd}{bc+bd+cd} 

300

 x^2+14x-10=0 

One solution to the equation above can be expressed as

x=\frac{-14+sqrtK}{2},

where K is a constant. What is the value of K?

236

400

For the function g, the value of g(x) decreases by 13% for each increase in the value of x by 2.

If g(2)=10, which of the following could define g? 

A.  g(x)=10(0.13)^{2x} 

B.  g(x)=10(0.13)^{\frac{x-2}{2} 

C.  g(x)=10(0.87)^{2x-2} 

D.  g(x)=10(0.87)^frac{x-2}{2}

D.  g(x)=10(0.87)^frac{x-2}{2} 

500

Three coins each with diameter 4 cm are arranged as shown on a tabletop. A rubber band is wrapped tightly around them. What is the length of the rubber band, in cm?

A.  4pi+6 

B.  2pi+6 

C.  \frac{4}{3}pi+6 

D.  \frac{2}{3}pi+6 

A.  4pi+6