Trigonometry
The solution to the equation
tan(x)=-1, -pi/2lex<pi/2
in radians.
What is x=-pi/4?
The value of k such that the line through
(2,3) and (4,k)
is perpendicular to y=2x+5
What is k=2 ? (slope must be -1/2
The exact solution to the equation e^(2x)=7 . (No calculator)
What is (ln7)/2 ?
The common ratio of the geometric sequence: 27, -9, 3, -1, ...
What is -1/3?
The number of possible license plates if they must consist of 3 letters followed by 3 digits and repetition is allowed?
What is 17,576,000 (26^3)(10^3)
The value of tan(theta) if theta is in QIII and sin(theta)=-4/5 .
What is tan(theta)=4/3?
The equation of a quadratic function (in standard form) with x-intercepts at x=-1 and x=3 , and passing through (0,-6) .
What is f(x)=2x^2-4x-6
log_5x in terms of ln using the change-of-base formula.
What is (lnx)/ln5 ?
The series 3 + 6 + 9 + 12 + 15 in sigma notation starting with n=1
What is sum_(n=1)^5(3n) ?
The number of possible hands containing 1 Ace and 2 Twos when you are dealt a 5-card hand.
What is 22704? ((._4C_1)(._4C_2)(._44C_2))
`The expression sin(x)cot(x)sec(x), fully simplified
What is 1?
The coordinates of the point(s) where the line y=3x-1 intersects the parabola y=x^2+1 .
What are (1,2) and (2,5) ?
The continuous yearly decay rate (r) , of a radioactive substance with a half-life of 10 years.
What is r=(ln(1/2))/10approx-0.0693 or -6.93%
1/2=e^(10r)
The 20th term of the sequence defined recursively by t_1=4 and t_n=t_(n-1)+3
What is 61? (t_20=4+3*19)
The probabiity of landing on Green when spinning a spinner divided into three regions (Red, Green, and Blue) with a probability of landing on Red =1/3 , and a probabiity of landing on Blue
=2/5
What is 4/15 ? (or approx26.7%)
(The total probabilities of all outcomes must add to 1)
The exact length of side c in a triangle where a=5, b=8 and mangleC=60°.
What is 7? (sqrt(25+64-2(5)(8)(0.5))=sqrt49)
The equation of a bridge arch in the shape of a downward opening parabola, 100 feet wide and 25 feet high at its center with vertex placed at (0,25).
What is y=-1/100x^2+25?
The solution to the equation:
ln(x-3)-ln(x+1)=ln2
What is NO SOLUTION? (x=-5 is extraneous)
The fractional equivalent of the repeating decimal 0.232323... using infinite geometric series.
What is 23/99 ? S=.23/(1-.01)
The probability of getting exactly 4 correct, guessing randomly, if a test has 5 multiple-choice questions with 4 options each.
What is 15/1024( (._5C_4)(0.25)^4(0.75)^1)
The solutions to:
2sin^2xcosx-cosx=0 in the interval 0lex<2pi.
What are x=pi/2, (3pi)/2 or x=pi/4, (3pi)/4, (5pi)/4, (7pi)/4
The number of total participants needed to maximize revenue if a tour operator charges $200 per person for a trip when 30 people sign up, and for each additional person who signs up past 30, the price for everyone drops by $2.
What is 65 people (yielding a maximum revenue of $8,450)
R(x)=(30+x)(200-2x)
maximum at vertex x=-b/(2a)=-140/(2(-2)=35.
R(35)=(30+35)(200-70)=65(130)=8450
5^(log_5(2)+log_5(3) evaluated without a calculator
What is 6?
The sum of the first n terms of an arithmetic sequence if t_1=5, t_n=45, and d=4
\(a_1 = 5\), \(a_n = 45\), and the common difference \(d = 4\).
What is 275? (S_11=(5+45)(11/2))
The exact probability of selecting more red slices than green slices when randomly selecting 4 slices all at once from a box containing 5 red apple slices and 7 green apple slices.
What is 75/495?
=(('_5C_3)('_7C_1)+('_5C_4)('_7C_0))/('_12C_4)