Logic questions
There are 20 problems in a mathematics competition. The scores of each problem are allocated in the following ways: 2 marks will be given for a correct answer, 0 marks will be given for a blank answer or a wrong answer.
Find the minimum number of candidate(s) to ensure that 2 candidates will have the same scores in the competition.
2
How many solutions can a quadratic equation have?
Zero, one, or two
Which field originally drove the development of trigonometry?
Astronomy
How are velocity and acceleration related using calculus?
Velocity is the integration of acceleration; acceleration is the derivative of velocity
There are 6 pieces of white chopsticks, 8 pieces of yellow chopsticks and 10 pieces of blue chopsticks mixed together. If you want to get 4 pairs of chopsticks with same colours in the dark, at least how many pieces of chopsticks are needed to be taken?
10
A father is four times as old as his son, and his daughter is 5 years younger than the son. If the sum of their ages 5 years ago was 70 years, find the present age of the father.
Father: 60
Son: 15
Daughter: 10
If x, y and z are all prime and 4x^y+y^x=z ,
find the minimum value of z.
41
If sin A = b, what is the value of the product sin A · cos A · tan A in terms of b?
b^2
A particle moves such that its velocity v m/s at time t s is
v=6t-t^2
Find the total distance travelled.
36
In a class, every student likes to play either volleyball or badminton. There are 7 students who like to play volleyball, 9 students who like to play badminton, and 4 students like to play both.
How many students are there in that class?
12
Counting from 1 to 10 000, how many numbers are there that have exactly two digit “5”s and only one digit “4” ?
96
If root(5)((x^50+x^60+x^70)/13)=3 , x in R then what is the value of
x^10+x^20+x^30 = ?
39
What is the simplest form of 4sinx(2cos^3x-cosx)?
sin4x
Evaluate
int_0^1e^x/(e^x+1)dx
ln((e+1)/2)
A box contains 100 coloured pens: 40 blue, 30 red, 20 green and 10 yellow. Ivy takes some pens from the box without looking at the colours of the pens. What is the least number of pens she must take so that she has pens with at least 3 colours?
71
Selena’s dessert is stolen, she asked her 4 guests and received replies as follows:
Hera: “David’s stolen it.”
David: “Hera’s stolen it.”
Ruby: “I have not stolen it.”
Steve: “David is lying.”
Given that only one of them had told the truth, who stole Selena’s dessert?
Ruby
If 4^x+10^x=25^x, then what is the exact value of (5/2)^x
(1+sqrt(5))/2
The first two terms of a geometric progression are
1 and tan^2x/3 respectively,
where 0<x<pi/2 .
Find the set of values of for which the progression is convergent.
0<x<pi/3
Evaluate
int1/(1+sinx)dx
tan x - sec x +C
Find the number of different selections of 4 letters from the 9 letters of the word HAPPINESS which contain no Ps and either one or two Ss.
20
John wrote a 4-digit number on a piece of paper and asked Peter to guess it.
Peter asked: “Is the number 4321?”
John replied: “Three digits are correct, the positions of those digits are also correct.”
Peter asked again: “Is the number 6420?”
John replied: “Two digits are correct, but the positions of those digits are both wrong.”
What is the number written by John?
4301
If
(x^12+1)/x^6=6
then what is the value of
(x^36+1)/x^18?
198
If sin(x) = 3/5, find cos(2x)
7/25
The volume of a cube is increasing at the rate of 16 cm3/s. At what rate is its total surface area increasing when the length of an edge is 6 cm?
32/3 cm2/s
Given 8 letters, ABCDEFGH, how many ways can you arrange them such that each letter is not in its original spot?
14833