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Questions ( 18 )
  • Jane has 9 pieces of bite-size chocolate in the fridge. She is going to take at least 1 piece every day, In how many ways can she finish the chocolate?

  • There are 12 points on a circle

    (a) How many triangles can be formed using any 3 points as their vertices?

    (b) How many quadrilaterals can be formed using any 4 points as their vertices?

  • How many numbers from 1 to 200 do not have the digit 2?

  • In the number sequence 1,2,5,13,34,89,..., from the 2nd term onwards, the sum of the number preceding it and the number processing it is 3 times its value , Is the 2002nd term even or odd

  • The sum of 7 consecutive odd number is 1337. Find the odd numbers

  • r, s and t are all positive integers.

    There is are x integers among \(\dfrac{1}{2}\left(r+s\right),\dfrac{1}{2}\left(r+t\right)and\dfrac{1}{2}\left(s+t\right)\)

  • There is a kind of four-digit number, where all the four digits are different. Find the number of such even numbers 2000 to 5000

  • If a is an integer, then (a3 + a2 + 1) is

  • Find a value of n that satisfies the following:

    (a) \(\dfrac{n}{3}\)is a square number

    (b) \(\dfrac{n}{5}\)is a cubic number, A cubic number has the form a x a x a = a3

  • The side of a square is S cm.

    The length and width of a rectangle is (S+3) cm and (S-3) cm respectively. Find the sum of the areas of the square and rectangle

  • Use a simple method to compute 

    12 - 22 + 32 - 42 + ... + 19992 - 20002

  • (a+22) is a square number: (a-23) is another square number . Find the value of a

  • Use a simple method to compute

    \(\dfrac{\left(2002\right)^2}{\left(2001\right)^2+\left(2003\right)^2-2}\)

  • Observe the pattern for multiplication of polynomials

    (x-1)(x+1) = x2-1

    (x-1)(x2+x+1) = x3-1

    (x-1)(x3+x2+x+1) = x4-1

    The result of (x-1)(xn+xn-1+xn-2+...+1) is

  • If a2 + a = 0, then a2001 + a2000 + 7 = 

  • Evaluate 

    \(\left(1-\dfrac{1}{2^2}\right)\left(1-\dfrac{1}{3^2}\right)...\left(1-\dfrac{1}{11^2}\right)\left(1-\dfrac{1}{12^2}\right)\)

  • The result of (234567)2 - 234557 x 234577 is  ... when we use a simple method to compute

  • It is given n is a positive integer . The units digit of n2 is 9 and the units digit of (n+1)2 is 6. The units digit of (n-1)2 is

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