NIGERIAN MATHEMATICS OLYMPIAD (NIMO) PRACTICE QUESTIONS (JUNIOR AND SENIOR CATEGORY) IN PREPARATION OF 2017/2018 COMPETITIONS (FIRST ROUND AND SECOND ROUND)

ATTEMPT THE FOLLOWING QUESTIONS:

Find n if nC1 = nC2

Find the maximum area of a rectangle whose perimeter is 100cm.

Find the values of b if the equation x^2 + bx + 9 = 0 has equal roots

If x is the length of one side of a regular pentagon, find the area of the pentagon in terms of x

If a and b are the roots of the equation 3x^2 + 7x + 5 = 0, find the equation whose roots are a^3 + b^3.

Given that 1 + 2 + 3 + 4 +…+n = n(n + 1)/2, find the sum of the 5th n natural numbers.

If 100 straight lines are drawn on a board, what is the maximum number of intersections between them?

Evaluate (9^27) mod 11.

6 fair coins are tossed once. Find the probability of obtaining at least 4 heads.

Find the mean of 1,2,3,4,5,6,…,n and hence find the mean when n = 29.

Solutions

nC1 = n!/(n-1)!1! and nC2 = n!/(n-2)!2!. This implies that n!/(n-1)!1! = n!/(n-2)!2! Reducing the equation leads to 2n-4 = n-1 therefore n=3.

let l,b and A represent the length,breath and area of the rectangle respectively. –> 2(l+b) = 100 and lb=A. This implies l+b = 50 and lb =A. Solving simultaneously l=50-b —>b(50-b) = A —>50b – b^2 =A….Since A is at maximum then A’ is 0–> 50 – 2b = 0 –> b = 25. Since l+b=50 and b=25, l=25. Therefore the rectangle will have a maximum area when it is a square of side length 25cm.

Since the equation has equal roots then b^2 = 4 x 1 x 9=36–> b=+6

Coming soon…

See the answers to NIMO 2017/2018 written on Nov 18 2017 here

Pls be fast