NSF Phase2 Mathcounts Practice SET1

8/10/2019 NSF Phase2 Mathcounts Practice SET1

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Phase II Mathcounts

Practice Questions

SET I

North South Foundation



Problem 1

• Find the area of a triangle with side lengths 13,

14, and 15.



Problem 2

• What is the area of a square with a diagonal

that is 8 units long?



Problem 3

• What is the area of the plane enclosed by the

equation24|||| y x



Problem 4

• Find the number of diagonals that can be

formed by a polygon of 100 sides.



Problem 5

• Sam gives a dinner party to six guests.

What is the number of ways in which theymay be selected from among ten friends, if

two of the friends will not attend the party

together?



Problem 6

• A box contains 2 white balls, 3 black balls

and 4 red balls. What is the number ofways in which three balls can be drawn

from the box so that at least one of the

balls is black?



Problem 7

• How many numbers greater than 1000,

but not greater than 4000 can be formedwith the digits 0, 1, 2, 3, 4, repetition of

digits being allowed?



Problem 8

• The sides AB, BC, CA of a triangle ABC

have 3, 4, and 5 interior pointsrespectively on them. What is the number

of triangles that can be constructed using

these points as vertices?



Problem 9

• If all letters of the word AGAIN are

permuted in all possible ways and thewords so formed (including nonsense

words) are written as in dictionary, then

what is the 50th word?



Problem 10

• A table has 7 seats, 4 being on one side

facing the window and 3 being on oppositeside. In how many ways can 7 people be

seated on the table, if 3 people A, B, C

must sit on the side facing the window?



Problem 11

• There are 10 points in a plane out of which

4 are collinear. Find the number of linesthat can be formed from the ten points.



Problem 12

• We want to make bouquets from 11

different flowers so that each bouquetshould contain not less than 3 flowers.

Find the number of different ways of

forming such a bouquet.



Problem 13

• Find the number of positive integers less

than 30 which are relatively prime with 30.



Problem 14

• On Valentine’s day, every student of a

class sends a card to every other student.The mailman delivers 600 cards. How

many students are there in the class?



Problem 15

• Six “x” marks have to be placed in the

rectangles of the figure given below suchthan each row contains at least one “x”. In

how many different ways can this be

done?



Problem 16

• Find the total number of squares in a

chess board.



Problem 17

• Find the total number of rectangles in a

chess board.



Problem 18

• Given 10 French books, 20 Spanish

books, 8 German books, 15 Russianbooks and 25 Italian books, how many

books must be chosen to guarantee that

there are 12 books of the same language?



Problem 19

Both x and y are positive integers and x > y.

Find all positive integer(s) that xy+x+y=13



Problem 20

• In an isosceles triangle with two sides of

measure AB=AC=17, a line AD measuring16 is drawn from the vertex to the base.

Find BD.

x

A

B D C

NSF Phase2 Mathcounts Practice SET1

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