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Math Problem : Middle School Problems

9:32 PM

Muhammad Yusuf , Posted in Math Competitions , 0 Comments

________mL 1) You have a recipe that requires 0.25 L of milk. Your measuring cup is

marked only in milliliters. How many milliliters of milk do you need?

__________ 2) How many of the numbers 11, 21, 31, 41, 51, 61, 71, 81, 91 are prime?

__________ 3) What is the numerical difference between 5/6 and its reciprocal?

__________ 4) When I divide my age by 5, the remainder is 3. Your age is twice my

age. If I divide your age by 5, what will the remainder be?

__________ 5) Your bad hair day began 720 minutes before 7:20 p.m. At what time

did your bad hair day start? INCLUDE ALL NECESSARY UNITS IN YOUR ANSWER.

________ft 6) The area of a square room is 256 square feet. How many feet are in

the perimeter of the room?

__________ 7) A number n is subtracted from 18. The result is four less than n. What

is the value of n?

$_________ 8) The first 12 contestants won an average of $80. The next 20 won an

average of $70. What was the average amount won by all 32 contestants?

__________ 9) Solve: (301 + 302 + 303 + . . . + 325) – (1 + 2 + 3 + . . . 25)

__________ 10) Order from least to greatest: 0.2 ¼ 3.3% 2^-3

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Math Problems : Practices

9:27 PM

Muhammad Yusuf , Posted in Problem Of The Day , 0 Comments

1. Two players, A and B, are playing the following game. They take turns writing down the digits of a six-digit number from left to right; A writes down the first digit, which must be nonzero, and repetition of digits is not permitted. Player A wins the game if the resulting six-digit number is divisible by 2, 3 or 5, and B wins otherwise.

Prove that A has a winning strategy.

2. Prove that nn - n is divisible by 24 for all odd positive integers n.

3. Let a and b be real numbers. Prove that the inequality

holds.

When does equality hold?

4. Let ABCD be a quadrilateral. The circumcircle of the triangle ABC intersects the sides CD and DA in the points P and Q respectively, while the circumcircle of CDA intersects the sides AB and BC in the points R and S. The straight lines BP and BQ intersect the straight line RS in the points M and N respectively. Prove that the points M, N, P and Q lie on the same circle.

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Math Problems : Line and Area

8:55 PM

Muhammad Yusuf , Posted in Math Competitions , 0 Comments

In the diagram, D and E are the midpoints of AB and BC respectively.

(a) Determine an equation of the line passing through the points C and D.

(b) Determine the coordinates of F, the point of intersection of AE and CD.

(c) Determine the area of ΔDBC.

(d) Determine the area of quadrilateral DBEF.

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Problem Of The Day - Filled each circle

8:48 PM

Muhammad Yusuf , Posted in Problem Of The Day , 0 Comments

Each of the integers 1 to 7 is to be written, one in each circle in the diagram. The sum of the three integers in any straight line is to be the same. In how many different ways can the centre circle be filled?

(A) 1 (B) 2 (C) 3

(D) 4 (E) 5

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Math Problems : Grade 7 (2)

10:43 PM

Muhammad Yusuf , Posted in Math Competitions , 0 Comments

1. A 4 x 4 x 4 cube consisting of smaller cubes is painted and then broken apart. How many of the smaller cubes will have exactly 2 painted sides?

(A) 8 (B) 16 (C) 20 (D) 24 (E) 32

2. How many three digit numbers can be constructed using the digits 1, 2, 3, 4 and 5 if the same digit cannot appear twice in a row in any of the numbers?

(A) 60 (B) 65 (C) 80 (D) 120 (E) None of these

3. A rectangular floor is completely covered with tiles whose size is 1 x 2. If the tiles are not cut and do not overlap, the size of the floor cannot be

(A) 4 x 9 (B) 8 x 8 (C) 11 x 7 (D) 16 x 5 (E) None of these

4. How many ways can the number 10 be written as the sum of exactly three positive and not necessarily different integers if the order in which the sum is written does not matter? For instance, 10 = 1 + 4 + 5 is one such sum. This sum is the same as 10 = 4 + 1 + 5.

(A) 5 (B) 6 (C) 7 (D) 8 (E) 10

5. Paul’s calculator can make only two operations: add 12 to the number displayed, or subtract 7 from it. Today, it shows the number 1998. What is the minimal number of steps needed to display the number 2000?

(A) 4 (B) 12 (C) 16 (D) 21 (E) 24

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Math Probems : Grade 7

10:41 PM

Muhammad Yusuf , Posted in Math Competitions , 0 Comments

1. Everyday, Lisa puts her spare change (nickels and dimes) in a piggy-bank. This weekend she decides to count her savings. She finds that she has 72 coins with a total value of $4.95. How many dimes does she have?

(A) 14 (B) 23 (C) 25 (D) 27 (E)

2. Ève has two more marbles than Solène. Solène has twice as many marbles as Steve. Steve has 7 less marbles than Ève. How many marbles do they have between them?

(A) 13 (B) 20 (C) 27 (D) 34 (E) None of these

3. One day in math class, Shelley asks the teacher: “Mr. Nelson, how old are you?” Mr. Nelson responds: “This year I am three times as old as my sister. However, six years ago, I was five times as old as she was.” How old is the mathematics teacher?

(A) 36 (B) 40 (C) 49 (D) 55 (E) None of these

4. Four tennis players enter a tournament. How many different ways can the pairings be made for the first round games?

(A) 3 (B) 6 (C) 8 (D) 12 (E) 24

5. A box contains some apples. Andrée takes ½ of them along with one extra apple. Beatrice takes 1/3 of the remaining apples along but put two apples back in the box and finally, Corrine takes 5/6 of the remaining apples along with one more apple. There are now seven apples left in the box. How many apples were in the box before Andrée took her share?

(A) 16 (B) 44 (C) 110 (D) 140 (E) None of these

6. The “floor” of a fraction is defined to be the largest integer which is not greater than that fraction. For instance, floor (10 / 3) = 3. Evaluate

floor ( floor ( 1000 / 7 ) / (floor ( 71 / 2 ) ).

(A) 4 (B) 5 (C) 7 (D) 10 (E) 500

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