Free Printable Math Olympiad 2024

Worksheets

Math Olympiad 2024

Total questions: 50

Worksheet time: 3hrs 30mins

Name

Class

Date

At Terb Etrah Middle School, there are 100 6th graders. There are 3 options for electives: Sculpture, Cooking, and Symphony. Each student must take at least 1 elective and can take up to 3 electives. If 51 students take symphony, 53 students take sculpture, 51 students take cooking, and 9 students take all 3 electives, how many students take exactly 2 electives?

(a)

123 + 2023 =

(a)

0.6 is equivalent to...

3/5

6/11

3/7

6/9

What is 6! (where ! stands for factorial)?

(a)

Calculate 1x2x3x4x5x6x0

(a)

Is 23/107 or 23/99 larger?

23/107

23/99

How many distinct positive integer factors does 12 have? (Type only an integer)

(a)

If 6 violins take 30 minutes to play a song how many minutes does it take one violin?

180

If two interior angles of a triangle are 30 and 47 degrees, what is the measure of the third angle? (Type only an Integer)

(a)

10.

What is the volume of a 2 x 3 x 3 rectangular prism? (Type only an integer)

(a)

11.

What is $10^6$ ?

100

1000

10000

1000000

12.

What is $17\times281$ ?

(a)

13.

What is $\frac{3}{7}\div\frac{2}{3}$ ?

$\frac{6}{21}$

$\frac{5}{10}$

$\frac{9}{14}$

$\frac{9}{21}$

14.

What is $3.7+⅘+2$ (in decimals)?

(a)

15.

I am thinking of 2 whole numbers. Their product is 56 and their sum is 15. What is the larger number?

(a)

16.

Lia is eating dumplings. There are 30 dumplings and she is eating at a rate of 4 dumplings per minute. After she has been eating for 3 minutes, her brother Liam who eats dumplings at a rate of 2 dumplings per minute joins her. How many minutes after Liam joins will the dumplings be finished?

1.5 minutes

2 minutes

3 minutes

4.2 minutes

17.

Two dice are thrown. What is the probability that neither of the dice land on an odd number?

1/2

1/3

1/4

1/6

18.

What is the number of solutions in positive integers of 2x+3y=34?

19.

What is the units digit of 3^2023 ?

(a)

20.

Among the integers 1, 2, 3, …120, what is the maximum number of integers that can be selected such that the sum of any two selected numbers is not a multiple of 5?

21.

Ben buys 2 croissants and 3 muffins for $25.00. Jerry buys 4 croissants and 1 muffin for $30.00. What is the cost of a muffin?

3.5

22.

What is the length of the missing side of the right triangle?

(a)

23.

I am thinking of a number. When my number is divided by 5, the remainder is 1. When my number is divided by 7, the remainder is 2. What is the smallest positive number I could be thinking of?

(a)

24.

What is $1+2+3+4+5\times0$ ?

(a)

25.

A shirt that is currently 15% off costs $17. What was the original cost of the shirt?

$20

$32

$40

$45

26.

A phone company offers two options. Option one costs a base fee of $50 and an additional $0.05 for every call. Option two costs a base fee of $40 and an additional $0.07 for every call. At what number of calls will the two options cost the same amount?

(a)

27.

Ana and Banana are meeting up at a cafe. Ana arrives some time between 1 pm and 2 pm. If Banana isn’t there, she waits for Banana for 20 minutes then leaves if Banana still hasn’t arrived. Banana arrives some time between 1:30 pm and 2:30 pm. If Ana isn’t there, she waits for Ana for 20 minutes then leaves if Ana still hasn’t arrived. What is the probability that Ana and Banana don’t meet?

1/3

2/3

2/5

17/42

28.

Let $x=2^5\times3^3\times5^4\times7$ . How many divisors of $x^2$ are less than $x$ ?

(a)

29.

Which of the following is prime?

7777, 7177, 7113, 7775, 7689

7777

7177

7113

7775

7689

30.

Integers a and b are positive. The greatest common factor of a and b is 6. The least common multiple of a and b is 54. What is the product ab?

(a)

31.

Anna draws a card from a standard 52 card deck. What is the probability that it is not a heart or spade?

1/4

1/3

1/2

2/3

32.

6235a78 is divisible by 9. What is a?

(a)

33.

How many ways are there to seat 5 students in a row if 2 of the students don’t want to sit next to each other?

(a)

34.

How many 2-digit numbers contain the digit 8?

35.

What is the measure of the acute angle formed by the hands of the clock at 3:00?

60 degrees

90 degrees

100 degrees

300 degrees

36.

x is a 3-digit number:

-x is divisible by 15

-the difference between the least and greatest digits of x is 2

-x is greater than 300

Find the smallest possible value of x

(a)

37.

The Math Club has 22 members. How many ways can they make a 3 member council?

135

1440

1540

38.

Alvin, Bruce, Claire, and Dil are in a line. Claire is not first. Bruce is behind Dil. Alice is in front of Dil. Claire is not next to Alice. Who is 2nd in line?

Alice

Bruce

Claire

Dil

39.

Harvey has a whole pie. For lunch, he eats ⅓ of the pie. His sister eats ⅖ of what is remaining. In the afternoon, his dog eats all the remaining pie. How much pie did his dog eat?

1/3

2/15

2/5

1/7

40.

On a map, 16 cm represents 24 km. How many km does 18 cm represent?

27 km

28 km

30 km

32 km

41.

Four circles are drawn within a plane. The circles have the following equations:

x^2+(y-2)^2=4

x^2+(y+2)^2=4

(x-2)^2+y^2=4

(x+2)^2+y^2=4

What is the area of the combined region contained within the 4 circles?

$4+16\pi$

$4+6\pi$

$16+8\pi$

$4+4\pi$

42.

Suppose a and b are positive odd integers. Which of the following must also be an odd integer?

$a^2+b^2$ , $a-2b$ , $3a^2+b$ , $a+b$ , $3a+b$

$a^2+b^2$

$a-2b$

$3a^2+b$

$a+b$

$3a+b$

43.

What is the area of the following figure?

(a)

44.

What is the perimeter of the following figure?

(a)

45.

A mochi donut is formed by 6 externally tangent circles of radius 1. What is the area of the shaded region?

$6\ \sqrt[]{3}-2\pi$

$2\ \sqrt[]{3}-4\pi$

$\sqrt[]{3}-6\pi$

$12\ \sqrt[]{3}+3\pi$

46.

Ralph is playing a money game on a machine. There is a 70% chance of losing all your money and a 30% of doubling your money. Ralph starts off with $100. What is the expected value of the money Ralph has after he plays the game?

$30

$40

$50

$60

47.

The first term of an arithmetic sequence is 5. The common difference is 3. What is the 17th term of the sequence?

5, 8, 11, 14…

(a)

48.

Amy has a 8 cm by 5 cm rectangular poptart. There is a 1 cm border between the frosting and the edge of the poptart. Amy takes a semi circle bite of the poptart as shown. What is the area of the frosting (shaded region)?

$18+\sqrt[]{3}-\frac{4\pi}{3}$

$40-\frac{5\pi}{3}$

$18+2\ \sqrt[\ ]{3}-\frac{4\pi}{3}$

$40-\frac{10\pi}{3}$

49.

What is $2\times\left(6+7+8\right)$

(a)

50.

What is the reciprocal of $\frac{1}{6}$ ?

(a)

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Math Olympiad 2024

Total questions: 50

Worksheet time: 3hrs 30mins

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