Quiz about 5/27 Theta Math Club Activity

Question 1

A 1-by-2 rectangle is inscribed in a semicircle with its longer side on the diameter. What is the area of the semicircle?

Accepted Answer

$$\pi$$

Answer

$$\frac{\pi}{2}$$

Answer

$$\frac{2\pi}{3}$$

Answer

$$\frac{4\pi}{3}$$

Answer

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

Question 2

Hint: the area of a triangle with an inscribed circle may also be represented as the product of its semi-perimeter (sum of the triangle's sides divided by 2) and the inradius (what we want) of the inscribed circle

Accepted Answer

10/3

Answer

7/6

Answer

13/5

Answer

59/18

Answer

60/13

Question 3

Hint: connect points B and D to form a right triangle

Accepted Answer

24

Answer

12

Answer

26

Answer

30

Answer

36

Question 4

Question 4.

Accepted Answer

24

Answer

8

Answer

9

Answer

12

Answer

36

Question 5

Question 5.

Accepted Answer

7

Answer

0

Answer

2

Answer

4

Answer

5

Question 6

Which of the following numbers is not a perfect square?

Accepted Answer

$$2^{2017}$$

Answer

$$1^{2016}$$

Answer

$$3^{2018}$$

Answer

$$4^{2019}$$

Answer

$$5^{2020}$$

Question 7

Determine how many two-digit numbers satisfy the following property: when the number is added to the number obtained by reversing its digits, the sum is 132.

Accepted Answer

7

Answer

5

Answer

9

Answer

11

Answer

12

Question 8

Dylan and Franklin are running laps around a 400-meter oval track. They started together, but Dylan has pulled ahead, because he runs 25% faster than Franklin. How many laps will Dylan have run when he first passes Franklin?

Accepted Answer

5

Answer

5/4

Answer

10/3

Answer

4

Answer

25

Question 9

2023 MATHCOUNTS Chapter Spring Round

Accepted Answer

5

Answer

3

Answer

4

Answer

6

Question 10

2023 MATHCOUNTS Chapter Sprint Round

Accepted Answer

$$\frac{\sqrt[]{30}}{8}$$

Answer

3

Answer

$$\sqrt[]{8}$$

Answer

30

Question 11

2023 MATHCOUNTS Chapter Spring Round

Accepted Answer

$$36\sqrt[]{7}$$

Answer

$$36\sqrt[]{5}$$

Answer

36

Answer

24

Question 12

How many real roots can a quadratic function contain?

Accepted Answer

Up to 2

Answer

None

Answer

Up to 1

Answer

Up to 3

Question 13

Which of the following expressions gives the sum of the roots to a quadratic equation with the standard form ax² + bx + c?

Accepted Answer

-b/a

Answer

c/a

Answer

a + b

Answer

b/a

Question 14

Which of the following expressions gives the product of the roots to a quadratic in the standard form ax² + bx + c?

Accepted Answer

c/a

Answer

a/c

Answer

-a/c

Answer

-c/a

Question 15

Which expression gives the explicit formula of an arithmetic sequence? (Note that a₁ represents the first term in the sequence, and d represents the common difference.)

Accepted Answer

$$a_1+d\left(n-1\right)$$

Answer

$$a_1+nd$$

Answer

$$a_1d$$

Answer

None of these expressions are correct.

Question 16

Define a chord (of a circle).

Accepted Answer

A line that connects two points on the circumference of a circle

Answer

A line that touches the circle at a single point

Answer

A line that intersects the circle at exactly one point

Answer

A line that represents double the radius of the circle

Question 17

Decide which expression is true given the intersection of two chords.

Accepted Answer

$$\overline{AP}\cdot\overline{DP}=\overline{BP}\cdot\overline{CP}$$

Answer

$$\overline{AP}\cdot\overline{CP}=\overline{BP}\cdot\overline{DP}$$

Question 18

Let N be the greatest five-digit number whose digits have a product of 120. What is the sum of the digits of N?

Accepted Answer

18

Answer

15

Answer

16

Answer

17

Answer

19

Question 19

Question 19.

Accepted Answer

1

Answer

1/4

Answer

1/3

Answer

1/2

Answer

pi/2

Question 20

A cube with an edge of 3 in. is to be constructed from 27 smaller cubes with 1-inch edges. Twenty-one of the cubes are colored red and 6 are colored white. If the 3-inch cube is constructed to have the smallest possible white surface area showing, what fraction of the surface area is white?

Accepted Answer

5/54

Answer

1/9

Answer

5/27

Answer

2/9

Answer

1/3

Question 21

Question 21.

Accepted Answer

90

Answer

75

Answer

80

Answer

120

Answer

150

Question 22

Given that for the integers n and m, n² + m² is even, which of the following conditions may never be true?

Accepted Answer

n + m is odd

Answer

n and m are even

Answer

n and m are odd

Answer

n + m is even

Answer

None of these are impossible.

Question 23

Question 23.

Accepted Answer

$$28-2\pi$$

Answer

$$16-4\pi$$

Answer

$$16-2\pi$$

Answer

$$28-4\pi$$

Question 24

Question 24.

Accepted Answer

2/3

Answer

1/4

Answer

1/3

Answer

1/2

Answer

3/4

Question 25

It takes 20 minutes for Jerome's mother to drive Jerome to school in rush-hour traffic. When there is no traffic, his mother can drive him 18 miles per hour faster so that Jerome gets to school in 12 minutes. How far in miles is it to school?

Accepted Answer

9

Answer

4

Answer

6

Answer

8

Answer

12

Question 26

Question 26.

Accepted Answer

7

Answer

4

Answer

5

Answer

6

Answer

8

Question 27

Question 27.

Accepted Answer

4/11

Answer

2/15

Answer

11/30

Answer

3/8

Answer

11/15

Question 28

Question 28.

Accepted Answer

5760

Answer

1440

Answer

2880

Answer

182,440

Answer

362,880

Question 29

Evaluate the following series: $$\frac{1}{2019}+\frac{2}{2019}+\frac{3}{2019}+...+\frac{2018}{2019}$$ .

Accepted Answer

1009

Answer

$$1009-\frac{1}{2019}$$

Answer

$$1009+\frac{1}{2019}$$

Answer

1010

Answer

$$1010-\frac{1}{2019}$$

Question 30

If 4²⁰¹⁹ + 7²⁰¹⁹ - N is divisible by 9, where N is a single digit. Find N.

Accepted Answer

2

Answer

1

Answer

4

Answer

5

Answer

8

Question 31

Hint: the area of a sector in degrees is $$\frac{ heta}{360^{\circ}}\pi r^2$$ and the length of a sector is $$\frac{ heta}{360^{\circ}}2\pi r$$

Accepted Answer

2

Answer

1.5

Answer

$$\frac{\pi}{2}$$

Answer

$$\frac{\pi^2}{4}$$

Answer

2.5

Question 32

Alice, Bob, Cindy, David, and Emily sit in a circle. Alice refuses to sit to the right of Bob, and Emily sits next to Cindy. If David sits next to two girls, determine who could sit immediately to the right of Alice.

Accepted Answer

Bob

Answer

Cindy

Answer

David

Answer

Emily

Question 33

A festive number is a four-digit integer that contains one of each of the digits 0, 1, 2, and 4 in its decimal representation. How many festive numbers are there?

Accepted Answer

18

Answer

12

Answer

14

Answer

16

Answer

20

Question 34

Mastery Question

Accepted Answer

6

Answer

4

Answer

8

Answer

10

Answer

12

Question 35

The increasing sequence 2, 3, 5, 6, 7, 10, 11, . . . consists of all positive integers that are neither the square nor cube of a positive integer. Find the 500th term of the sequence. (Mastery Question)

Accepted Answer

528

Answer

440

Answer

526

Answer

530

Answer

532

Question 36

Mastery Question

Accepted Answer

400

Answer

340

Answer

360

Answer

380

Answer

420

Question 37

Mastery Question

Accepted Answer

84

Answer

72

Answer

96

Answer

108

Answer

120

Question 38

Mastery Question

Accepted Answer

$$10\pi+4\sqrt[]{3}$$

Answer

$$13\pi-\sqrt[]{3}$$

Answer

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

Answer

$$10\pi+9$$

Answer

$$13\pi$$

Question 39

The top prizes today are (1) a $15 Starbucks gift card, (2) a pack of BIC mechanical pencils, and (3) a pack of Pentel erasers. Will YOU be one of today's lucky contestants?

Accepted Answer

I like it.

Accepted Answer

Wow. I am stunned.

Accepted Answer

This is truly a work of art.

Accepted Answer

I humbly bow in the presence of your wondrous grace.

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