Mathing at Northside

Are you a Mu

100

 How many of the 26 letters in the English alphabet appear in both of the words 𝐼𝑁𝑇𝐸𝐺𝑅𝐴𝐿 and 𝐷𝐸𝑅𝐼𝑉𝐴𝑇𝐼𝑉𝐸?

5

200

 A square with area 18 is rotated about one of its diagonals to create a solid. What is the volume of this

solid?

18𝜋

300

 A square with area 18 is rotated about one of its diagonals to create a solid. What is the surface area of

this solid?

18𝜋√2

400

 The function 𝑓(𝑥) = |𝑥| + 1/|𝑥+1| has two local minima at the points (𝑎, 𝑏) and (𝑐, 𝑑). Compute 𝑎𝑏𝑐𝑑.

0

500

 Numerically, the area of a rectangle with integer side lengths is 2 greater than its perimeter. Find the sum of all possible values for the length of the shorter side of the rectangle.

7

600

 Consider the polynomial x³−9x² + tx + 165, where t is a real number. At what value of t does this polynomial have three distinct roots in arithmetic progression?

-37

700

 There are eight crewmates and two impostors on a ship. Every second, one person is randomly thrown off the ship. What is the probability that before the ship is emptied, there are always more crewmates than impostors on board?

3/5

800

 The number 1234312 has three distinct prime factors. Compute their sum.

836

900

 An SRS of 576 American households found an average of $475 spent on groceries monthly. It is known that the true population standard deviation of the amount spent on groceries monthly for all American households is $96 exactly. What is the 90% confidence interval for the true mean amount spent on groceries monthly for American households? Round the appropriate critical value to 3 decimal places.

475±6.580

1000

 There are 6 boxes, indexed 1,2,…,6, each of which contains 64 balls where each ball is either blue or red. The number of blue balls in box 𝑛 is equal to 2ⁿ. A box is randomly selected and a ball is randomly selected from the box. Given the ball is red, the probability that the 4th box was chosen is 𝑚/𝑛 in simplified form. What is 𝑚+𝑛?

51

Are you an Alpha

100

 Grogu and Mando are hiding away on the planet Sorgan. Grogu’s hut can be modeled by the pyramid bounded

by the plane 2x + 3y + 6z = 12 and the coordinate planes. What is the volume of Grogu’s hut?

8

200

 If the acute angle between the planes 9x + 6y−2z = 7 and−8x + 4y + z = 11 is θ, what is cos(θ)?

50/99

300

 What is the maximum value of 3^{-x^2}·9^3x/27 ?

36

400

 Which of the following is equal to 1−cos 2θ?

 2 sin² θ

500

 Max’s function is f(x) = (x−2)² + 1. Evaluate f(f(4)).

10

600

 θ is−π/4 . Find the value of sin θ + cos θ.

0

700

 The monthly rent for an apartment in Atlanta is $2600 less than the cost of renting the apartment for 3 months. How much does it cost to rent the apartment for a year?

$15600

800

 Two sequences are given below with sums of A and B. What is the value of A−B?

2 + 4 + 6 + 8 + 10 +. . . + 198 + 200= A

1 + 2 + 3 + 4 + 5 +. . . + 99 + 100= B

 5050

900

 Jaden brings in one complete cake. He then brings in 2 half cakes. He then brings in 3 quarter cakes. He continues to bring in cakes increasing in quantity by one but decreasing in size by a half. What is the total amount of cake he brings in?

4

1000

 The last question is usually easy. What is cos 90?

(A)−1 

(B) 0 

(C) 1 

(D) √2/2 

(E) NOTA

E

Are you a Theta

100

 Consider the functions f (x) = ax + 4 and g(x) =−x + 10. If f (g(x)) = g( f (x)), determine the value of a.

1/5

200

 Find the number of asymptotes the function f (x) =x³ −8/x² −4 has.

2

300

 Find the sum of x for the following equation: log₂ (x−1) + log₄ (x−4) = 2

5

400

 A line passing through the point (0, 4) intersects the graph of y= x2 + 1 in two distinct points. The positive difference in x-coordinates of these two points is 6. Compute the positive difference between the points’ y-coordinates.

12√6

500

 A quadratic function g passes through the points (1, 3), (4, 7), and (5, 11). Find the value of g(2).

3

600

 Find the coefficient of the x²y term of the function 

f(x,y) = (2x−5y)³

.

-60

700

 Alejandro works at a factory where he earns $9 per hour. He currently has $300. What is the least amount of integer hours he must work to be able to afford a $500 TV?

23

800

 Scott starts at 𝐴 and looks up to 𝐷 at an angle of elevation of 30∘. He walks forward a distance of 20 feet to point 𝐵. From 𝐵, he looks up again to 𝐷 at an angle of elevation of 45∘. What is the distance 𝐷𝐶?

10(√3 + 1)

900

 Ohm’s Law states 𝑉 = 𝐼𝑅 where 𝑉 is the voltage, 𝐼 is the current, and 𝑅 is the resistance in a circuit. If the resistance is (2 − 3𝑖) and the voltage is (21 + 𝑖), what is the current?

 3 + 5𝑖

1000

 How many arrangements of the letters of the word “GEMINI” are there?

 360

Algebra GT

100

 What is the smallest positive integer n such that 4 √n+ 2023 is an integer?

 Solution: 378

200

 A circle in the coordinate plane has its center at (0,0) and passes through the points (3,a) and (a−2,4). What is a?

Solution: 11/4

300

 The areas of three triangles form an arithmetic progression. If one of the triangles has side lengths 8, 15, and 17, and another one of the triangles has side lengths 7, 24, and 25, what is the sum of the possible areas of the third triangle?

Solution: 216

400

 Suppose that a rectangle ABCD satisfies AB : AC = 8 : 17. If the area of ABCD is 24/5 , what is the length of BC?

Solution: 3

500

 A high school math team has 10 different students and 15 identical cookies to hand out. If each student receives at least one cookie, and no student gets more than two cookies, in how many ways can the cookies be distributed?

Solution: 252

600

6. A farmer must bring water to her sick cow. The farmer is at coordinates (0,12) and the cow is at coordinates (10,8). The river where she will fill her bucket from is the line y= 0. At which point (x,0) along the river should the farmer walk towards to yield the shortest round trip to the cow?

Solution: x= 6

700

 Let p and q be the roots of x² −6x+ 4 with p>q. What is p² −q2?

Solution: 12√5

800

 Suppose an and b are irrational numbers such that a3 ≈31.00627 and b3 ≈20.08554. What is 

(a−b) (a+ b)2 −ab , rounded to the nearest hundredth?

Solution: 10.92

900

 A 60 person party wants to order pizza. There are 40 people who want pepperoni, 16 who want cheese, and 50 who want supreme. A total of 40 people want at least two kinds of pizza and 12 want all three kinds. How many people don’t want any pizza?

Solution: This is a direct application of the inclusion-exclusion principle. The number of people who want pizza is 40 + 16 + 50−(40 + 2 ∗12) + 12 = 54, so 6 people do not want pizza.

1000

 Given that f(x) = 4x³ −6x² + 4x−1, what is

f(2) + f(3) +···+ f(100)?

Solution: 99999999

ASU

100

 Given the system of linear equations 5𝑥 + 2𝑦 = 11

𝑥 − 3𝑦 = 9

What is the value of 2𝑥 + 5𝑦 ?

-4

200

 Given the quadratic equation 𝑦 = −5𝑥2 + 30𝑥 + 7, what is the maximum value of y ?

52

300

 How many prime numbers are between 50 and 100 ?

10

400

 What are the coordinates of the x intercept of the rational function 𝑓(𝑥) =10-2x/𝑥−6?

(5,0)

500

 In the figure below the area of the trapezoid ABCD is 90. Also AB is 12 , BE is 9 , CD is 𝑥 and DE is 𝑦. Find the value of 2𝑥 + 3𝑦.

28

600

 Solve 3𝑏𝑥 + 9 = 4(3𝑥 − 𝑏) + 2 for 𝑥.

-4b+7/3b+12

700

 Two cards are drawn, without replacement, from a standard deck of playing cards. Find the probability that both are red.

25/102

800

How many six digit multiples of 5 can be formed from the digits 1, 2, 3, 4, 5, and 6 using each of the digits exactly one time?

120

900

 There are 93 sixth graders and 108 seventh graders entering a raffle. In each grade, the number of dog owners is twice the number of students who do not own a dog. What is the probability that a seventh grader who does not own a dog wins the raffle? Express your answer as a common fraction.

12/67

1000

 If f(x) = -4x - 5 and g(x) = 3 - x, what is g(-4) + f(1)?

-2