Vinculum Round 1

Permutations and combinations

100

5!

120

200

5C3

10

300

A committee of 4 people must be chosen from 7 men and 6 women. How many ways can this be done if the committee must include at least one woman?

680

400

Find the number of ways to arrange the letters in the word "ARRANGE" such that the two 'R's are never together.

900

500

State the first three terms in decreasing powers of x in the expansion of (2x + 3)⁵ in simplest form.

32x⁵+240x⁴+720x³

^(Sheild)

Area and Volume

100

A square has a perimeter of 40 cm. What is the area of the square in square centimeters.

100 cm²

200

The formula for the volume of a cone

(1/3)(πr²h)

300

A circular sector has a radius of 9 cm and an area of 27π cm². What is the measure of the sector's central angle, in degrees.

120°

(Steal Question)

400

A sphere is inscribed inside a cube such that it touches all six faces. If the volume of the cube is 64 cm³, what is the volume of the sphere, expressed in terms of π.

32π/3

500

A right cylinder has a volume of 288π cm³ and a height of 8 cm. What is the total surface area of the cylinder.

168π cm²

Summing it up

100

199+174

373

200

Calculate: 15 - (6 + 1)² ÷ 7

8

(Switch question)

300

Find the value of: 24 ÷ [8 - {5 - (4 - 1)}]

4

400

Solve: 2 + 3² × (4 - 1) ÷ 5

7.4

(Double points)

500

Solve: 60 ÷ 5 × (7 - 3)² ÷ 6

32

Indices/Surds

100

Simplify (2x²)³

8x⁶

^{(Steal points)}

200

solve for x: 8^x=2^x+5

x=5/2

300

Simplify the expression (3ⁿ⁺¹-3ⁿ)/3^n-1

6

400

Simplify (6/√3)+√12 in the form a√b

4√3

500

solve for x: 9^x-4(3^x)+3=0

x=1 and x=3

Famous Mathematicians

100

This 18th-century Swiss genius introduced the notation f(x) for a function and e for the base of the natural logarithm. His last name is also the name of a famous formula connecting complex numbers to trigonometry.

Leonhard Euler

200

This ancient Greek mathematician and philosopher is best known for the theorem that bears his name, which relates the sides of a right-angled triangle.

Pythagoras

300

This Italian medieval mathematician introduced the Hindu-Arabic numeral system to the Western world through his book Liber Abaci. He is best known today for the simple sequence that bears his name.

Fibonacci(Leonardo Pisano)

400

This British mathematician has a theorem named after him and Hamilton which states that every square matrix satisfies its own characteristic equation. He also pioneered the theory of algebraic invariants.

Arthur Cayley 

(Hint)

500

These early 19th-century mathematicians one French, one Hungarian, and one Russian all independently discovered non-Euclidean geometry, shattering the 2000-year-old belief that Euclid's parallel postulate could be proven. Name one of the three.

János Bolyai, Nikolai Lobachevsky and Carl Friedrich Gauss