Vinculum H1

Areas and Volumes

100

Find the volume of a cube with edge 5 cm.

125 cm³

200

A rectangle is 10 cm long and 4 cm wide. A square of side 2 cm is cut out from it. What is the remaining area?

36 cm²

300

A rectangle is 12 cm by 10 cm. Inside it, there is a triangle with base 12 cm and height 5 cm. What is the area of the shaded region outside the triangle?

90 cm²

400

What is the volume of a cylinder, in terms of pi, with height 10 cm and radius 3 cm? 

90pi cm³

Hint

500

A cone and a cylinder have the same radius and height. If the volume of the cylinder is 150 cm³, what is the volume of the cone?

50 cm³

What are the Chances?

100

Probability of drawing 3 yellow marbles in a row from a bag of 27 yellow marbles.

1

200

What is the probability of rolling a number less than 3 on a fair die?

1/3
Steal Question

300

A bag has 2 red and 1 green ball. Two balls are drawn without replacement. What is the probability both are red?

1/3

Shield

400

Two dice are rolled. What is the probability that both show the same number?

1/6

500

A bag has 5 red, 4 green, and 3 blue balls. Two balls are drawn without replacement. As the simplest fraction, what is the probability that both are green ?

1/11

Famous Mathematicians

100

Which scholar wrote a book that laid the foundation for algebra and introduced the term "al-jabr"?

Muhammad ibn Musa al-Khawarizmi

200

Which mathematician introduced the notation for functions, popularized the constant e, and made major contributions to graph theory and calculus?

Leonhard Euler

300

Which mathematician, known as the "Prince of Mathematics," made groundbreaking contributions to number theory, astronomy, and magnetism from a young age?

Carl Friedrich Gauss

400

Which mathematician developed formulas to calculate the volume and surface area of spheres and cylinders, laying the foundation for integral calculus?

Archimedes

500

Which mathematician became the first woman to win the Fields Medal for her pioneering work in geometry and dynamical systems?

Maryam Mirzakhani

Switch Question

Logarithms

100

What is log⁡₁₀100?

2

200

Simplify log₂8

3

300

Simplify log₁₀10 + log₁₀100

3

400

Simplify log₃27 - log₂64

-3

Double Points

500

Simplify log₂16 + log₄2

4.5

Plus/Minus

100

Simplify:
12− (5−3) + 412 - (5 - 3)

420

Steal Points

200

11(x+4) - 4(x+11)

7x

300

Simplify:
√50−√18+√2

3√2

400

Simplify:
2x + 3/4 - x - 1/4

x + 1/2

500

Simplify:

5a- [2a-(3-a)] + 4

2a+7