Q 01/05

Young Carl Friedrich Gauss is said to have quickly summed the whole numbers 1 to 100; what total did he reach?

A) 505

B) 5,050

C) 10,100

D) 50,500

Answer · why

B) 5,050

5,050 is the total: pairing 1 with 100, 2 with 99 and so on gives 50 pairs that each add up to 101. The same trick sums any arithmetic series.

Q 02/05

The mnemonic All Students Take Calculus helps trigonometry students recall which fact about the six trig functions?

A) Their values at special angles

B) Their order of derivatives

C) Their signs in each quadrant

D) Their reciprocal partners

Answer · why

C) Their signs in each quadrant

Their signs in each quadrant are what the initials track: all are positive in the first quadrant, only sine in the second, tangent in the third and co...

Q 03/05

Johannes Kepler's first law says each planet travels around the Sun along which curve rather than a perfect circle?

A) Parabola

B) Hyperbola

C) Ellipse

D) Spiral

Answer · why

C) Ellipse

An ellipse, a stretched circle, is the path; Kepler published the law in 1609 after fitting Tycho Brahe's careful observations of Mars.

Q 04/05

Which French philosopher, living in the Netherlands at the time, gives the Cartesian coordinate plane its name?

A) René Descartes

B) Pierre de Fermat

C) Marin Mersenne

D) Pierre-Simon Laplace

Answer · why

A) René Descartes

René Descartes set out the idea in 1637, letting algebra describe geometry; Pierre de Fermat found it independently but never published.

Q 05/05

One radian is the angle at a circle's center whose arc is exactly as long as which part of the circle?

A) Diameter

B) Semicircle

C) Chord

D) Radius

Answer · why

D) Radius

The radius sets the size of the unit, so one radian is the same angle on a coin as on a planet's orbit: about 57.3 degrees.