1. The amount of turn between two lines.
   The ratio of two lines.
2. The dimensions of a triangle.
   The sin, cos, and tan of a triangle.

Put your arms out to 90 degrees then look along one. Now the other. You have just turned your head through an angle! That's because an angle is the amount of turn.

1. Negative
   Positive
2. It depends.
   Negative or positive, but always a whole number.

Think of how, "I ain't got none" means that technically, you do have some. Negative numbers are like this: Multiply them together and they are positive. Negative people, alas, do not work this way!

1. 6
   1
2. 11
   12

11/12 has a numerator (top number) and a denominator (bottom number).

1. 0.35
   0.3
2. 0.351
   0.350000000

35% is 35/100 as a fraction, and 0.35 as a decimal. Decimals to percentages are typically pretty easy; you just divide by 100.

1. 83
   11
2. 49
   29

A prime number is a whole number that cannot be divided by anything but itself and 1. They are very important in a variety of mathematical principles and theories. 49/7 = 7, hence it is not a prime.

1. 0
   1
2. Trick question: it doesn't!
   100

This graph doesn't touch the X axis. It certainly LOOKS like it does because ink takes up space on paper and you can't draw infinity - but it doesn't. It's two curves that swoop from Y to X and never touch either axis.

1. When you don't know the answer.
   When the answer is not knowable.
2. When there is more than one answer.
   Apparent randomness.

Chaos simply means things are random. A chaotic graph has points dotted about with no pattern. A chaotic math lesson has some students sleeping, some listening and some passing notes, and an unknown number being sent to the principal's office. A chaotic set of numbers bear no relation to one another, etc.

1. 180
   45
2. 90
   360

Complementary angles add up to 90. That means if you put them together, you get a shape with an outline that has a right angle in it.

1. x^2
   x
2. x^-1
   2x

The reciprocal of x/y is y/x; that is, you just invert it. Thus, 1/x is the reciprocal of x/1. Of course, the correct way to write that is just ... x.

1. 360
   180
2. 57
   22

A radian is a way of measuring angles and turn that is designed to deal with the reality of Pi being the trickiest darn number there is. There are two times Pi radians in a circle, hence a single radian is 360 / (2*3.14159...) = 57.296 degrees!

1. 100
   20
2. 10
   5

The lowest common denominator isn't how we choose politicians (though it often is that!). It's the lowest number you could use as a denominator for all the fractions in a set. In this example, you could write the three fractions as 4/10, 7/10, and 3/10.

1. A number higher than zero.
   A number that is NOT a prime.
2. A whole number.
   A number in an algebraic equation that is known (ie not X).

Integers are whole numbers with no decimals or fractions.

1. 2/3
   7/11
2. 4/9
   11/7

An improper fraction is one where the numerator is bigger than the denominator. That is, 11/7 is improper because 11 is bigger than 7.

1. ≠
   ≥
2. ≤
   =

The greater number is on the wide side, so in this case, you look for a symbol that is more open on the left. The underscore on the bottom shows the "equal to" part. Hence, ≥ is the right answer.

1. 1, 4, 9, 16, 25
   1, 3, 6, 10, 15
2. 1, 2, 5, 7, 12
   1, 8, 21, 40, 65

Triangular numbers mean you can make a perfectly equilateral (same-length sides) triangle out of dots in that number. The right answer is 1, 3, 6, 10, 15. The wrong answers here, for fun, are actually the square, pentagonal, and octagonal numbers!

1. Pythagoras
   Isaac Newton
2. Blaise Pascal
   Alan Turing

Newton is one of the most important mathematicians of all time. Gravity is only one of his contributions; he also made enormous contributions to the broader field of calculus.

1. The ratio of the opposite side to the hypotenuse.
   The ratio of the adjacent side to the opposite side.
2. The opposite of the tangent.
   The ratio of the adjacent side to the hypotenuse.

The cosine of an angle in a right-handed triangle is the length of the adjacent side divided by the length of the hypotenuse. That is, how long the nearest side is compared to the longest side. It means even if you only know one side and the cosine of one angle, you can calculate the other sides.

1. 200
   120
2. 50
   15

This is called a factorial. It's when you multiply a number by each term smaller. So 5*4*3*2*1 = 120. Amusingly when you read the ! symbol aloud, in math, you pronounce it "shriek". So for this one, you'd say "five shriek".

1. The square of the long side.
   The area of the triangle.
2. Half the square of the long side.
   Twice the square of the long side.

This is Pythagoras' Theorem, and it's likely the first big theorem you'll learn in math. On a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

1. Acceleration
   Size
2. Speed
   Rates of change

Differentiation is when you calculate how something changes over time. Speed is the differential of location (ie, it's how fast the latter is changing). Acceleration is the differential of speed (ie, how fast speed is changing).

1. 1, 2, 3, 4, 5
   1, 2, 3, 5, 7
2. 1, 1, 2, 3, 5
   1, 4, 6, 9, 12

Fibonacci's Sequence is where you add two consecuritve terms to get the next. It's actually incredibly common in nature; go find it in the spirals on the face of a sunflower, plus a million other places.

1. 1
   3
2. 4
   10

A tetrahedron means a pyramid with a triangular base. A vertex (plural vertices) means a corner on such a shape. A tetrahedron has four.

1. One that goes on forever without repeating.
   One that has the same number more than once.
2. One that has a repeating pattern going on forever.
   One that cannot be expressed as a fraction.

Recurring decimals have a pattern that repeats. It also never stops. Some of them can be expressed as a fraction though eg 0.333333333 ... can be shown as 1/3.

1. 1/12
   1/8
2. 1/18
   1/19

Half is 0.5. A quarter is 0.25. Thus, 0.125 is an eighth!

1. Cartesian Plane
   Fermat's Last Theorem
2. Avogadro's number
   The Doppler Effect

A mole is not just a super cute but dangerous pest. It's also the amount that a substance weighs if you have an Avogadro's number of molecules of it. The number is 6.022140857 × 10^23, which is a lot. And don't worry, this is by far the hardest question on the test!

1. Polynomial
   Quadratic
2. Imaginary number
   Irrational number

A polynomial is a fancy way of saying a rather complicated-looking equation, or rather, one that has several algebraic terms in it. It's especially common for them to have different powers of one variable, for example: x^3 - 2x^2 +4 is a polynomial.

1. x, y
   1, 2
2. 0, 3
   All of the above, potentially.

A Cartesian coordinate system means you know where something is in two dimensions because it's pinpointed on two axes (usually x and y). So any of these COULD be Cartesian coordinates. It depends what the context is!

1. Parabola
   Horseshoe
2. Straight
   Curve

The shape of this graph, like any exponential graph, is parabolic. That's the shape that a Frisbee or ball makes if you throw it properly.

1. Sine wave.
   Exponential graph.
2. Linear graph.
   Logarithm.

Plotted on a graph, sine and cosine are both wiggly lines like a snake. Tan is where things get super weird-looking; it's sort of a series of monumental spikes with a jink in the middle as they each go up toward an infinite limit.

1. 20, 21, 29
   5, 4, 3
2. 5, 12, 13
   4, 9.7, 10

Pythagorean Triples are sets of numbers that describe right-angled triangles whose sides are integers of the measuring unit (whether cm, m, or other). These triples always require integers.

1. Yes
   No
2. Only if you express it as a fraction.
   Only if you express it as a radion.

Pi goes on forever. That means you can't write it a a fraction, and thus it is considered to be an "irrational number".

1. 90
   180
2. 360
   720

Supplementary angles add up to 180 degrees. That means if you put them together you get an outline that has a straight line on one side.

1. The factorizing of a polynomial.
   The center of gravity of a cone.
2. The factorizing of any quadratic equation.
   The center of gravity of a tetrahedron.

A quadratic equation is one which looks like this: ax² + bx + c = 0. The above formula will help you calculate literally any quadratic equation. What's fun about it is the proof, which is actually rather beautiful.

1. 1 : 1.777
   1 : 1.812
2. 1 : 1.618
   2 : 7

This ratio is very important in nature. You see it in buildings, for example the Parthenon is built almost entirely using it. It also expresses the ratio of terms in the Fibonacci Sequence with increasing accuracy as they get bigger.

1. If the triangle is on the surface of a sphere.
   If the triangle is on the side of any three-dimensional object.
2. If the triangle is of a certain size.
   Trick question! It is always true!

On a sphere, all bets are off. If you draw a "perfect" right-angled triangle linking three towns that are really far apart on the surface of the Earth, then test the distances between them, you'll see that the square of the "hypotenuse" on your map actually is NOT the sum of the square of the other two sides. This is called "non-Euclidean geometry" and it'll blow your mind.