Can You Answer These Basic Math Questions Everyone Should Know?

By: Zoe Samuel
Image: Shutterstock

About This Quiz

Math is, sadly, one of the worst-taught subjects out there. There is no reason it needs to be dull or - below collegiate level - excessively difficult. What it needs is to be taught by enthusiastic teachers to students whose parents support them and understand that failing a lot in order to succeed once is a perfectly decent way to make it as a student. Unfortunately, far too many of us hit a wall and feel too embarrassed or stupid to say so, then we don't get the tools we need to realize that we can actually get over that wall and scale the giddy heights of numeracy.

Smartphones only make this problem worse, by masking mathematical illiteracy behind the veil of tip-calculating apps and suchlike. However, you do need to be able to do mental arithmetic and to know mathematical concepts and ideas without using anything that has an "on" switch. You need this because the language of math underlies everything we do. It helps keep your brain flexible and ready for work, and stops you having your life ruined by the errors of your accountant, bank or landlord. Math fluency is a vital life skill. Do you have it?

What is an angle?

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.

What is the product of two negative numbers?

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!

Which is the denominator in the fraction 11/12?

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

What is 35% expressed as a decimal?

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.

Which of the below is NOT a prime number?

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.

At what point does the graph for x^-1 touch the X axis?

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.

What is chaos, mathematically speaking?

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.

What is the sum of two complementary angles, in degrees?

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.

What is the reciprocal of 1/x?

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.

How many degrees is one radian, to the nearest integer?

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!

What is the lowest common denominator of 4/10, 14/20 and 30/100?

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.

What is an integer?

Integers are whole numbers with no decimals or fractions.

Which of the below is an improper fraction?

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.

Which of these symbols means "greater than or equal to"?

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.

Which of the below are the first five of the Triangular Numbers?

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!

Who discovered the law of gravity?

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.

What is cosine?

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.

What is 5! (and do note that exclamation mark)?

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".

To what is the sum of the square of the two shorter sides of a right-angled triangle equal?

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.

What does differentiation measure?

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).

Which of the below is the first five numbers of the Fibonacci Sequence?

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.

How many vertices does a tetrahedron have?

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

What is a recurring decimal?

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.

What is 0.125 expressed as a fraction?

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

By what name are the number of molecules in a single mole known (where a mole is a substance's molecular weight in grams)?

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!

What is a the term defined by the following: "an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable"?

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.

Which of the below are an example of Cartesian coordinates?

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!

What shape is the graph for x^2?

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.

What graph looks like a perfect pattern drawn in sand by the progress of a snake?

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.

Which of these is NOT a Pythagorean Triple?

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.

Is Pi a rational number?

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

What is the sum of two supplementary angles, in degrees?

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.

What is described by the formula x=(-b=/-√b^2-4ac)/2a?

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.

What is the Golden Ratio?

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.

Where is it NOT true that a^2 + b^2 = c^2 on a right-angled triangle?

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.

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