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Maths Fundamentals

Quick Arithmetic

Many pub quiz questions boil down to simple arithmetic. The trick isn't just knowing how to add, subtract, multiply, and divide, but doing it quickly in your head. Let's cover some mental shortcuts.

When multiplying, look for easy numbers. To calculate 15×1215 \times 12, you could multiply 15×1015 \times 10 (which is 150) and then add 15×215 \times 2 (which is 30). Add them together: 150+30=180150 + 30 = 180. This is often faster than trying to do the full multiplication in one step.

For division, breaking down the number can help. Trying to divide 96 by 4? Halve it twice. Half of 96 is 48, and half of 48 is 24. So, 96÷4=2496 \div 4 = 24. This works for dividing by any power of 2 (4, 8, 16, etc.).

A useful trick for multiplying by 5 is to multiply by 10 and then halve the result. For example, 88×588 \times 5 is the same as 880÷2880 \div 2, which is 440.

Fractions and Percentages

Fractions, decimals, and percentages are just different ways of saying the same thing. Being able to switch between them is a quiz superpower. The most common ones are worth memorizing.

FractionDecimalPercentage
1/20.550%
1/3~0.33~33.3%
1/40.2525%
3/40.7575%
1/50.220%
1/100.110%

To find a percentage of a number, it's often easiest to find 10% first. Say you need to calculate 30% of 80. Start with 10% of 80, which is just 8. Since 30% is three times 10%, you just multiply that result by three: 8×3=248 \times 3 = 24.

What about 35% of 80? You already know 30% is 24. Now you just need 5%. Since 5% is half of 10%, you can take half of 8, which is 4. Add them up: 24+4=2824 + 4 = 28.

A Bit of Algebra

Don't let the word "algebra" scare you. In a pub quiz context, it's usually just a

Lesson image

The golden rule of algebra is: whatever you do to one side of an equation, you must do to the other. Your goal is to get the unknown variable (usually xx) by itself.

Consider this equation:

3x+7=193x + 7 = 19

First, we want to isolate the term with xx. To get rid of the +7 on the left side, we subtract 7. To keep the equation balanced, we must also subtract 7 from the right side.

3x+77=1973x=12\begin{aligned} \\ 3x + 7 - 7 &= 19 - 7 \\ 3x &= 12 \\ \end{aligned}

Now, 3x3x means "3 times xx". To undo the multiplication, we do the opposite: division. We divide both sides by 3.

3x3=123x=4\begin{aligned} \\ \frac{3x}{3} &= \frac{12}{3} \\ x &= 4 \\ \end{aligned}

Geometry Basics

Quiz questions about geometry usually stick to the basics: areas, perimeters, and angles. You likely won't need to prove any complex theorems.

Here are a few key formulas to remember:

  • Area of a rectangle: Length × Width
  • Perimeter of a rectangle: 2 × (Length + Width)
  • Area of a triangle: (Base × Height) / 2
  • Area of a circle: πr2\pi r^2 (where rr is the radius)
  • Circumference of a circle: 2πr2\pi r

For quiz purposes, you can usually approximate π\pi as 3.14. Also, remember that a straight line is 180 degrees, and the angles inside any triangle always add up to 180 degrees. The angles in a four-sided shape like a square or rectangle always add up to 360 degrees.

A common trick question involves the relationship between a circle's radius and its diameter. The radius is the distance from the center to the edge, while the diameter is the distance all the way across. The diameter is always twice the radius.

Now let's see how much you've learned. It's time for a quick quiz.

Quiz Questions 1/5

Using the mental shortcut of breaking down numbers, what is the result of 16×1316 \times 13?

Quiz Questions 2/5

To solve 128÷8128 \div 8 in your head, you can just halve the number three times.

Keep these techniques in mind. With a little practice, you'll be able to tackle the math rounds with confidence.