Here you will learn some interesting and fun facts about the number 27. There are many mathematical properties of 27, such as, 27 is a cube number.
Sometimes you will be asked to reflect a shape on a coordinate grid. If the question asks you to reflect the shape in the x-axis then the x-axis is acting as the mirror line. If the question asks you to reflect the shape in the y-axis then the...
More non-math facts about the number 28: In chemistry, 28 is the atomic number of nickel. In biology, the average human menstrual cycles is 28 days. The shortest month of the year with 28 days is February. In astrophysics, the surface of the...
A proper divisor of a number is a positive whole number that divides exactly into the number except from itself. So in order to work out all the proper divisors of a number first find all the divisors of your number then exclude the largest...
More non-math facts about the number 29: In religion, there are 29 principles given by Guru Jambheshwar. In music, “29” is a song by The Gin Blossoms. Other song titles which include 29 in their name are “29 X the pain”, “29 ways”...
Here are some math facts about the number 30: The number 30 is an even number – the 15th even number. The number 30 has 8 factors which are 1, 2, 3, 5, 6, 10,15 and 30. Also the prime factors of 30 are 2, 3 and 5. The prime factor...
Here I will show you a number trick that can be used to multiply two numbers that have a difference of 2. For example, 17 × 19, 22 ×20, 41 × 43... and so on. The only downside is that you need to know your square number well. Here are the first...
Here are some math facts about the number 44: The number 44 is an even number – the 22nd even number. The number 44 has 6 divisors which are 1,2,4,11,22 and 44. Two are these factors are prime factors which are 2 and 11. 44 can also be...
If you are looking for a quick way of multiplying by 5 then follow these couple of steps: Step 1: Multiply your number by 10. Step 2: Work out half of your answer from step 1. Let’s put these two steps into practice. Example 1 Use the...
Fun facts about the number 45 In music, there are lots of songs with the number 45 in them, some of these include, “45 and Fat” by Baby bird, “45” by Elvis Costello and in the song “Brimful of Asha” by Cornershop the number 45 is...
Some interesting non-math facts about the number 46: In chemistry, 46 is the atomic number of Palladium. In human biology, there are 46 human chromosomes. There are 22 pairs of autosomes and one pair of sex chromosomes. In religion, 46 is the...
Math facts of the number 47 The number 47 is the 24th odd number. The number 47 only has 2 divisors - so the number 47 is a prime number. It is also the fifteenth prime number (2, 3, 5, 7, 11, 13, 17, 19,23,29,31,37,41,43 and 47) The square...
Some interesting non-math facts about the number 48: In religion, Siddhartha Gautama sat under a bodhi tree for 48 days thinking about the nature of our universe. 48 is the atomic number of cadmium. 48 is the number of Ptolemaic constellations...
Here are some math facts about the number 50: The number 50 is an even number – moreover it’s the 25th even number. The factors of 50 are 1,2,5,10,25 and 50 – so 50 is divisible by 6 numbers. The prime factors of 50 are 2 and 5 (as these...
The main property of a trapezium (as known in Great Britain) or trapezoid (as known in the United States) is that it is a 4-sided shape with exactly one pair of parallel sides. Read on to learn about some other qualities of this amazing shape!
Outliers are extreme values that lie within a set of data. If you had to draw a box and whisker diagram then the outliers should be marked on with a cross. In order to identify an outlier first find the Lower Quartile, Upper Quartile and Inter...
A brief guide to using the bracket power rule.
Read on to find the modal class from a grouped frequency table – it's actually quite easy to do. All you need to do is to look for the group that has the highest frequency.
3 of the main conversions between metric and imperial conversions are: 5 miles = 8 kilometres (Length Conversion) 1kilogram = 2.2 pounds (Weight Conversion) 1 gallon = 4.5 litres (Volume Conversion) Let’s look at some examples on...
The cumulative frequency can be calculated by adding up the frequencies in the frequency table. Start by writing the first frequency cumulative frequency columns and keep adding on the next frequency onto the last cumulative frequency. Lets’...
Trying to find surface areas of various shapes? The surface area of a triangular prism can be found in the same way as any other type of prism. All you need to do is calculate the total area of all of its faces. Read on for my full explanation.
Trying to calculate density? Learn about the relationships between mass, volume, and density and how to calculate each using a visual tool called the density-mass-volume triangle. Example problems with step-by-step solutions are provided to help illustrate these concepts.
If you are carrying out a percentage increase question then you are making the amount larger by a given percentage. Here are two methods that you can use to work out a percentage increase question: Method 1 1. Work out 1% of your number. Do this...
Learn how to calculate the area of a composite or compound shape.
Learn how to get the mean average from a frequency table.
Here you will learn all the basics of fractions. You will find help on converting between improper and mixed numbers, adding fractions, subtracting fractions, multiplying fractions, dividing fractions, equivalent fractions and simplifying fractions.
In this Hub I will show you what a reciprocal graph looks like. The most simple types of reciprocal graphs take the form of y = A/x where A can be a positive or negative value. Let’s take a look at a couple of examples of reciprocal graphs and...
On this page you will be shown the method for working out the area of a circle, a semicircle (half a circle) and a quadrant (a quarter of a circle). The area of a circle can be found by using the formula A = πr². The symbol π is Pi and is a...
If you are given an amount and you need share this amount by a ratio then you can apply the following 3 steps to solve the problem: Step 1 Add up all of the parts in the ratio. Step 2 Divide the amount by your answer from step 1. This will...
First of all let’s take a look at square roots. If you want to find a square root of a number then you need to look for a number when multiplied by itself to give the number that you are square rooting. So if you have √a then ? × ? = a ...
In math you will often have to multiply out parentheses (brackets). The correct name given to multiplying out a parenthesis is call expanding. The term at the start of the bracket must multiply the values inside the bracket. Let’s take a look at a...
This article explores how to calculate the area of compound H-shapes with step-by-step guidance.
In lower grade math questions a word can be used to describe the probability of an event happening. If an event is never going to happen then you can describe the probability as impossible. For example, the probability of rolling a 7 on an...
This article teaches you what a C shape is and provides step-by-step instructions for calculating the perimeter and area of such a shape.
A perpendicular line is a line that is at right angles to another line. If you multiply the gradients of these lines together you will get -1. So if the gradient of the first line is m then the gradient of the second line is -1/m: Perpendicular...
Learn how to calculate the 3-point moving averages from a list of numbers and describe the trend.
Speed, distance and time can be calculated using a magic triangle. D (the distance) goes in the top of the triangle, S (speed) goes in the bottom left of the triangle, and T (time) goes in the bottom right of the triangle. Read on for my full explanation!
Before you attempt enlarging shaping with negative scale factors make sure you can enlarge shape with positive scale factors. In order to enlarge a shape with a negative scale factor: a) First make sure that you have marked on the centre of...
There are 3 main angle facts to get to grips with in your math exams: 1) Angles on a straight line add up to 180⁰ (also known as angles in a half circle) 2) Angle around a point add up to 360⁰ (also known as angles in a full circle) 3)...
When you are given all of the 3 sides of a triangle then any angle inside the triangle can be found by applying the cosine rule (the angle version is easiest to apply). The formula for this is: CosA = (b² + c² - a²)/(2bc) A is the angle that...
Pythagoras and trigonometry both work in right-angled triangles. In this article, you will be shown how to choose the correct one.
A square is probably one of the first mathematical shapes that you will recognise. Here are a few more mathematical facts about a square: A square has four equal side lengths. All the interior angles of a square are 90⁰ (right angles). Since...
A quick way to divide by 0.5 or ½ is to double the number (or multiply the number by 2). The reason for this is that two halves go into a whole.
The total of all the inside angles of a polygon is known as the sum of interior angles. To work out the sum of interior angles for a polygon follow these two simple steps: Step 1: Pick a corner and draw all the diagonals from this corner (a...
Given a 3D shape drawn on isometric paper (triangular paper) you could be asked to draw the side elevation, the front elevation or the plan. The plan view is probably the hardest one to carry out as this is the view you will see if you were...
If you have a number sequence then the numbers in the sequence are called the terms. So if you are asked for the term to term rule then you are looking for a rule that takes you from the previous term in the sequence to the next term in the...
Long division is a similar method to short division. The only difference being is that you put more working out down underneath the division. If you are not to good dividing and taking numbers away in your head then long division will stop you...
A quadrilateral is the name given to any shape with 4 sides. All the angles in a quadrilateral will sum to 360⁰. In this hub we will take a look at the main quadrilaterals that come up in math tests and list their main mathematical properties: A...
In math exams you may be asked to round your answers off to 2 decimal places, so this hub will show you how to do this. If you are dealing with money problems then the answer will have to be given to the nearest whole or to 2 decimal places. ...
What is Pythagoras used for? Pythagoras (or Pythagoras Theorem) is used to calculate an unknown side length of a right angled triangle. What information do you need to know to carry out Pythagoras? You will need to know the lengths of 2 other...
Learn how you can translate a shape on a coordinate grid using a vector.
Read on to learn how to find the area of a quadrant.
If you take a part of the circumference of a circle then the distance along this arc is called the arc length. So since the arc length is part of the circumference of a circle, then the arc length of the sector can be found by using the following...
A line of a reflective symmetry can be placed through a shape so that one side of the shape is a mirror image of the other side of the shape. A good method to decide if a shape has reflective symmetry is to draw the shape out on paper and cut it...
The double angle trigonometric identities can be derived from the addition trigonometric identities: Basically, all you need to do change all of the B’s to A’s. Let’s start off with the sine addition identity: sin (A+B) = sinAcosB +...
If you are asked to work out the product of two numbers, then you need to multiply the two numbers together. If you are asked to find the sum of two numbers, then you need to add the numbers together.
In order to write down all of the integers that satisfy an inequality between two numbers, you'll need to be familiar with both positive and negative integers and a few simple mathematical symbols. Let's take a look!
In this hub I will explain the difference between inverse proportion and direct proportion. If m is directly proportional to n then the formula is: m = kn If m is inversely proportional to n then the formula is: m = k/n k is known as...
If y is directly proportional to x, then the formula connecting y and x is y = kx. Direct proportion means as x increases then so does y. k is known as the constant of proportionality and this is found by substituting the boundary conditions...
In this hub page I will show you how you can prove the cosine rule: a² = b² + c² -2bcCosA First of all draw a scalene triangle and name the vertices A,B and C. The capital letters represent the angles and the small letters represent the side...
Predicting the topics that come up on the GCSE maths foundation calculator paper is much easier to do than for non-calculator paper. Here, I will go over some of the topics that are most likely to show up on this years’ maths calculator paper....
Here you will find 5 topics to go over to help you reach a grade 4 or 5 for the new GCSE foundation exam. These topics are relevant to all the main UK examination boards (Edexcel, OCR and AQA)
BODMAS, BIDMAS and BEDMAS all help you to carry out operations in the correct order. For younger students it is a good idea to start off with BODMAS: Brackets Orders of Division Multiplication Addition Subtraction Once a...
Here I will show you how to multiply a 2 digit number by a 2 digit number using the long multiplication method. Before you start, make sure you can do the short multiplication method. Start by writing the largest number at the top and the smaller...
If a maths problem asks you to round your answer to an appropriate degree of accuracy then you need to look at the numbers in the question and see what these numbers have been rounded to. So for example, if the numbers in the question have been...
To figure out a fraction of a number, all you need to do is divide that number by the denominator of the fraction and then multiply that result by the numerator.
To plot a graph of the form y = ax² + bx + c, first you need to work out the y coordinate in the range specified. To do this all you need to do is substitute the x coordinates into your formula. Be careful with the x² and remember that if you...
When a number is rounded off, the lower bound is the smallest possible value that the number could have been, and the upper bound is the highest possible value that the number could have been. Let’s take a look at a few questions on finding...
Learn how to find the angles of a triangle when written in algebraic form with just three simple steps. Includes example problems and solutions.
This article explains how to calculate the area of a circle in terms of pi (π) using a simple formula. Example problems with solutions are provided to help illustrate the process.
A factor tree can be used to express a number as a product of prime factors. Make sure you know your first 5 prime numbers before you start these examples. These are 2,3,5,7 and 11 (a prime number can only be divided by 1 and itself). Example 1...
Area is the amount of space contained inside a 2D shape. If the shape is drawn accurately on squared paper, then all you need to do is count the amount of squares that are contained inside the shape. To keep track of how many squares you have put dots inside each square.
In this hub I will explain to you the names of different parts of a circle. 1) The circumference is the distance around the circle (basically it’s the perimeter of the circle) 2) The diameter is the distance across the centre of...
Find the nth term of a quadratic number sequence.
In this article we shall be covering some more worked example on rearranging a formula (making subjects). All the examples below only require one inverse to solve. All you need to do is to apply the inverse operations to both sides of the formula...
To find the perimeter of a semicircle follow these 2 simple steps: Step 1 First find the arc length of the semicircle (the curved edge of the circle). Do this by multiplying Pi by the diameter of the semicircle and halving your answer. You can...
Before I show you how to change a normal number into standard index form let me explain the definition of standard index form. Standard index form is a mathematical system of writing down small and large numbers. A number in standard index form will...
A compound shape is a shape that is made up of other simple shapes. In this article, we will be working out the area of an L shape (made up of 2 rectangles). To find the area of a compound shape, follow these simple steps.
How to find the nth term of a decreasing linear sequence.
The nth term of a number sequence is a formula that gives you the values in the numbers sequence from the position number (some people call it the position to term rule).
To find the area of a semicircle first you need to find the area of the whole circle and divide your answer by 2, as a semicircle takes up half the space of a circle. To find the area of the circle use A=π×r2. (A stands for the area of the...
When writing down expressions in algebra you need to write them down in a specific way. In algebra a letter can be used to stand for an unknown quantity. Adding and taking away are straightforward: x+7 means x add 7 x -7 means x take away 7...