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In the Spotlight
## Fraction Help. A complete guide to everything you need to know about fractions in your math exam.

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 Continue »

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### Math Facts About the Number 27 (27 in Science, Religion and the Arts)

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.

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### Examples on how to reflect a shape in the x-axis or y-axis on a coordinate grid.

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...

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### The number 28 (twenty eight). Interesting and fun facts about 28.

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...

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### Proper Divisors. What Is a Proper Divisor and How to Work Them Out?

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...

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### Facts about the number 29. The importance of twenty nine in math, music and religion.

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”...

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### Number 30. Facts about the number thirty (math facts and fun facts).

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...

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### Number Tricks. How to Work out the Product of Two Numbers That Differ by 2 (Mental Math Tricks).

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...

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### Math facts about the number 44. Plus other fun facts about forty four.

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...

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### Multiplying by 5. a Cool Math Trick for Multiplying Any Number by 5 (Number Trick)

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...

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### The number 45. Math facts, music facts, movie facts and other fun facts of forty five.

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...

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### Math Facts Of The Number 46 And Other Fun Facts About Forty-Six.

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...

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### 47. Math Facts And Other Fun Facts About The Number 47.

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...

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### The Number 48 in Film, Music and Religion. Also Lots Of Maths Facts About Forty Eight.

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...

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### The number 50. Fun math facts and the meaning of fifty biblically.

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...

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### Properties of a trapezium or trapezoid (math facts)

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 side shape with exactly one pair of parallel sides. Depending on how the trapezium is drawn determines how many lines of...

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### Box Plots With Outliers. What Is an Outlier and How to Find These Extreme Points.

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...

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### Powers in Brackets: How to Use the Bracket Power Rule

Here you will be shown how to simplify expressions involving brackets and powers. The general rule is: (xm)n = xmn So basically all you need to do is multiply the powers. This may also be called the exponent bracket rule or indices bracket rule...

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### How to Work out the Modal Class Interval from a Grouped Frequency Table

Finding the modal class from a grouped frequency table is actually quite easy to do. All you need to do is to look for the group that has the highest frequency. This is because the mode is the number that comes up the most times. Make sure you write...

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### An Easy Way to Change Between Imperial and Metric Untis of Lenght, Weight and Volume.

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...

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### Cumulative Frequency Tables. How to work out the the cumulative frequencies from a frequency table.

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’...

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### How to Find the Surface Area of Right-Angled and Isosceles Triangular Prisms

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.

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### Using the Density-Mass-Volume Triangle 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.

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### How to Work out Percentage Increases (1% Method and Decimal Multiplier Method).

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...

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### How To Calculate The Area Of A Composite Or Compound Shape (rectangles, triangles, circles).

A composite shape or compound shape is a shape that is made from other shapes such as two rectangles (L-shape) or a triangle and a rectangle. If you are going to calculate the area of a composite shape then you need to break up composite shape into...

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### How to Get the Mean Average From a Frequency Table

The mean average from an ungrouped frequency table can be found by following these three simple steps: Step 1. First you will need to add a new column onto the end of the frequency table. You can label this column fx as you are going to multiply...

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### Fraction Help. A complete guide to everything you need to know about fractions in your math exam.

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.

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### Reciprocal Graphs. What does a reciprocal graph look like and it's characteristics?

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...

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### The method for working out the area of a circle, semicircle and a quadrant (math help).

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...

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### Ratio problems. How to share £42 between 2 people in the ratio 5:2.

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...

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### How to Work out the Square Root and Cube Root of a Number?

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 ...

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### Expanding Parentheses. How to Multiply out a Simple Bracket.

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...

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### Calculating the Area of Compound H Shapes

A compound H-shape is made up of 3 rectangles. Make sure you can work out the area of an L-shape first before you attempt this one. If you are finding the area of a compound H-shape all you need to do is split the H-shape up into 3 rectangles and...

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### Impossible, unlikely, even, likely and certain events (the probability number line).

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...

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### Compound C Shapes: How to Calculate the Perimeter and Area of a C Shape.

Here you will be shown to work out the area and perimeter of a C shape. A C shape is a compound shape made up of 3 rectangles. Make sure you know how to find the area and perimeter of an L shape before you attempt this lesson on C shapes. To work...

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### Perpendicular gradients. Calculating the perpendicular gradient of a linear graph.

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...

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### How to Calculate the 3 Point Moving Averages from a List of Numbers and Describe the Trend

To calculate the 3 point moving averages form a list of numbers, follow these steps: 1. Add up the first 3 numbers in the list and divide your answer by 3. Write this answer down as this is your first 3 point moving average. 2. Add up the next 3...

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### Using the Magic Triangle for Speed, Distance and Time (Compound Measures)

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. If you want to calculate...

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### How to enlarge a shape by a negative or minus scale factor from a centre of enlargement.

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...

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### Basic math angle facts; angles in a triangle, on a straight line and around a point.

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)...

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### The Cosine Rule. How to Work out an Angle Inside any Triangle Given 3 Side Lengths.

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...

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### Pythagoras vs. Trigonometry—How to Know When to Use Trig or Pythag in Your Math Exams

Pythagoras and trigonometry (basic) both work in right angled triangles. In this hub you will be shown how to choose the correct one. Pythagoras is used when you have a right angled triangle and you need to work out one of the missing side...

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### What are the math facts about a square? (mathematical properties of a square)

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...

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### Dividing by 0.5: A Simple Method to Divide by a Half

A quick way to divide by 0.5 or ½ is to double the number (or multiply number by 2). The reason for this is because two halves go into a whole.

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### How to Work out the Sum of Interior Angles of a Polygon in 2 Easy Steps (Heptagon and Decagon Examples)

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...

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### 3D shapes. How to draw the plan, side and front elevations of a 3D shape.

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...

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### How to find the term to term rule and the position to term rule of a number sequence.

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...

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### Long Division Method. How to carry out long division. Numeracy math help.

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...

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### Properties of Quadrilaterals - square, rectangle, rhombus, parallelogram, kite, trapezoid

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...

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### How to round off a number to 2 decimal places (2dp math rounding help)

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. ...

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### Pythagoras for dummies. A quick and easy guide to work out an unknown side using Pythagoras.

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...

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### How to translate a shape on a coordinate grid using a vector. Math help.

If you are asked to translate a shape then you need to move the shape to a new position on the coordinate grid. Usually, the directions of the translation are given in terms of a vector. The vector contains 2 numbers which are written vertically...

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### How to Find the Area of a Quadrant (a Quarter of a Circle)

A quadrant is a quarter of a circle. So to work out the area of a quadrant, first work out the area of the whole circle (use the formula A = π ×r²) and then divide the answer by 4. Alternatively, you could substitute the radius of the quadrant...

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### How to work out the arc length and perimeter of a sector (part of the circumference of a circle)

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...

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### How do you find lines of reflective symmetry? (Taj Mahal India is a famous building with reflective symmetry)

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...

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### The double angle identities: sin2A, cos2A and tan 2A derived from the trigonometric addition formulas.

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 +...

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### How to Find the Product and Sum of Two (Or More) Numbers

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.

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### How to Solve an Inequality Between Two Numbers (With Examples)

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!

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### Direct and inverse proportion examples with graphs (inversely and directly proportional formulas)

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...

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### Direct proportion. How to write down a formula if y is directly proportional to x. Maths GCSE.

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...

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### Proof of the cosine rule. Proving the cosine rule using Pythagoras and Trigonometry.

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...

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### 2019 GCSE Maths Calculator Paper, Key Grade 4 Topics

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....

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### 2019 GCSE Maths Foundation Exam. 5 Topics to Revise to Achieve a Grade 4 or 5.

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)

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### Understanding BODMAS, BIDMAS or BEDMAS (order of operations).

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...

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### How to Carry out Long Multiplication (2 Digit Numbers Multiplied by 2 Digit Numbers).

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...

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### How to round a number off to an appropriate degree of accuracy. What does this mean?

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...

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### Math Help: How to Work Out a Fraction of a Number

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. This article includes a video demonstration and a set of example problems with solutions.

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### How to Draw a Quadratic Graph (a Curve or Parabola). Like Y=x^2 -2x -5

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...

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### How to calculate the lower bound and upper bound. Math number help.

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...

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### How to Work Out the Angles in a Triangle When the Angles Are in Algebra.

If the angles in a triangle are given as algebra (usually in terms of x), and you are asked to find out the size of each angle, then you can follow these 3 simple steps to find all of the angles. Step 1 Add up the 3 angles that are given and...

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### How to Calculate the Area of Circle in Terms of pi (π)

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.

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### Factor Trees and the Product of Prime Factors. Easy Method With Examples.

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...

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### How to Find the Area of a Shape Which Is Drawn on Squared Paper

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.

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### Where are the Circumference, Radius, Diameter, Chord and Tangent on a Circle?

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...

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### Quadratic Sequences: The Nth Term of a Quadratic Number Sequence

Find the nth term of a quadratic number sequence.

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### Rearranging a formula method. Express x in terms of y (1 inverse only)

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...

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### How to calculate the perimeter of a semicircle using 2 simple steps (semicircles)

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...

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### Standard form help. How to convert large numbers into standard index form.

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...

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### Compound Shapes: How to Find the Area of an L-Shape

A compound shape is a shape that is made up from other simple shapes. In this article we will be working out the area of a L shape (made up from 2 rectangles). To find the area of a compound shape, follow these simple steps: Step 1: Work out the...

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### Finding the nth term of decreasing linear sequences (math help)

Finding the nth term of a decreasing linear sequence can by harder to do than increasing sequences, as you have to be confident with your negative numbers. A decreasing linear sequence is a sequence that goes down by the same amount each time....

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### How to Find the nth Term of an Increasing 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). Example 1 Find the nth term of this sequence. 5 8 11 14 17 First of...

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### Area of a semicircle. Finding the area of semi circles.

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...

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### Math Expressions. How to Write Simple Mathematical Expressions.

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...

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