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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...

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### Reflections. How to reflect a shape without tracing paper on squared paper.

Here I will show you how to reflect a shape in a mirror line without using tracing paper. All you need to do is measure the length (shortest distance) from each corner of your shape to the mirror line. Then measure...

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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...

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### Sphenic Numbers. How to identify if a number is sphenic or not spenic.

A sphenic number is a positive whole number that can be written as product of three distinct prime factors. So in order decide if a number is a sphenic number or not follow these two simple steps: Step 1 Work out the...

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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...

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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...

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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...

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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...

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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...

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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,...

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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...

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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...

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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...

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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...

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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...

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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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### The Density, Mass and Volume Magic Triangle: How to Calculate Density of a Solid Shape

The density, mass and volume triangle is as follows: So if you wanted to work out the density, you would cover up density in the magic triangle to give: Density = Mass/Volume (since mass is above volume) So if...

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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...

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### Mean From A Frequency Table. How To Work Out 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...

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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...

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### Recurring Decimals. How to covert a recurring decimal into a fraction?

The method for converting a recurring decimal into a fraction is a little bit unusual. To do this you need to make some equations which eliminate the decimals. This is much easier to see if we carry out some examples. ...

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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...

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### nth term worksheet or homework sheet. Includes answers (increasing sequences).

Here are some extra questions to help you working out the nth term of a number sequence. 1. Write down the nth term of this number sequence 3, 7,11,15,19... 2. Write down the nth term of this number sequence...

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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....

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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...

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### Compound H Shapes. Calculating the area of this H shape by splitting it up into 3 rectangles.

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...

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### What is the derivative of sin(Pix) and the derivative of cos(Pix)?

Finding the derivative of sin(ax) can be done using the following result: d/dx[sin(ax)] = acos(ax) Let’s take a look at some examples of working out the derivative of sin(ax). Example 1 Work out the derivative...

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### Length, Area and Volume scale factors of mathematically similar shapes.

On this page you will learn how two calculate the area or volume of two mathematically similar shapes. Similar shapes are shapes whose lengths have been enlarged by the same scale factor. To solve these type of...

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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...

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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...

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### Simplifying surds. How to write root 12 in the form a root b.

Sometimes you will be asked to simplify a surd or write the surd in the form a√b. To do this you will need to think of two integers that multiply together to give the number underneath the surd. One of the numbers...

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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...

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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...

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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...

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### How to draw a 30 degree angle from a 60 degree angle with a compass and ruler only.

In order to draw a 30⁰ degree angle without a protractor first you will need to construct a 60⁰ angle and then bisect this 60⁰ angle. Bisect means cut into two equal halves. Drawing a 60⁰ angle is quite easy...

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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...

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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...

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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...

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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...

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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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### Proportion problems. How to solve those recipe questions on your maths GCSE paper.

In these examples, you will be given the values of two related quantities and you will be asked to find the value of one of the quantities when the other quantity changes. These simple types of proportion problems are...

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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...

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### Differentiating the exponential function. The derivative of e^x.

The exponential function is probably one of the easiest functions to differentiate as the derivative is the same function. This means that the derivative of exponential is exponential: So if y = ex then dy/dx = ex ...

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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...

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### The integral of cosine. How to integrate cos(ax+b), eg cos2x = 1/2sin2x + c

The integral of cosine is sine: Therefore: ∫cosdx = sinx + c However, this is probably a more useful result to remember when integrating: ∫cos(ax + b) = (1/a)sin(ax+b) + c Let’s take a look at a few...

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### Histograms and frequency density. How to draw a histogram from a frequency table.

A histogram is can be drawn if the data you have is continuous and the groups are of unequal width. A histogram looks a bit like a bar chart except that the y-axis represents the frequency density. So the first thing to...

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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...

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### Fractional Exponent Law. How to work out the value of fraction exponents.

A fractional exponent can be worked out by applying the following rule: am/n = (n√a)m This means the nth root of a raised to the power of m. This is easier to see if you take a look at some numerical examples: ...

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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...

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### Volumes of triangular shaped prisms. How to work out the volume of a triangular prism.

Working out the volume of a triangular prism is basically a two step problem: First you will need to calculate the cross-sectional area of the triangular prism (area of the triangle at the front of the shape). To find...

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### Mixed numbers. Changing mixed numbers into improper fraction using a quick method.

A mixed number is a number that is made up of a whole number and fractional part. It may also be referred to a mixed fraction. 3 ¼ is an example of a mixed number. An improper fraction is a fraction where the...

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### Rotational Symmetry. What is the order of rotational symmetry of a rectangle?

A shape has rotational symmetry if you can rotate the shape onto itself more than once in a full 360⁰ turn. The amount of times you can turn the shape onto itself is known as the order of rotational symmetry. If 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...

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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...

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### Rotations Math. How to rotate a shape 90, 180 or 270 degrees clockwise or anticlockwise.

If you are asked to rotate a shape then you need to turn the shape around. In most questions the rotations will be: ¼ turn or 90⁰ turn ½ turn or 180⁰ turn ¾ turn or 270⁰ turn Also make sure that the...

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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...

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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...

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### What is the sum of all the angles in a 4 sided shape (angles in a quadrilateral add up to 360 degrees)

Angles in a quadrilateral add up to 360⁰. This is because you can divide up a quadrilateral into 2 triangles and since the angles in a triangle add up to 180⁰, then 2 × 180⁰ = 360⁰. So if you are asked to find...

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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...

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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...

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### Percentage Profit Formula Questions (from the buying price and selling price)

Before you can work out a percentage profit first you need to understand a few terms: Buying Price (cost price) – this is the amount you purchased your item for (usually from the warehouse) Selling Price – this...

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### Rectangles, Properties and mathematical facts of a rectangle (oblong)

A rectangle is probably one of the first shapes you recognise, but knowing all of the mathematical of a rectangle is a little trickier. Here are the main mathematical properties of a rectangle, many obvious but others...

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### Squaring numbers math help. How to square negatives, fractions and decimals (x^2)

To work out the square of a number just multiply the number by itself. A little 2, written on the top right of the number, means that you are squaring the number. So, 7² means you need to work out the square of 7...

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### Frequency tables and the median class interval. (working out the median group from a frequency table)

Finding the median average from a frequency table can first be done by working out the total frequency. Now the median number is the middle value - so you need to halve the total frequency. This number is where the...

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### Understanding metric units. Choosing the most suitable metric unit of measurement in different situations.

Thought I would write this hub to help you understand metric measurements of length, weight and volume. The main metric units of length are: millimetres (1 mm is about the width of a tip of a pencil) centimetres (1...

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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:...

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### Trigonometric Addition and Difference Formulas (Identities) Also double angle formulas.

The addition and difference formulas used in trigonometry are as follows: sin (A+B) = sinAcosB + cosAsinB sin(A-B) = sinAcosB – cosAsinB cos(A+B) = cosAcosB – sinAsinB cos(A-B) = cosAcosB + sinAsinB ...

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### Math Help—How to Work out the Product and Sum of Two 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 write down all the integers that satisfy an inequality between two numbers.

If you are asked to write down all the integers that satisfy the inequality -3 < x ≤ 4, then you are looking for all the values of x that are more -3 and less than or equal to 4. This is because -3 < x means x >...

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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...

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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...

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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...

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### Hot maths topics for the 2013 GCSE maths foundation calculator paper.

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...

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### 2015 GCSE Maths Foundation Exam. 5 top topics to revise to help you get a grade C (non-calc paper)

In this hub I will go over some of the more mathematical topics that will have a high proabability of showing on this years maths GCSE non-calculator foundation exam. All the topics covered here are grade D and C...

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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 ...

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### How to find the perimeter of a shape, if the shape is drawn on centimetre squared paper.

Perimeter is the distance around the outside of a 2D shape. If the shape is drawn on centimetre squared paper all you need to do is go round the edge of the shape counting each edge of the shape. It’s a good idea to...

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### Regular ocatagons, what are the mathematical properties of a regular octagon (math facts)

There are many mathematical properties of a regular octagon: 1) A regular octagon has 8 equal side lengths. 2) A regular octagon has 8 equal angles. 3) A regular octagon has 8 lines of reflectional symmetry. ...

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### What is a reciprocal? For example, why is the reciprocal of 8 equal to 0.125?

In order to take a reciprocal of a number all you need to do is divide the number into 1. That is: Reciprocal = 1 ÷ your number Reciprocals can be useful in calculus and working out the gradient of a normal line....

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### How do you know when to use the quadratic formula in a maths exam question.

In most examination questions it won’t always tell you when to use the quadratic formula. So you need to be able to identify which quadratic equations require the use of the quadratic formula. First of all, you...

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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...

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### How to work out a fraction of a number (fractions of numbers help)

To work out a fraction of a number all you need to do is divide the number by the denominator of the fraction and multiply this answer by the numerator. Example 1 Work out 3/8 of 48. First of all divide 48 by...

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### How to write down a ratio in its simplest form (simplifying ratio method).

Ratios can be simplified in exactly the same ways as a fraction. All you to do is divide both sides of the ratio by the greatest common divisor of the two numbers in the ratio. Let’s take a look at a few examples on...

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### How to round a number off to 1 significant figure (1sf or 1 sig fig)

Rounding to 1 significant figure is very useful when you need to estimate. Your 1st significant figure is the first number from the start of the number you need to round (ignoring any zeros at the start). Let’s take a...

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### Short multiplication method. How to multiply a number by a single digit number using short multiplication.

Short multiplication is one of the easiest methods to use when multiplying a number by a single digit number. All you need to do is work from right to left and multiply each digit in your number by the number 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...

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### Solving triangles. How to work out the angles in a triangle when the angles given 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...

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### How to measure a bearing in math (a 3 digit angle measured clockwise from north)

A bearing is a 3 digit number measured clockwise from a north line (north is 000⁰) If the question asks you to work out the bearing of B from A follow these steps: Step 1. First of all join the points A and B with...

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### How to write down a simple probability as a fraction (math and statistics help).

Probability is the likelihood of an event happening. Using a fraction is the easiest way to express probability and this can be done by using the following formula: (Number of successful outcomes)/(Total number...

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### How to calculate the area of circle giving your answer in terms of Pi.

In this hub I will show you how to find the area of circle giving your answer in terms of Pi (π). First of all you need to remember the formula for calculating the area of a circle: A = πr² A stands for...

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### How to find the area of shape by counting the squares (Year 6 maths)

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...

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### How to calculate a cube number. (examples include 2 cubed and 4 cubed).

A cube number is found by multiplying a number by itself 3 times. A tiny 3 on the top right of a number means you have to cube the number. Example 1 Work out the cube of 2 (which can be written as 2³). To...

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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...

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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...

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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...

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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...

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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...

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### How to find the area of trapezium.

A trapezium is a 4 shaded shape with one pair of parallel sides. In order to find the area of a trapezium follow these simple steps: Step A Add together the parallel side lengths. Step B Times this answer by...

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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...

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### Johnny 5 Best Quotes - Short Circuit Movie Review

Short circuit is a 1986 science fiction comedy starring Ally Sheedy and Steve Guttenberg. A highly experimental and dangerous robot created by the military accidentally gets struck by lightning and comes to life. The...