Maths
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GCSE
In this GCSE Maths video, we look at whole numbers. There are many different types of numbers, including integers, rational numbers, square numbers, surds, prime and factors, plus many more. Numbers can be written in words. Both positive and negative numbers can be added, subtracted, multiplied and divided using rules. These rules must be applied in a specific order.
In this video, we take a look at the topic of AQA GCSE Maths Decimals. Decimal points are used in numbers to separate the whole number from parts of the whole. Like whole numbers, numbers written as decimals can be either positive or negative, for example, 2.6 or -2.6. Decimals are just one way of expressing numbers that are parts of wholes. These numbers can also be written as fractions or percentages. The number 1.5 (decimal) could also be written as (fraction) or 150% (percentage). They are all exactly the same number. Knowledge of converting between decimals, fractions and percentages is important.
Fractions, decimals and percentages are frequently used in everyday life. Knowing how to convert between them improves general number work and problem-solving skills. To convert a decimal to a fraction, use place value. The first number after the decimal place is worth tenths, the next is worth hundredths, the next thousandths and so on. Once a number is written as a decimal, it can be converted to a percentage. Remember that 'per cent' means 'per hundred', so converting from a decimal to a percentage can be done by multiplying by 100 (move the digits two places to the left).
In this AQA GCSE maths video, we are looking at approximation. This is where we round a number up or down to the nearest whole number, decimal or fraction. We also look at truncation and estimation. Truncation is when we cut off a number after a certain point, and estimation is when we guess a value for a number. Finally, we look at bounds which are upper and lower limits that a value falls between.
Sometimes it is a good idea to estimate the value of a calculation rather than work it out exactly. In this situation, round the numbers in the question before performing the calculation. Usually, numbers are rounded to one significant figure. The 'approximately equal to' sign, ≈, is used to show that values have been rounded.
In this video, we take a look at fractions and the 3 sub-topics. Improper fractions, fractions of numbers and arithmetic. This is a key skill for GCSE maths students!
We cover topics such as converting improper fractions to mixed numbers and vice versa, finding the value of fractions, comparing fractions and more!
Follow along as we show you how to work out a number of AQA GCSE exam questions on Fractions, such as “Work out 1 3/5 divided by ¾” and “a class has 29 students. 16 of the students are girls. What fraction of the students are boys?”
This AQA GCSE Maths video covers factors, multiples and prime factorisation. It looks at how to find the factors of a number, what is a multiple of a number and how to find the prime factors of a number.
The video also looks at square numbers and cube numbers and how to use the prime factor tree to help find the LCM and HCF of two or more numbers.
A multiple of a number is any integer multiplied by the number.
A factor is an integer (whole number) that will divide exactly into another number.
Factor pairs are two numbers which multiply together to make a particular number.
In this video, we look at the Laws of indices and give rules for simplifying calculations or expressions involving powers of the same base. We have base numbers and indexes or powers when writing certain formulas. For example; 24. 2 is the base number and 4 is known as the power or index number.
Calculations with very big or small numbers can be made easier by converting numbers in and out of standard form.
Standard form, or standard index form, is a system of writing numbers which can be particularly useful for working with very large or very small numbers. It is based on using powers of 10 to express how big or small a number is.
A surd is an expression that includes a square root, cube root or another root symbol. Surds are used to write irrational numbers precisely – because the decimals of irrational numbers do not terminate or recur, they cannot be written exactly in decimal form.
In this video, we cover the AQA GCSE Maths topic of financial maths which is needed for all jobs, from calculating wages to working out profit, loss and VAT. Knowledge of financial maths is also required to be able to understand bank statements and savings. We discuss subtopics like gross pay (the full amount paid to an employee before any deductions are made), deductions (income tax, national insurance and sometimes pension contributions) and net pay (what's left after deductions have been made from gross pay. This is the amount an employee actually receives).
In formulae, letters can be used to stand for unknown values or interchangeable values. These formulas can be written and equations solved for a range of problems in industries such as science and engineering. In algebra, letters are used to stand for values that can change (variables) or for values that are not known (unknowns). Collecting like terms means simplifying terms in expressions in which the variables are the same.
Factorising is the reverse process of expanding brackets. A factorised answer will always contain a set of brackets.
A formula is a math rule or relationship that incorporates letters to represent amounts that can be changed. These are known as variables and are commonly portrayed as either a, b, c or x. Formulae are used in daily life, from working out areas and volumes to converting units of measurement. Knowing how to use and rearrange formulae are beneficial skills.
In this video, we take a look at linear equations and how to solve them using BIDMAS (Brackets, Indices, Division, Multiplication, Addition and Subtraction) and why it is so important to follow the golden rule of linear equations "Always do the SAME thing to both sides of the equation".
In this video, we find out that simultaneous equations are equations that have more than a single unknown and can have an infinite number of solutions.
We break down the 2 methods by which you can calculate simultaneous equations; cancelling and substitution.
The most common method for solving a simultaneous equation is the elimination method which is where one of the unknowns is removed from the question, meaning that the remaining unknown can then be calculated.
As well as break down some AQA GCSE maths exam paper questions and answers.
Let's look at how to solve quadratic equations using the Quadratic Formula. We also factorise quadratic expressions and use iteration to find approximate solutions. Quadratic algebraic equations contain terms up to x^2; the highest power for quadratic equations is 2. They are polynomial equations because they consist of two or more algebraic terms.
At GCSE the solutions to polynomial equations such as quadratics will always give real numbers but they can be either irrational and rational numbers.
This video is perfect for AQA GCSE Maths students studying Module 2: Algebra and anyone who simply wants to learn more about solving quadratic equations.
Let's explore the basics of inequalities - what they are and how to solve them.
Inequalities show the relationship between two expressions that are not equal. They are useful when looking to project profits and breakeven figures.
We look at examples on a number line and see how the solution is found by moving along the line until we reach a point where the inequality symbol is valid.
Sequences can be linear, quadratic or practical and are based upon real-world situations. If you can find some general rules then it will help you find terms in sequences.
Number sequences are sets of numbers that follow a particular pattern or rule.
If the rule is to add or subtract a number each time, this is called an arithmetic sequence.
If the rule is to multiply or divide by a number each time, then it is called a geometric sequence.
Each number in a sequence is known as a term.
A sequence which increases or decreases by the same amount each time is called a linear sequence.
In this AQA GCSE Maths video, we take a look at straight line graphs and how to find their y-intercept and gradient. We also look at how to determine whether two lines are parallel or not.
Graphs are used to show the relationship between two different variables and are found throughout the world in everyday life, whether they are seen in newspapers, businesses or the media to help indicate data in an easy-to-understand way.
The most common professions that usually use graphs involve maths and science.
There are 4 commonly occurring graphs, these are; quadratic, cubic, reciprocal, exponential and circle graphs. Each of their equations can be used to plot a particular shape or curve on a graph.
A quadratic graph is produced when you have an equation of the form Y = ax^2 + bx + c, where b and c can be zero but a cannot be zero.
All quadratic graphs have a line of symmetry.
A cubic equation contains only terms up to and including x³.
A graph in the form of y = 1/x is known as a reciprocal graph.
Exponential graphs are found in the form of y = k^x. These graphs increase rapidly in the direction of y and will never fall below the x-axis.
Take a look at the transformation of curves with us. We look at translation and reflection to see how these can be used to change shapes. This is an AQA GCSE Maths topic, but the concepts are applicable to all levels of maths.
Functions of graphs can be transformed to show shifts and reflections. Graphic designers and 3D modellers use transformations of graphs to design objects and images.
In this video, we will be looking at algebraic fractions. First of all, let's remind ourselves what an algebraic fraction is. An algebraic fraction is a fraction where the numerator and denominator are both polynomials. In order to simplify an algebraic fraction, we need to do two things: first of all, cancel any common factors in the numerator and denominator; secondly, reduce the fractions if possible.
This is a great tutorial for AQA GCSE maths students, but it can be useful for anyone who wants to learn more about algebraic fractions.
In this video, we take a look at how to use and interpret graphs. This is an AQA GCSE Maths topic, but the skills you learn here are applicable to many other subjects.
We start by looking at what a graph is and what different types of graphs there are. We then move on to looking at how to read data from a graph, including understanding scales and axes. Finally, we see how to interpret graphs in order to make deductions about trends or relationships by answering some exam-style questions and going through how to answer them.
Ratios are seen in everyday life. They can be used when adding ingredients to make a meal, when deciding how much pocket money children get or when reading a map.
Ratios are used to show how things are shared. They can have more than 2 numbers, such as 4:2:1.
Ratios can also be fully simplified just like fractions. To simplify a ratio, divide all of the numbers in the ratio by the same number until they cannot be divided anymore.
A common example of a ratio in everyday life is when mixing paint colours. For example; 2 parts blue to 1 part yellow will make green.
A percentage is a proportion that shows a number as parts per hundred. The % symbol represents the percentage. An example; 12% can be displayed as 12/100 or 12 out of every 100.
Percentages are just one way of expressing numbers that are part of a whole. These numbers can also be written as fractions or decimals. 50% can also be written as a fraction, 1/2, or a decimal, 0.5. They are all exactly the same amount.
Proportion is used to show how quantities and amounts are related to each other. The amount that quantities change in relation to each other is governed by proportion rules.
Direct proportion is when one value of 2 is a multiple of the other. As an example; 1 cm equals 10 mm. In order to convert mm into cm you ALWAYS multiply by 10.
If one value is inversely proportional to another then it is written using the proportionality symbol in a different way. Inverse proportion occurs when one value increases and the other decreases. For example, more workers on a job would reduce the time to complete the task. They are inversely proportional.
Polygons are multi-sided shapes with different properties. Shapes have symmetrical properties and some can tessellate. There are 360° in a full turn, 180° in a half turn and 90° in a quarter turn. A quarter turn is called a right angle. Angles around a point add up to 360°. This fact can be used to calculate missing angles. Angles on a straight line add up to 180°. This fact can also be used to calculate angles.
Polygons are multi-sided shapes with different properties. Shapes have symmetrical properties and some can tessellate. Parallel lines are lines which are always the same distance apart and never meet. Arrowheads show lines are parallel. When a pair of parallel lines is cut with another line known as an intersecting transversal, it creates pairs of angles with special properties.
Loci are a set of points with the same property. Loci can be used to accurately construct lines and shapes. Bearings are three-figure angles measured clockwise from North.
A locus is a path formed by a point which moves according to a rule. The plural is loci.
2-dimensional shapes are flat. The perimeter of a 2D shape is the total distance around the outside of the shape. The area of a 2D shape is the space inside the shape. 2D shapes only have 2 dimensions, length and width. A polygon is known as a closed 2D shape with straight sides. Examples of polygons include triangles, quadrilaterals, pentagons, hexagons and octagons. Regular polygons have sides that are equal in length and have equal angles.
3D shapes have faces, vertices & edges and can be viewed from different points. All 3D shapes have 3 dimensions - length, width and height. 3D shapes unlike 2D shapes have a volume as there is space inside of them.
Types of 3D shapes:
Cylinder
Cube
Pyramid
Triangular prism
Cone
Cuboid
Hexagonal prism
Sphere
Hemisphere
Plus many more...
The volume of a 3D shape is the space that occupies the inside. The surface area of a 3D shape is the total area of all the faces.
To calculate the volume of an object depends upon the shape of the object.
Cuboid volume = length x width x height
Prism volume = area of cross section x length
Cylinder volume = pie x radius2 x height
Transformations change the size or position of shapes. Congruent shapes are identical but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape.
Equations are incredibly important in transformations as they help determine lines of symmetry, centres of rotation and many more...
Here in this video, we will learn about circles, arcs and sectors, including how to find the area and circumference of a circle and how to find the area and arc length of a sector. Circles are round plane figures whose boundaries consist of equidistant points from a fixed point in the centre.
Each part of the circle has a specific name and properties.
Minor Arc
Major Arc
Minor Segment
Major Segment
Tangent
Sector
Diameter
Radius
Chord
What exactly are circle theorems then? Well, they are properties that show relationships between certain angles in the geometry of a circle. We use these theorems alongside prior knowledge of other angle properties to calculate any angles that might be missing, without the need for a protractor.
There are seven main circle theorems:
Alternate segment circle theorem
The angle at the centre circle theorem
Angles in the same segment circle theorem
Angle in a semi-circle theorem
Chord circle theorem
Tangent circle theorem
Cyclic quadrilateral circle theorem
Pythagoras' theorem states that, in any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares on the other two sides.
The longest side of a right-angled triangle is the hypotenuse. The hypotenuse is always opposite the right angle.
Pythagoras’ theorem can be used to calculate the length of any side in a right-angled triangle. Pythagoras’ theorem can be applied to solve 3-dimensional problems.
There are two systems used for measuring quantities - metric and imperial.
The metric system uses three main units for measuring:
Length in metres (m)
Mass in kilograms (kg)
Volume in cubic metres (m3)
The imperial system uses the following units:
Length in inches, feet and yards.
Mass in pounds (lb), ounces (oz) and stones.
Volume in gallons.
The three trigonometric ratios; sine, cosine and tangent are used to calculate angles and lengths in right-angled triangles. The sine and cosine rules calculate lengths and angles in any triangle.
A vector has both size and direction and they can be added to, subtracted from and multiplied by a scalar. Most geometrical problems encountered in everyday life can be solved using vectors.
A vector describes a movement from one point of origin to another. A vector quantity has both direction and magnitude whereas a scalar quantity only has a magnitude which is a fancy word for size. Vectors are represented by lines with an arrow in the centre of them.
Probability is about estimating or calculating how likely or probable something is to occur. The chance of a particular event transpiring can be described using words like "certain", "impossible" or "likely". In Maths, the probability is always displayed as either a fraction, decimal or percentage with values between 0 and 1. Any outcome deemed to be impossible will have a probability of 0 whilst an outcome that is certain will be 1. Probabilities cannot be larger than the value of 1.
Many companies and organisations collect data to improve their information and products. Skills in collecting data can make this process more efficient and reliable. Data is a collective name for information recorded for statistical purposes. There are many different types of data:
Discrete data - numerical data that can only take certain values, for example, the number of children in a classroom or a shoe size.
Continuous data - numerical data that can take any value within a given range, for example, the masses of 10 babies or the heights of some adults.
Primary data - data that has been collected from the original source for a specific purpose, for example, if a school wanted to know what their students thought of the school canteen service they would question the pupils directly.
Secondary data - data that is not originally collected by a group for a specific purpose, for example, finding out the average cost of cars in a car park by using national statistics.
Data is represented in many different forms. Using bar charts, pie charts and frequency diagrams can make information easier to digest.
There are many different ways to display data, for example:
Frequency Tables
Bar Charts
Pictograms
Pie Charts
Scatter graphs and many more...
In statistics, there are three types of averages: the mean, the median and the mode. Measures of spread such as the range and the interquartile range can be used to reach statistical conclusions.
The mean is the most commonly used average. The median is the middle number in a set of data when the data has been written in ascending or descending size order. The mode is the number, or item, which occurs most often in a set of data. In statistics, a range shows how spread out a set of data is. The bigger the range, the more spread out the data. If the range is small, the data is closer together or more consistent.
Let's take a look at how to approach problem-solving questions in GCSE maths.
We'll discuss some general tips for approaching these types of questions, as well as looking at some specific methods that can be used for different question types whilst running through some practice exam questions.
This video is ideal for students who are studying GCSE maths and need help with problem-solving questions.
In this video, we look at some GCSE maths number problems. We'll be looking at how to solve them using BIDMAS (Brackets, Indices, Division, Multiplication, Addition and Subtraction), standard form and factorisation.
We run through some practice exam questions and answers to help you put your knowledge into practice. Feel free to pause and attempt to answer the questions before we go through our workings out to test yourself.
This video is perfect for anyone studying GCSE maths or wanting to brush up on their problem-solving skills!
GCSE Maths graphical problems questions will commonly be linked to real-life scenarios and situations such as travel graphs, temperature graphs and conversion graphs to name a few. This video breaks down the common framework used to tackle graphical problems.
The scale of graphs is important so it is essential to have a basic understanding of the scale and what each notch on the axes equals in order to solve the problem correctly.
We tackle geometric problems in this video. Standard geometric problems often have diagrams provided involving triangles, quadrilaterals and other polygons. It is important to know the properties of shapes as multiple questions involve knowing angle and length properties. The standard problem-solving framework should be used to approach geometry problems.
Algebra problems can relate to any area of maths. Problems often include a mix of algebra, numbers and geometry. A framework can be used to tackle these problems. Most algebraic problems require one or two steps in order to arrive at the correct answer. Most of the difficult problems involve forming equations and solving them before being able to use the answer in some way.
Statistical problems come in 2 forms. Finding the mean, median, mode and range for some data and extracting certain aspects of information given to us in a statistical chart or diagram. The problems involve basic number work but algebra may be required so it is important to apply the basic number problem-solving framework.
