OCR Foundation Maths: Statistics and Probability

Overview

• This is a compilation of maths tutorials for the OCR Foundation Maths course.
• They are all taught by corbettmaths.
• The playlist contains 268 videos and has 26,528 views.
• The playlist was last updated on May 19, 2023.
• The topics covered include statistics, probability, algebra, sequences, graphs, decimals, fractions, percentages, multiplication, division, rounding, and more.

Frequency Trees

• Frequency trees are a way of displaying data in a tree diagram, where each branch represents a different category or outcome.
• They are used to solve probability problems.

Two Way Tables

• Two-way tables display data for two categorical variables.
• They show how many times each combination of categories occurs.

Pictograms

• Pictograms use pictures or symbols to represent data.
• Drawing pictograms involves choosing a suitable symbol and scale.
• Reading pictograms involves counting the symbols and multiplying by the scale.

Bar Charts

• Bar charts use bars of different lengths to represent data.
• Drawing bar charts involves choosing a suitable scale and drawing the bars to the correct height.
• Reading bar charts involves reading the height of the bars and multiplying by the scale.

Frequency Polygons

• Frequency polygons are line graphs that connect the midpoints of the tops of the bars in a histogram
• They are used to show the shape of a distribution.

Line Graphs

• Line graphs connect data points with lines to show trends over time or relationships between variables.

Pie Charts

• Pie charts are circular charts divided into sectors.
• Sectors represent the proportion of each category in a data set.
• Drawing pie charts involves calculating the angle of each sector and drawing it accurately.
• Interpreting pie charts involves measuring the angle of each sector and calculating the corresponding proportion.

Scatter Graphs

• Scatter graphs show the relationship between two variables.
• Correlation describes the strength and direction of the relationship.
• Positive correlation means that as one variable increases, the other variable also increases.
• Negative correlation means that as one variable increases, the other variable decreases.
• No correlation means that there is no relationship between the variables.

Probability

• Probability is the measure of how likely an event is to occur.
• The probability scale ranges from 0 to 1.
• Listing outcomes involves writing down all the possible results of an event.
• The probability of an event not happening is 1 minus the probability of it happening.

Tree Diagrams

• Tree diagrams are used to show the possible outcomes of a series of events.
• Each branch represents a different outcome, and the probabilities are written on the branches.
• The probabilities of all the branches from a single point must add up to 1.

Mode, Median, Mean and Range

• The mode is the most frequent value in a data set.
• The median is the middle value in a data set when the data is arranged in order.
• The mean is the average of all the values in a data set.
• The range is the difference between the highest and lowest values in a data set.

Estimated Means from Grouped Data

• Estimated means from grouped data is a method of estimating the mean of a data set when the data is grouped into classes.

Venn Diagrams

• Venn diagrams are used to show the relationships between sets.
• They consist of overlapping circles, where each circle represents a different set.
• The overlapping areas represent the intersection of the sets and elements that belong to multiple sets.

Reading Tables

• Reading tables involves extracting information from rows and columns.

Coordinates

• Coordinates are used to specify the position of a point on a coordinate plane.
• They consist of two numbers, the x-coordinate and the y-coordinate, written as (x, y).

Algebra

• Substitution into expressions involves replacing variables with numbers to evaluate the expression.
• Forming algebraic expressions involves translating word problems into mathematical expressions.
• Collecting like terms involves simplifying an algebraic expression by combining the terms with the same variable and exponent.
• Dividing algebraic expressions involves dividing the coefficients and subtracting the exponents of the variables.
• Multiplying terms involves multiplying the coefficients and adding the exponents of the variables.
• Fibonacci sequences are sequences where each term is generated by adding the two previous terms (e.g., 1, 1, 2, 3, 5, 8...).
• nth term is a formula that allows you to calculate any term in a sequence directly, without knowing the previous terms.
• Expanding brackets involves multiplying each term inside the bracket by the term outside the bracket.
• Factorising is the reverse of expanding brackets.

Equations

• Forming equations involves creating a mathematical equation from a word problem or a real-life situation.
• Equations involving perimeter and angles may require knowledge of geometric properties to set up and solve.
• Solving equations with letters on both sides requires isolating the variable on one side of the equation.
• Solving equations involves finding the value of the variable that makes the equation true.

Inequalities

• Inequalities on a number line represent the range of values that satisfy the inequality.
• Inequalities involve comparing two expressions using symbols such as <, >, ≤, and ≥.
• Solving inequalities may involve manipulating the inequality to isolate the variable.

Exchange Rates

• Exchange rates are used to convert one currency into another.
• To convert from one currency to another, you multiply by the exchange rate.

Conversion Graphs

• Conversion graphs are used to convert between two different units of measurement.
• To convert from one unit to another, you read the graph at the corresponding point.

Linear Graphs and Parallel Lines

• Linear graphs are straight lines that can be represented by an equation of the form y = mx + c, where m is the gradient and c is the y-intercept.
• Parallel lines have the same gradient.
• Finding the equation of a linear graph involves finding the gradient and y-intercept and substituting them into the equation y = mx + c.
• Drawing linear graphs using gradient and intercept involves plotting the y-intercept and then using the gradient to find another point on the line.
• Drawing graphs xy table involves creating a table of x and y values that satisfy the equation and then plotting the points on a graph.
• Equation of a line can be determined from a graph or from two points on the line.

Changing the Subject

• Changing the subject of a formula involves rearranging the formula to isolate a different variable.

Simultaneous Equations

• Simultaneous equations are a set of two or more equations that share the same variables.
• Solving simultaneous equations involves finding the values of the variables that satisfy all the equations simultaneously.
• The elimination method involves eliminating one of the variables by adding or subtracting the equations.

Quadratic Equations

• Solving quadratic equations graphically involves plotting the graph of the quadratic equation and finding the points where the graph intersects the x-axis.
• Drawing quadratics involves plotting the graph of the quadratic equation.

Cubic and Reciprocal Graphs

• Cubic graphs are graphs of cubic equations, which have the form y = ax³ + bx² + cx + d.
• Reciprocal graphs are graphs of reciprocal equations, which have the form y = k/x, where k is a constant.

Multiplying and Dividing

• Multiplying decimals involves multiplying the numbers as if they were whole numbers and then placing the decimal point in the correct position.
• Multiplying fractions involves multiplying the numerators and denominators.
• Multiplying negatives involves multiplying the numbers and then applying the rule that a negative times a negative is a positive.
• Multiplication column method involves multiplying two numbers together using the column method.
• Division involves dividing one number by another.
• Division by decimals involves multiplying both numbers by a power of 10 to make the divisor a whole number and then dividing.
• Division with remainders involves dividing one number by another and finding the remainder.

Addition and Subtraction

• Addition involves adding two or more numbers together.
• Subtraction involves subtracting one number from another.
• Adding decimals involves lining up the decimal points and then adding the numbers as if they were whole numbers.
• Subtracting decimals involves lining up the decimal points and then subtracting the numbers as if they were whole numbers.

Rounding

• Rounding involves approximating a number to a given degree of accuracy.
• Rounding to the nearest whole number involves rounding to the nearest integer.
• Rounding to significant figures involves rounding to a specified number of non-zero digits.
• Rounding to 1 and 2 decimal places involves rounding to one or two digits after the decimal point.
• Rounding to the nearest hundred involves rounding to the nearest multiple of 100.
• Rounding to the nearest ten involves rounding to the nearest multiple of 10.

Approximations and Estimation

• Approximations to calculations involve rounding numbers to make calculations easier.

Number Properties and Operations

• Place value operations involve understanding the value of each digit in a number and using this to perform calculations.
• Order of operations (PEMDAS/BODMAS) dictates the sequence in which mathematical operations should be performed: Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction.
• Ordering fractions involves arranging fractions in order of size.
• Ordering decimals involves arranging decimals in order of size.
• Important fractions, decimals and percentages need memorization for quick conversions.
• Ordering fractions decimals percentages requires converting all to the same format for comparison.
• Halfway between two numbers involves finding the number that is exactly halfway between two given numbers.
• Decimals to Fractions / Fractions to Decimals can be achieved using calculator functions.
• Decimals to Percentages involves multiplying the decimal by 100.
• Percentages to Decimals involves dividing the percentage by 100.
• Multiples are numbers that can be divided evenly by a given number.
• LCM (Least Common Multiple) and Common Multiples are the smallest number that is a multiple of two or more numbers.
• Prime Numbers are numbers that have only two factors: 1 and themselves.
• Common Factors and HCF (Highest Common Factor) involve finding the largest number that divides two or more numbers exactly.