Maths Summer EOY Assesment Flashcards

Surds

Irrational numbers that can be expressed as the root of a whole number, such as √2 or √3, which cannot be simplified to remove the square root.

Calculate With Surds

performing arithmetic operations like addition, subtraction, multiplication, and division with numbers expressed as square roots (or other roots) that cannot be simplified to whole numbers or rational numbers

Expand Brackets with Surds

multiplying out expressions that contain square roots (surds) within parentheses

Rationalise The Denominator

the process of transforming a fraction with an irrational denominator (like a square root) into an equivalent fraction with a rational denominator (a whole number)

Expand Double Brackets

the process of multiplying two binomials together, resulting in a polynomial expression that combines like terms

Factorise Quadratics

the process of rewriting a quadratic expression as the product of two binomials.

Difference of two squares

a mathematical identity that states that the difference between two squares can be factored into the product of their sum and difference, expressed as a² - b² = (a + b)(a - b).

expand triple brackets

the process of multiplying three binomials together, resulting in a polynomial expression that combines like terms.

compare coefficients in an identity

the method of equating the coefficients of corresponding terms from both sides of an equation to determine the values of unknowns.

solve linear equations

the process of finding the value of the variable that makes the equation true, usually involving isolating the variable on one side of the equation.

solve quadratic equations

the process of finding the values of the variable that satisfy a quadratic equation, typically using methods such as factoring, completing the square, or the quadratic formula.

solve simultaneous equations

the method of finding the values of variables that satisfy multiple equations at the same time, often using substitution or elimination techniques.

simultaneous equations on a graph

representing equations where the solutions are the points where the lines intersect, showing all possible solutions visually.

use Pythagoras’ Theorem’

a mathematical principle that relates the lengths of the sides of a right triangle, stating that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Pythagoras on a coordinate grid

applying Pythagoras' theorem to find distances between points and determine relationships between triangles on the coordinate plane.

Trigonometry

the branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right triangles.

Simplifying Algebraic Fractions

the process of reducing algebraic fractions to their simplest form by factoring and canceling common factors.

Calculations with algebraic fractions

involves operations such as addition, subtraction, multiplication, and division of fractions containing algebraic expressions.

Quadratic sequences

Quadratic sequences are generated by a quadratic function, where the nth term can be expressed in the form an² + bn + c.

similar shapes (Length, Area, Volume)

are shapes that have the same shape but may differ in size, maintaining proportional dimensions between corresponding sides.

Ratio With Algebra

is a relationship between two quantities expressed in terms of variables, showing how much of one quantity exists in relation to another.

Algebraic direct and inverse proportion

refers to the relationships between two variables that either increase or decrease together (direct) or one variable increases while the other decreases (inverse). In direct proportion, the ratio remains constant, while in inverse proportion, the product of the variables remains constant.

Percentage of an amount /increase/decrease

is a way to express a fraction of a total amount, indicating how much a quantity has increased or decreased compared to its original value, usually represented as a fraction of 100.

Reverse Percentages

is a method used to find the original amount before a percentage increase or decrease was applied, often used in problems involving discounts or tax calculations.

Simple and Compound Interest

Simple interest is a fixed percentage of the principal amount, while compound interest is calculated on the principal plus any accumulated interest.

Linear Graphs

straight line graph that visually represents a linear relationship between two variables