**ALGEBRA LESSONS - CONTENT LIST**

**Please note: **This list of for viewing purposes only, showing list of lessons that are available on the website - each of the links once registered will link to suitable lesson as described. The right hand column will also link to worksheets which accompany the given lessons to be delivered to help you plan required resources.

Title | Description/Objectives | GCSE papers requiring relevant topic | Calculator required | Lesson requires printed documents | |

Solving quadratic inequalities | To be able plot inequalities on a graph, by plotting quadratic graphs. Extending to re-arranging inequality in form ax^2 + bx + c > 0 | ||||

Solve inequalities with one or two variables | To be able solve inequalities. Beginning with 1 step equations, then 2 step equations, followed by double inequalities. Extending to using negative numbers. | ||||

Solving quadratic equations by factorising | To be able solving simple quadratic equations by factorising into 2 brackets (coefficients of x is always 1). Extending to re-arranging equation to form x^2 + bx + c = 0 first. | ||||

Expression, Equation, Identity and Formula | To be able to identify expressions, equations, formulaes and identities | ||||

Solving quadratic equations by using the formula | To be able to accurately use the quadratic formula to solve equations | ||||

Simplifying Expressions | To be able to add and subtract terms with common unknowns, and to be also able to multiply out simple terms . | ||||

Use Trial and Improvement to find approximate solutions of equations | To be able to apply trial and improvement method to find solution to specified decimal placing, starting with 1dp moving to 2dp, extending to 3dp. | ||||

Parallel and perpendicular lines | To be able to calculate perpendicular gradient, given just gradient (using m1xm2 = -1), leading onto finding equations of perpendicular lines to given a linear equation on the point of intersection, then finding equations of perpendicular or parallel lines | ||||

Change the subject of a Formula | To be able to change the subject of the formula by re-arranging, leading onto working with powers and then re-arranging formulas with unknowns on both sides. | ||||

Factorising using difference of two squares | To be able to factorise expressions using the difference of 2 squares | ||||

Find the equation of a straight line from gradient and co-ordinates | To be able to find the equation of a line initially given a gradient and a co-ordinate, leading onto finding the equation from 2 co-ordinates, not given the gradient. | ||||

Find the gradient of a straight line graph from 2 points | To be able to find the gradient of a line given 2 co-ordinates, extending to 2 co-ordinates which involve negative numbers | ||||

Find the mid-point and length of a line | To be able to find the midpoint of a line from a drawn line, extending to finding midpoint between 2 co-ordinates. To also be able to calculate the length of a line from a drawn line, leading onto between 2 co-ordinates. | ||||

Understand and plot points in four quadrants | To be able to plot co-ordinates in different quadrants, leading to any quadrant, followed by reading co-ordinates in all quadrants. | ||||

Geometric sequence (Common Ratio) | To be able to identify a common ratio of a sequnece, followed by being able to find a term given first number and common ratio. | ||||

Co-ordinates in one quadrant | To be able to plot co-ordinates in the 1st quadrant, followed by reading co-ordinates in the 1st quadrant | ||||

Solving quadratic equations by completing the square | To be able to completethe square with co-efficients of x^2 as 1, extending to completing the square where the co-efficient of x is not 1 | ||||

Completing the square of quadratic expressions | To be able to solve equations by completing the square, leading onto equations which have co-efficients of x, and extending to re-arranging equation to form x^2 + bx + c = 0 first. | ||||

Solve equations that include brackets | To be able to solve equations which contain brackets. Expanding brackets prior to re-arranging and solving. | ||||

Solve equations that include powers | To be able to solve equations which containing powers - a short lesson (used as an add ont) | ||||

Working with Algebraic Fractions | To be able to add and subtract algebraic fractions, moving onto simplifying - followed by multiplying and dividing | ||||

Solving Fractional equations | To be able to solve equations which involve algebraic fractions with more than one unknown. | ||||

Solve equations with unknown on both sides including negative numbers | To be able to solve multiple step equations with unknowns on both sides, with differing order of operations. | ||||

Re-arranging & solving simple one step equations | To be able to solve simple one step equations split between adding & subtracting, dividing and multiplying with a fraction. | ||||

Solve two step equations with unknown on one side and involving fractions | To be able to solve simple two step equations, with differing order of operations. | ||||

Use elimination or substitution to solve simultaneous equations | To be able to solve simultaneous equations by elimination or subsitution. Solve by adding or subtracting, extending to having to multiply one or both equations. | ||||

Using number sequences & describe a rule of a sequence | To be able to spot the linear sequence, the term to term rule and find then create a sequence knowing a specific rule. | ||||

Substitute Numbers into Formula | To be able to substiute numbers into increasingly challenging formulas. | ||||

Substitute Numbers into Expressions | To be able to substiute numbers into increasingly challenging expressions, including mixed variables and extending to negatives | ||||

Find & Use the nth term expression for a sequence | To be able to use linear nth terns to find a specific term in a sequence and then to be able to find the nth term of a written linear number sequence. | ||||

Find the nth term expression for a quadratic sequence | To be able to use quadratic nth terns to find a specific term in a sequence and then to be able to find the quadratic nth term of a written quadratic number sequence. | ||||

Circle equations in the form x² + y² = r² | To be able to work out equation of a circle given it's radius and centre, leading onto being able to find equation of a tangent given centre and co-ordinate on a circle. | ||||

Forming Expressions, Equations or Formula | To be write or derive expressions, equations, formulaes and identities from given information. | ||||

Iteration | To be able to use iteration to find roots of equations | ||||

Quadratic Simultaneous Equations | To be able to solve simultaneous equations, where one equation is a a quadratic, and the other is linear. | ||||

Turning Points | To be able to find the turning point of a quadratic equation / function | ||||

Triple Brackets | To be able to expand triple brackets - with varying degrees of difficulty | ||||

Finding the Equation of a Line | To be able to find the y-intercept, the gradient 'm' followed by the whole equation of a line | ||||

Quadratic Graphs | To be able to plot quadratic graphs, find the solution from quadratic graphs - leading onto solving simultaneous equations involving a quadratic graph | Graph Paper Required |
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Factorising Linear Expressions | To be able to factorise expressions, starting from integer factors, then algebraic factors leading onto combined factors | ||||

Expanding Single Brackets | To be able to expand and simply brackets, starting with 1 bracket moving onto 2 brackets | ||||

Expanding Double Brackets | To be able to expand double brackets using either grid method or combination method. Questions extending to brackets with coefficients of x | ||||

Factorsing Quadratics into 2 Brackets | To be able to factorise quadratics, starting with X^2 moving onto quadratics with coefficient of x more than one. | ||||

Drawing Straight Line Graphs | To be able to draw straight line graphs using a table or otherwise, extending to solving simultaneous equations by drawing graphs |