Algebra 1 - Master Key Algebra Techniques

Students will give examples of exponents and explain what they mean.

Students will use the rules of exponents in algebra and calculations.

Students will work with negative powers and powers of zero in algebra and in calculations.

After this class students will be able to evaluate fractional powers but using roots.

Students will describe what a radical (surd) is and give examples of what is, and what is not, a radical.

Students will confidently add and subtract radicals.

Students will confidently multiply and divide radicals.

Students will rationalise fractions using a standard technique.

Check how much you've learnt about Exponents & Radicals by trying these practice questions. Remember to check your work against the step by step solutions provided.

Students will describe what an algebraic formula is and give examples of made-up and meaningful formulae.

Students will use formulae by substituting values into them.

Students will practice rearranging formulas to any variable in the expression.

Students will describe the various elements that make up algebraic expressions and be able to construct algebraic expressions.

Students will simplify algebraic expressions by grouping and combining like terms.

Students will expand brackets and simplify the resulting expression.

Students will factorise algebraic expressions into one bracket using a common factor.

Check how much you've learnt about Algebraic Expressions by trying these practice questions. Remember to check your work against the step by step solutions provided.

Students will describe the key features of a quadratic expression and state quadratic expressions in different forms.

Students will factorise quadratic expressions by recognising a common factor.

Students will factorise a difference of two squares into two brackets.

Students will factorise a trinomial quadratic expression into two brackets.

Students will write quadratic expressions in completed square format.

Check how much you've learnt about Quadratic Expressions by trying these practice questions. Remember to check your work against the step by step solutions provided.

After this class students will be able to simplify algebraic fractions by factorising and cancelling terms.

After this class students will be able to multiply and divide algebraic fractions.

After this class students will be able to add and subtract algebraic fractions.

Check how much you've learnt about Algebraic Fractions by trying these practice questions. Remember to check your work against the step by step solutions provided.

Students will use a standard technique to solve one-step linear equations.

Students will solve equations with parentheses (brackets) in them.

Students will solve inequations by separation of variables.

Students will solve inequations which involve multiplying or dividing by a negative.

Students will describe what a system of equations is and explain what the solution to a system of equations represents.

Students will use the method of elimination of a variable to solve simultaneous equations.

Students will solve simultaneous equations where the variables don’t match by elimination of a variable.

Check how much you've learnt about Equations & Inequations by trying these practice questions. Remember to check your work against the step by step solutions provided.

Students will describe what a sequence is and give examples of sequences.

Students will find formulas to determine the general term of a sequence.

Students will give examples of a convergent and divergent sequence, and describe how that relates to the limit of the sequence.

Students will describe what the limit of a sequence is and give examples of sequences with and without limits.

Students will describe what an arithmetic sequence is and give examples of arithmetic sequences. Students will also be able to find the Nth term of such a sequence.

Students will describe what a geometric sequence is and give examples of geometric sequences. Students will also be able to find the Nth term of such a sequence.

Check how much you've learnt about Sequences by trying these practice questions. Remember to check your work against the step by step solutions provided.

Students will describe what the Cartesian co-ordinate system is and plot ordered pairs of co-ordinates.

Students will describe the key features of the graph of a straight line and give examples of such.

Students will find the gradient of a straight-line graph from two points.

Students will describe the format and features of the equation of a straight line and write the equation given the gradient and y-intercept.

Students will find the x and y intercepts of a straight-line graph algebraically.

Students will state the gradient of vertical and horizontal lines and describe why they have those gradients.

Students will sketch a straight line from given information.

Students will write the equation of a straight line given a sketch of its graph.

Check how much you've learnt about Graphs by trying these practice questions. Remember to check your work against the step by step solutions provided.

Students will describe what a Mathematical function is and give examples of functions.

Students will write formulas for various types of function and recognise different types of function from their formulas.

Students will sketch the graph of a function from its formula.

Students will describe what the maximum and minimum values of a function are, and demonstrate how they relate to the graph of the function.

Students will describe what the domain and the range of a function is and give examples of restrictions on the domain of a function.

Students will determine the average rate of change of a function between two points.

Check how much you've learnt about Functions by trying these practice questions. Remember to check your work against the step by step solutions provided.

Students will describe what quadratic functions are and the various forms of quadratic functions.

Students will state the key features of the graph of a quadratic function and sketch various possible quadratic function graphs.

Students will confidently solve quadratic equations by factorising into two brackets.

Students will confidently solve quadratic equations by writing them in completed square format.

Students will confidently solve quadratic equations which cannot be factorised by using the quadratic formula.

Students will use the discriminant to determine the number of solutions of a quadratic equation.

Students will describe the graphical interpretation of solutions to quadratic equations where they exist and where they don’t exist.

Students will describe what the roots of a quadratic function is and confidently find the roots by factorising.

Students will describe what the turning point is and confidently find the turning point using the completed square form of a quadratic.

Students will describe what the y-intercept of the graph of a quadratic function is and find the y-intercept given the equation in different formats.

After this class students will be able to state the equation of the axis of symmetry of the graph of a quadratic function.

Check how much you've learnt about Quadratic Functions by trying these practice questions. Remember to check your work against the step by step solutions provided.