Algebra and Functions 1 
Resource description 
INDICES AND SURDS 

Basic rules of indices and spot the mistake  
Multiplying, dividing, brackets and fractional powers  
Mixture of basic, fractional and negative powers where the value of x is to be found  
Converting terms written using roots into powers and vice versa.  
Rules of Indices (mathsnet.net) 
Rules of indices including multiplication, division, brackets, fractions and negatives. 
Three exam questions on rules of indices


Easiteach file with a variety of exponential equations to use as a starter with whiteboards or a main lesson activity  
Numbers written in the form a root b, expand double brackets and simplify fractions.  
Simplifying Surds (mathsnet.net) 
Writing surds in the form a root b, multiplying out brackets and simplifying fractional surds 
Surds exam questions (mathsnet.net) 
Five exam questions on surds 
EXPAND BRACKETS AND FACTORISE 

Expand double brackets  
Expand Double Brackets (mathsnet.net) 
Expand double brackets 
Expand brackets with quadratic and cubic answers  
Factorise quadratics  
Factorise quadratics.


Factorise quadratics (mathsnet.net) 
Factorise quadratics including the difference of two squares 
Factorise quadratics, difference of two squares, factorise into one bracket  
SOLVE QUADRATICS, DISCRIMINANTS AND COMLETING THE SQUARE 

Solve quadratics by factorisation, including the difference of two squares.


Find the discriminant and determine how many roots the equation has. 

Investigate using Autograph or Omnigraph to visually understand the number of solutions of a quadratic graph 

Interactive graph allows you to discover what happens when you find the discriminant  
Discriminants exam questions (mathsnet.net) 
One discriminant exam question 
Use omnigraph or autograph to investigate lines of symmetry and turning points  
Investigate completing the square visually (mathsnet.net) 
See effect on curve of changing the values of a, b and c 
Complete the square to determine the line of symmetry of the curve.  
Completing the square (mathsnet.net) 
Completing the square of quadratic expressions 
Completing the square exam questions (mathsnet.net) 
Six exam questions on completing the square 
Solve quadratics by completing the square  
Solve quadratics using the formula  
Solve and leave answers in surd form  
Solve simultaneous equation by solving the quadratic  
Solve by factorising and finding equal roots  
SIMULTANEOUS EQUATIONS AND INEQUALITIES 

Solve simple linear simultaneous equations  
Solve simple linear simultaneous equations  
Rearrange the method to solve the simultaneous equation when one is linear and one quadratic.  
Solve 5 exam questions involving linear and quadratic simultaneous equations  
Solving simple inequalities  
Solve linear inequalities of the form ax+b<cx+d  
Solve quadratic inequalities by factorising  
5 exam questions on solving inequalities, both linear and quadratic  
TRANSFORMATIONS OF GRAPHS 

By changing the value of a discover whether the transformation is f(x)+a, f(x+a), af(x) or f(ax)  
Match the sketch graph with the correct transformation  
Sketch graphs on axes given a transformation such as f(x)+a, f(x+a), af(x), f(ax) and f(x)  
Coordinate Geometry 1 
Resource description 
EQUATIONS OF STRAIGHT LINES, GRADIENTS, MIDPOINTS AND LENGTHS 

Summary exercise of main skills involved in equation of a straight line  
Find gradients, lengths of line segments, midpoints of line segments and gradients of lines that are parallel and perpendicular  
Find gradient of line given two coordinates  
Sketch the line given the equation, find the equation given the gradient, find the equation given the two coordinates  
Given two coordinates, find the equation of the line in the form ax+by+c=0  
Show that one line is perpendicular to another line given the coordinates that lie on the two lines.  
Find the coordinates of a point where two lines intersect. Find the equation of a line perpendicular to another line.  
Typical exam questions  
Summary of information needed for coordinate geometry 1 section  
SEQUENCES AND SERIES 

Using correct notation and sigma notation  
Practice questions using the summation notation  
Given a series, write it using the summation notation  
Use the a + (n1)d notation  
Proof of nth term and sum of arithmetic series  
Using a+(n1)d rule in context  
Self marking worksheet using the rule for the sum of an arithmetic progression  
Self marking worksheet using the rule for the sum of an arithmetic progression  
Sum of arithmetic series exam question in context  
Worded exam question  
Sum of arithmetic series using the sigma notation in the question  
DIFFERENTIATION 

Show the gradient of the chord as it approaches the same point  
Show the gradient of the chord as it approaches the tangent to the curve  
Showing interactive method for differentiation from first principles of x squared.  
Showing the method for differentiation from first principles  
Rearrange to find the method for finding the tangent to a curve  
Use differentiation and yy1=m(xx1) to find equation of tangent  
Rearrange to find the method for finding the normal to a curve  
Use differentiaton, gradient of perpendicular and yy1=m(xx1) to find the equation of the normal  
Typical exam questions  