Algebra and Functions 1
Resource description
INDICES AND SURDS
Basic rules of indices and spot the mistake
Rules of indices-algebra
Multiplying, dividing, brackets and fractional powers
Rules of indices jigsaw puzzle
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
Solve Exponential Equations
Easiteach file with a variety of exponential equations to use as a starter with whiteboards or a main lesson activity
Surds
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.
Factorise quadratics (mathsnet.net)
Factorise quadratics including the difference of two squares
Mixed factorising - powerpoint plenary
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.
Understanding the Discriminant
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
One discriminant exam question
Investigate complete the square
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
Six exam questions on completing the square
Solve quadratics by completing the square
Solve quadratics using the formula
Solve using quadratic formula and leave in surd form (mathsnet.net)
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
SIMULTANEOUS EQU SOLVER
Solve simple linear simultaneous equations
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
Solve inequalities exam questions (mathsnet.net)
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
C1 gradient midpoint length parallel and perp
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 for coordinate geometry 1 (mathsnet.net)
Summary of information needed for coordinate geometry 1 section
SEQUENCES AND SERIES
C1 Sequences and series starter
Using correct notation and sigma notation
Understanding the summation notation (mathsnet.net)
Practice questions using the summation notation
Given a series, write it using the summation notation
nth term of a sequence exam question (mathsnet.net)
Use the a + (n-1)d notation
C1 Arithmetic series
Proof of nth term and sum of arithmetic series
Using a+(n-1)d rule in context
Summation of AP
Self marking worksheet using the rule for the sum of an arithmetic progression
Summation of AP 2
Self marking worksheet using the rule for the sum of an arithmetic progression
Sum of arithmetic series exam question (mathsnet.net)
Sum of arithmetic series exam question in context
Arithmetic Series Exam question (mathsnet.net)
Worded exam question
Summation notation exam questions (mathsnet.net)
Sum of arithmetic series using the sigma notation in the question
DIFFERENTIATION
The gradient of the curve y=xsquared (mathsnet.net)
Show the gradient of the chord as it approaches the same point
The gradient of the curve y=x cubed (mathsnet.net)
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
Finding tangents - the method (mathsnet.net)
Rearrange to find the method for finding the tangent to a curve
Find the equation of the tangent (mathsnet.net)
Use differentiation and y-y1=m(x-x1) to find equation of tangent
Finding normals - the method (mathsnet.net)
Rearrange to find the method for finding the normal to a curve
Find the equation of the normal to the curve (mathsnet.net)
Use differentiaton, gradient of perpendicular and y-y1=m(x-x1) to find the equation of the normal
Typical exam questions