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 + (n-1)d notation | |
| Proof of nth term and sum of arithmetic series | |
| Using a+(n-1)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 y-y1=m(x-x1) to find equation of tangent | |
| Rearrange to find the method for finding the normal to a curve | |
| Use differentiaton, gradient of perpendicular and y-y1=m(x-x1) to find the equation of the normal | |
| Typical exam questions | |