| Skills |
Learning Outcomes |
Booklet |
Worksheet |
Further |
| Laws of Indices |
• perform calculations using indices
• state and use the laws of indices
• use scientific notation |
HELM 1.2 Indices |
MathCentre Indices |
Indices and Powers |
| Laws of Logarithms |
• invert b = a^n using logarithms
• simplify expressions involving logarithms
• change bases in logarithms |
HELM 6.3 Logarithms |
MathCentre Logarithms |
Logarithms |
| Simultaneous Equations |
• solve pairs of simultaneous linear equations |
HELM 3.4 Simultaneous Equations |
MathCentre Simultaneous Equations |
Simultaneous Equations |
| Factorising Linear Equations |
• factorise simple expressions
(Sections 1-4) |
HELM Simple Factorising |
Coventry MathsCentre Factorising |
Factorising Quadratic Equations |
| Factorising Quadratic Equations |
• factorise quadratic expressions
(Sections 3-5) |
HELM Quadratic Factorisation |
MathCentre Factorising |
Quadratic Equations |
| Algebraic Fractions |
• add, subtract, multiply and divide algebraic fractions |
HELM Algebriac Fractions |
MathCentre Simplify Fractions |
Algebraic Fractions |
| Trignometric Ratios |
• define trigonometric functions both in right-angled triangles
• express angles in degrees
• express angles in radians
• calculate all the angles and sides in any right-angled triangle given certain information
• define trigonometric functions generally
• sketch the graphs of the three main trigonometric functions: sin, cos, tan |
HELM Trig Ratios |
HELM Trig Functions |
Trigonometric Ratios |
| Sine & Cosine Rules |
• solve triangles using the cosine formulae
• solve triangles using the sine formulae
• find areas of triangles |
MathCentre Sin & Cos Rules |
MathCentre Sin & Cos Rules |
Sine & Cosine Rules |
| Differentiation |
• explain what is meant by the tangent to a curve
• explain what is meant by the gradient of a curve at a point
(Sections 1-2) |
HELM Differentiation |
MathCentre Differentiation |
Differentiation |
| Integration |
• evaluate simple integrals by reversing the process of differentiation
• use a table of integrals |
HELM Integration |
MathCentre Integration |
Integration |
| Differentiation - Product and Quotient Rules |
• differentiate products and quotients of the standard functions
• differentiate a quotient using the product rule |
HELM Product/ Quotient Rules |
MathCentre Product/ Quotient Rules |
Differentation - Product Rule
Differentation - Quotient Rule |
| Integration - Definite Integrals |
• find simple definite integrals
• handle some integrals involving an infinite limit of integration |
HELM Definite Integrals |
MathCentre Definite Integrals |
Integration - Definite Integrals |
| The Constant of Integrals |
• explain the need for a constant of integration when finding indefinite integrals |
HELM Constant of Integrals |
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| Factor & Remainder Theorems |
• use the remainder and factor theorems to find factors of polynomials |
HELMFactor/ Remainder Theorems |
|
Remainder & Factor Theorems |
| Partial Fractions |
• distinguish between proper and improper fractions
• express an algebraic fraction as the sum of its partial fractions |
HELM Partial Fractions |
MathCentre Partial Fractions |
Integration using Partial Fractions |
| Integration by Substitution |
• make simple substitutions in order to find definite and indefinite integrals
• understand the technique used for evaluating integrals of the form f'(x)/f(x)dx
• use partial fractions to express an algebraic fraction in a simpler form and integrate it |
HELM Int by Substitution |
MathCentre Int by Substitution |
Integration by Substitution |
| Integration by Parts |
• decide when it is appropriate to use the method known as integration by parts
• apply the formula for integration by parts to definite and indefinite integrals
• perform integration by parts repeatedly if appropriate |
HELM Int by Parts |
MathCentre Int by Parts |
Integration by Parts |
