SL analysis and approaches (AA) Homepage
Algebra
Series and Expansions
Probability
Functions
Trigonometry
Differentiation
Revision
Number and Logs
Statistics
Integration
Complete Learning Outcomes
Algebra
| Find equations of horizontal and vertical straight lines |
| Understand the the terms gradient and y-intercept. |
| Find equations of diagonal straight lines. |
| Factorise simple quadratic equations such as x2+bx+c |
| Factorise simple quadratic equations such as ax2+bx+c where a>1. |
| Solve simple quadratic equations such as x2+bx+c=0 |
| Solve simple quadratic equations such as ax2+bx+c=0 where a>1. |
| Solve quadratic equations by use of a GDC. |
| Understand the term discriminant and how it is used to determine the number of roots of a quadratic. |
| To be able to complete the square for a quadratic. |
| To solve an equation from the completed the square form. |
| Find minimum points and lines of symmetry from graphs of quadratics. |
| Show simple numeric and algebraic proofs. |
Functions
| Understanding the concept of a function. |
| Substitute and solve equations using algebra. |
| Understand the terms domain and range. |
| Find the inverse of a function |
| Understand the terms one-to-one; many-to-one; one-to-many and their applications to functions and inverses. |
| Graph functions with and without a GDC. Note key points on graphs (intersection with axes, maximum and minimum). |
| Understand and use composite functions. |
| Substitute and solve equations using graphs, including composite functions. |
| Using reciprocal graphs, including finding asymptotes from functions with and without sketches. |
| Solve intersection of functions using a GDC. |
| Transformation of functions: reflections in x and y axes; reflection in y=x line; translations; vertical and horizontal stretches. |
| Using the inverse function and the reflection to solve equations. |
Number and Logarithms
| Write numbers in a x 10k (standard form). |
| Calculate in standard form. |
| Understand basic rules of exponents such as (multiplying, division, powers, fractional powers, negative powers, etc). |
| Find exponents of integers without a calculator. |
| Convert between exponent and logarithm form. |
| Use a calculator to solve logarithms. |
| Understand the basic rules of logarithms and relationship with exponent forms. |
| Understand and use the change of base rule. |
| Use the natural logarithm (ln) and interchange with its base (e). |
| Graphing logarithms and use with transformations and function rules. |
| Modelling with logarithms, such as population models. |
Series and Expansions
| Understand the term arithmetic sequence. |
| Understand the term geometric sequence. |
| Find the nth term of an arithmetic sequence. |
| Find the sum of n terms of an arithmetic series. |
| Find common differences and problem solve with arithmetic sequence and series. |
| Find the nth term of a geometric sequence. |
| Find the sum of n terms of a geometric series. |
| Find common differences and problem solve with geometric sequence and series. |
| Find the infinite sum of a geometric series. |
| Use the sigma sign for sums of both arithmetic and geometric series. |
| Use series to apply to compound interest problems. |
| Understand, use and generate Pascal’s triangle with and without a GDC. |
| Expanding a bracket such as (ax+b)n, where n>2. |
| Problem solving with binomial expansions, including finding terms and constants (independent) terms. |
Trigonometry
| Trigonometric ratios in a right angled triangle. SOHCAHTOA. |
| Sine, cosine rules in non-right angled triangles; ambiguous case of the sine rule. |
| Area of a triangle ½absinC. |
| Using SOHCAHTOA with 3d shapes, including pyramids, cones, spheres, and combinations of these. |
| Using trigonometry in problem solving (Pythagoras’, elevation and depression). |
| Radian and degree measure conversion. |
| Using radian measure, length of an arc and area of a sector. |
| Unit circle and Pythagorean identities, sin2x+cos2x=1, tanx=sinx/cosx. |
| Exact trig ratios for 2pi, pi, pi/2, pi/3, pi/4 and pi/6 and multiples of these. |
| Double angle identities for sine and cosine. |
| Circular functions and their periodic nature. |
| Trig graphs and the transformation of trig graphs. |
| Real life trigonometric graphs and modelling. |
| Solving trigonometric equations with and without a GDC. |
| Quadratic equations with trigonometric equations. |
Statistics
| Types of data: continuous and discrete. |
| Sampling: random samples, bias in samples and outliers. |
| Understand how to take a random sample, stratified data, systematic data. |
| Central tendency measure: mean, mode, median, range and quartiles, including grouped data. |
| Understand statistical diagrams such as histograms with even bar width. |
| Reading and constructing cumulative frequency and box and whisker plots. |
| Variance and standard deviation, and effect of constant changes on data. |
| Correlation and regression values, Pearsons’ product moment correlation coefficient. |
| Scatter diagrams, lines of best fit and predicting data from lines. |
Probability
| Understand set notation for number, union, intersection, contained in, element, inverse, null and universal. |
| Be able to draw and shade Venn diagrams with the use of set notation. |
| Solve problems by use of sets and Venn diagrams. |
| Understand the the terms mutually exclusive and independent. |
| Find simple probabilities involving one or two events, using the terms AND and OR. |
| Draw tree diagrams to represent probabilities. |
| Use the independence formulae to solve problems of independent probability. |
| Find conditional, or ‘given that’ probabilities. |
| Use Venn diagrams to solve probability problems. |
| Draw and interpret tree diagrams, using them for conditional and independent events. |
| Discrete random variables and their probability distributions. |
| Expected value (mean) for discrete standard variables. |
| Binomial distributions, including mean and variance of these distributions. |
| Normal distribution diagrammatic representation and using this for non-GDC calculations. |
| Using a GDC to find probabilities based on knowing the mean and standard deviation. |
| Finding z-values with normal distributions, and using for inverse calculations. |
Differentiation
| Understand the concept of a limit from a table or graph. |
| Understand that the derivative is a gradient or rate of change function, and its notation. |
| Understand when functions are increasing or decreasing. |
| Simple derivatives by reducing the powers, e.g axn |
| Find the equations of tangents and normals to functions. |
| Derivatives of sinx, cosx, lnx, and ex. |
| Use and understand the chain rule. |
| Use and understand the product and quotient rules. |
| Understand the concept of maximum and minimum points. |
| Find the second derivative, and use this distinguishing between maximum and minimum points |
| Finding points of inflexion. |
| Using differentiation for solving optimization problems. |
Integration
| Integrate by using anti-differentiation techniques. |
| Integration and finding the value of the constant, C. |
| Using definite integration in order to find areas under curves. |
| Integration techniques to find integrals of sin, cos, ln and x. |
| Integration to find composite functions such as integral of cos(3x+1). |
| Using reverse chain rule to integrate functions. |
| Using technology to find definite integrals. |
| Finding regions enclosed by two functions. |
| Using integration to solve kinetic problems: displacement, velocity, acceleration. |