SL applications and interpretations (AI) Homepage
Algebra
Number
Trigonometry
Differentiation
Functions
Series
Statistics
Integration
Voronoi Diagrams
Probability
Hypothesis
Revision
All 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. |
| Use straight lines to solve 2×2 simultaneous equations. |
| Use a GDC to solve 2×2 simultaneous equations. |
| 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 quadratic graph, including roots, lines of symmetry and minimum point. |
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, including the reflection of a function and its inverse. |
| Graph functions with a GDC. Note key points on graphs (intersection with axes, maximum and minimum). |
| Graphing linear, quadratics and cubic functions. |
| Substitute and solve equations using graphs, including composite functions. |
| Solve intersection of functions using a GDC. |
| Apply knowledge of functions to create and understand models. |
| Recognise appropriate models and their parameters. |
| Understand direct and inverse proportion. |
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, including the reflection of a function and its inverse. |
| Graph functions with a GDC. Note key points on graphs (intersection with axes, maximum and minimum). |
| Graphing linear, quadratics and cubic functions. |
| Substitute and solve equations using graphs, including composite functions. |
| Solve intersection of functions using a GDC. |
| Apply knowledge of functions to create and understand models. |
| Recognise appropriate models and their parameters. |
| Understand direct and inverse proportion. |
Voronoi Diagrams
| Finding the coordinate of a bisector of a line segment, or between two points. |
| Finding perpendicular line equations. |
| Understanding language of Voronoi diagrams: sites, vertices, edges, cells. |
| Nearest neighbour interpolation. |
| Solving Voronoi problems in context. |
Number and Logs
| 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. |
| Use the natural logarithm (ln) and interchange with its base (e). |
| Modelling with logarithms, such as population models. |
| Understanding and calculating simple and compound interest. |
| Using a GDC and other technology to find amortization and annuities. |
| Approximation to decimal places and significant figures. |
| Understanding and finding upper and lower bounds of rounded number. |
| Finding percentage error of rounded number. |
| Estimation of number. |
Series
| 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. |
| Use the sigma sign for sums of both arithmetic and geometric series. |
| Use series to apply to problem solving in modelling. |
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. |
| 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. |
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). |
| Length of an arc and area of a sector in degrees. |
| Circular functions and their periodic nature. |
| Trig graphs and the transformation of trig graphs. |
| Real life trigonometric graphs and modelling. |
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. |
| Correlation and regression values, Pearsons’ product moment correlation coefficient. |
| Scatter diagrams, lines of best fit and predicting data from lines. |
Hypothesis
| Calculate Spearman’s Rank coefficient and understand limitations. |
| Analyse outliers and use of Spearman’s rank and Pearson’s correlation on data. |
| Understand the null and alternative hypothesis for testing, the p-value, and significance levels. |
| Conduct and analyse a Chi Squared test for goodness of fit. |
| Conduct and analyse a Chi Squared test for independence. |
| Conduct a t-test to analyse the means of two populations, using one and two tailed data. |
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. |
| Understand the concept of maximum and minimum points. |
| 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. |
| Using technology to find definite integrals. |
| Using the trapezoid rule to estimate areas. |