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. |