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# SL applications and interpretations (AI) Homepage

##### 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.