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Applications and Interpretation

DP Mathematics Standard Level · Grad'27

Units

Mint units are the ones studied so far

Orange units are the ones we are working on now

Topic 1 · Number and algebra

1.1 Standard form - Haese Book 1, Ch 3E - under construction

Syllabus reference: 1.1 Operations with numbers in the form a × 10ᵏ where 1 ≤ a < 10 and k is an integer

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1.2 Arithmetic sequences and series - Haese Book 1, Ch 5A, 5B, 5F, 5G - under construction

Syllabus reference: 1.2 Arithmetic sequences and series; use of the formulas for the nth term and the sum of the first n terms; applications

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1.3 Geometric sequences and series - Haese Book 1, Ch 5C, 5H - under construction

Syllabus reference: 1.3 Geometric sequences and series; use of the formulas for the nth term and the sum of the first n terms; applications

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1.4 Compound interest and depreciation - Haese Book 1, Ch 5D, 5E - under construction

Syllabus reference: 1.4 Financial applications of geometric sequences and series: compound interest, annual depreciation

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1.5 Exponents and logarithms - Haese Book 1, Ch 3; Book 2, Ch 8G, 8H - under construction

Syllabus reference: 1.5 Laws of exponents with integer and rational exponents; introduction to logarithms in base 10 and base e

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1.6 Approximation and error - Haese Book 2, Ch 1 - under construction

Syllabus reference: 1.6 Approximation: decimal places, significant figures; upper and lower bounds of rounded numbers; percentage errors; estimation

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1.7 Loans and savings - Haese Book 2, Ch 2 - under construction

Syllabus reference: 1.7 Amortisation and annuities using technology

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1.8 Systems of equations - Haese Book 1, Ch 4 - under construction

Syllabus reference: 1.8 Solutions of systems of linear equations (up to 3 × 3); polynomial equations using technology

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Topic 2 · Functions

2.1 Straight lines - Haese Book 1, Ch 1 - under construction

Syllabus reference: 2.1 Equations of a straight line: gradient, intercepts, parallel and perpendicular lines

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2.2 Functions - Haese Book 2, Ch 3A to 3C, 3G - under construction

Syllabus reference: 2.2 Concept of a function, domain, range and graph; function notation; the inverse function

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2.3 Graphs of functions - Haese Book 2, Ch 3D to 3F - under construction

Syllabus reference: 2.3 The graph of a function; creating a sketch from information or context; using technology to graph functions

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2.4 Key features of graphs - Haese Book 2, Ch 3E, 6 - under construction

Syllabus reference: 2.4 Key features of graphs: intercepts, vertex, symmetry, asymptotes; finding the intersection of two curves

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2.5 Modelling with functions - Haese Book 2, Ch 6 to 9 - under construction

Syllabus reference: 2.5 Modelling with linear, quadratic, exponential, direct and inverse variation, cubic and sinusoidal functions

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2.6 Modelling skills - Haese Book 2, Ch 4 - under construction

Syllabus reference: 2.6 Modelling skills: developing, fitting, testing and reflecting on a model; piecewise models

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Topic 3 · Geometry and trigonometry

3.1 Three-dimensional geometry - under construction

Syllabus reference: 3.1 Distance and midpoint in 3D, volume and surface area of 3D solids, angles between lines and planes

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3.2 Right-angled trigonometry - under construction

Syllabus reference: 3.2 Use of sine, cosine and tangent ratios to find sides and angles in right-angled triangles

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3.3 Non-right-angled trigonometry - under construction

Syllabus reference: 3.2 Sine rule, cosine rule and the area of a triangle

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3.4 Applications of trigonometry - under construction

Syllabus reference: 3.2 Angles of elevation and depression, bearings and trigonometry in three dimensions

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3.5 Arcs and sectors - under construction

Syllabus reference: 3.4 Arc length and area of a sector of a circle

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3.6 Voronoi diagrams - under construction

Syllabus reference: 3.5 Voronoi diagrams: sites, cells, edges and vertices, perpendicular bisectors, nearest neighbour interpolation, toxic waste dump problem

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Topic 4 · Statistics and probability

4.1 Sampling - Haese Book 1, Ch 11 - under construction

Syllabus reference: 4.1 Concepts of population, sample, random sample, discrete and continuous data; reliability of data sources and bias in sampling; sampling techniques

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4.2 Presenting data - Haese Book 1, Ch 12F to 12I - under construction

Syllabus reference: 4.2 Presentation of data: frequency distributions, histograms, cumulative frequency graphs, box-and-whisker diagrams; outliers

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4.3 Summarising data - Haese Book 1, Ch 12A to 12E, 12J - under construction

Syllabus reference: 4.3 Measures of central tendency, dispersion; estimation of mean from grouped data; standard deviation; effect of constant changes

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4.4 Correlation and regression - Haese Book 2, Ch 5A to 5D - under construction

Syllabus reference: 4.4 Linear correlation of bivariate data; Pearson's product-moment correlation coefficient r; scatter diagrams; line of best fit; regression line of y on x

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4.5 Probability - Haese Book 1, Ch 10A to 10D - under construction

Syllabus reference: 4.5 Sample space, probability of an event, complement, expected number

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4.6 Diagrams, conditional probability and independence - Haese Book 1, Ch 2; Ch 10E to 10J - under construction

Syllabus reference: 4.6 Venn, tree and sample space diagrams; conditional and independent events

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4.7 Discrete random variables - Haese Book 2, Ch 14A to 14C - under construction

Syllabus reference: 4.7 Discrete random variables and expected value

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4.8 Binomial distribution - Haese Book 2, Ch 14D to 14F - under construction

Syllabus reference: 4.8 The binomial distribution; mean and variance of the binomial distribution; use of technology

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4.9 Normal distribution - Haese Book 2, Ch 15 - under construction

Syllabus reference: 4.9 The normal distribution and curve; properties; diagrammatic representation; normal probability calculations; inverse normal calculations

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4.10 Spearman's rank correlation - Haese Book 2, Ch 5E - under construction

Syllabus reference: 4.10 Spearman's rank correlation coefficient; appropriateness and limitations of Pearson's r and Spearman's rs

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4.11 Hypothesis testing - Haese Book 2, Ch 16 - under construction

Syllabus reference: 4.11 Hypotheses, significance level and p-values; chi-squared test for independence and goodness of fit; t-test

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Topic 5 · Calculus

5.1 Introduction to differentiation - under construction

Syllabus reference: 5.1 Concept of a limit, the derivative as a gradient and as a rate of change, derivative of axⁿ

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5.2 Using the derivative - under construction

Syllabus reference: 5.2 Increasing and decreasing functions, tangents and normals

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5.3 Stationary points and optimisation - under construction

Syllabus reference: 5.3 Local maximum and minimum points, optimisation

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5.4 Integration - under construction

Syllabus reference: 5.4 Anti-differentiation, definite integrals and area, trapezoidal rule

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