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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

Lessons in this unit
1.1 Write and calculate with numbers in standard form - under construction
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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

Lessons in this unit
1.2 (a) Find the nth term of an arithmetic sequence - under construction1.2 (b) Find the sum of an arithmetic series - under construction
1.2.1 slide 1 of 17
1.2.1 slide 2 of 17
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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

Lessons in this unit
1.3 (a) Find the nth term of a geometric sequence - under construction1.3 (b) Find the sum of a geometric series - under construction
1.3.1 slide 1 of 17
1.3.1 slide 2 of 17
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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

Lessons in this unit
1.4 (a) Calculate compound interest with different compounding periods - under construction1.4 (b) Model depreciation and inflation - under construction
1.4.1 slide 1 of 18
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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

Lessons in this unit
1.5 (a) Use the laws of exponents with integer and rational powers - under construction1.5 (b) Evaluate logarithms and solve equations of the form aˣ = b - under construction
1.5.1 slide 1 of 19
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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

Lessons in this unit
1.6 (a) Round, estimate and calculate percentage error - under construction1.6 (b) Find upper and lower bounds of rounded values and calculations - under construction
1.6.1 slide 1 of 19
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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

Lessons in this unit
1.7 Use the finance solver for loans and savings annuities - under construction
1.7.1 slide 1 of 19
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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

Lessons in this unit
1.8 (a) Solve simultaneous linear equations by hand and with the GDC - under construction1.8 (b) Solve polynomial equations using factorising and the GDC - under construction
1.8.1 slide 1 of 17
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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

Lessons in this unit
2.1 (a) Find the gradient and intercepts of a straight line and interpret them - under construction2.1 (b) Write the equation of a straight line in different forms - under construction2.1 (c) Use gradients to find parallel and perpendicular lines - under construction
2.1.1 slide 1 of 18
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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

Lessons in this unit
2.2 (a) Use function notation and find the domain and range of a function - under construction2.2 (b) Find the inverse of a function and state its domain and range - under construction
2.2.1 slide 1 of 20
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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

Lessons in this unit
2.3 Sketch graphs by hand and graph them using the GDC - under construction
2.3.1 slide 1 of 18
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Slide 1 of 18
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

Lessons in this unit
2.4 (a) Find intercepts, turning points, axes of symmetry and asymptotes - under construction2.4 (b) Solve equations by finding the intersection of two graphs - under construction
2.4.1 slide 1 of 20
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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

Lessons in this unit
2.5 (a) Build and interpret linear models - under construction2.5 (b) Build and use quadratic models - under construction2.5 (c) Build and use exponential growth and decay models - under construction2.5 (d) Use direct and inverse variation models - under construction2.5 (e) Use cubic models - under construction2.5 (f) Use sinusoidal models - under construction
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2.5.5 slide 1 of 19
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2.5.6 slide 1 of 18
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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

Lessons in this unit
2.6 Choose, test and improve a model - under construction
2.6.1 slide 1 of 20
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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

Lessons in this unit
3.1 (a) Find the distance between two points in three-dimensional space, and their midpoint - under construction3.1 (b) Find the volume and surface area of three-dimensional solids, including pyramids, cones, spheres, hemispheres and combinations - under construction3.1 (c) Find the size of an angle between two intersecting lines, or between a line and a plane - under construction
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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

Lessons in this unit
3.2 (a) Use sine, cosine and tangent to find unknown sides in right-angled triangles - under construction3.2 (b) Use inverse sine, cosine and tangent to find unknown angles in right-angled triangles - under construction
3.2.1 slide 1 of 19
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Slide 1 of 21
3.3 Non-right-angled trigonometry - under construction

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

Lessons in this unit
3.3 (a) Use the sine rule to find missing sides and angles, including the ambiguous case - under construction3.3 (b) Use the cosine rule to find missing sides and angles in any triangle - under construction3.3 (c) Find the area of a triangle using ½ab sin C - under construction
3.3.1 slide 1 of 20
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Slide 1 of 20
3.4 Applications of trigonometry - under construction

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

Lessons in this unit
3.4 (a) Use angles of elevation and depression in right-angled triangle problems - under construction3.4 (b) Use three-figure bearings, including back bearings, to solve problems - under construction3.4 (c) Use Pythagoras and trigonometry in three-dimensional figures, including the angle between a line and a plane - under construction
3.4.1 slide 1 of 23
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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

Lessons in this unit
3.5 Find the arc length and the area of a sector of a circle - under construction
3.5.1 slide 1 of 24
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Slide 1 of 24
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

Lessons in this unit
3.6 (a) Find the equation of a perpendicular bisector and use it to find points equidistant from two points - under construction3.6 (b) Construct a Voronoi diagram from sites using perpendicular bisectors, identify its cells, edges and vertices, and add a new site - under construction3.6 (c) Use Voronoi diagrams to estimate values, find the largest empty circle and solve toxic waste dump problems - under construction
3.6.1 slide 1 of 22
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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

Lessons in this unit
4.1 (a) Describe populations and sampling methods and take a stratified sample - under construction4.1 (b) Classify data and identify bias and reliability issues - under construction
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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

Lessons in this unit
4.2 (a) Build frequency tables and draw and describe histograms - under construction4.2 (b) Use cumulative frequency graphs and box plots, and test for outliers - under construction
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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

Lessons in this unit
4.3 (a) Find and compare the mean, median and mode - under construction4.3 (b) Estimate the mean and find the modal and median class from grouped data - under construction4.3 (c) Find and compare the range, IQR and standard deviation - under construction
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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

Lessons in this unit
4.4 (a) Draw scatter diagrams and describe correlation using Pearson's r - under construction4.4 (b) Find and use the regression line to make predictions - under construction
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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

Lessons in this unit
4.5 Use sample spaces to find probabilities, complements and expected numbers - under construction
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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

Lessons in this unit
4.6 (a) Use Venn diagrams and the addition law to find probabilities - under construction4.6 (b) Use tree diagrams to find probabilities, with and without replacement - under construction4.6 (c) Find conditional probabilities from tables, Venn diagrams and trees - under construction4.6 (d) Test whether two events are independent - under construction
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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

Lessons in this unit
4.7 (a) Describe a discrete random variable with a probability distribution - under construction4.7 (b) Find and interpret the expected value of a discrete random variable - under construction
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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

Lessons in this unit
4.8 (a) Use the binomial distribution to find P(X = k) and the mean - under construction4.8 (b) Find cumulative binomial probabilities for at most, at least and between - under construction
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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

Lessons in this unit
4.9 (a) Use the normal distribution to find probabilities - under construction4.9 (b) Use z-scores and inverse normal calculations - under construction
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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

Lessons in this unit
4.10 (a) Rank data and use the GDC to find Spearman's rank correlation coefficient - under construction4.10 (b) Choose between Pearson's r and Spearman's rs, and describe the effect of outliers - under construction
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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

Lessons in this unit
4.11 (a) Write null and alternative hypotheses and use p-values and significance levels to reach a conclusion - under construction4.11 (b) Use a chi-squared test for independence on a contingency table - under construction4.11 (c) Use a chi-squared goodness of fit test - under construction4.11 (d) Use a two-sample t-test to compare two population means - under construction
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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

Lessons in this unit
5.1 (a) Understand the derivative as the gradient of a tangent and as an instantaneous rate of change - under construction5.1 (b) Differentiate sums and differences of terms of the form axⁿ - under construction
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5.2 Using the derivative - under construction

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

Lessons in this unit
5.2 (a) Link the sign of the derivative to increasing and decreasing functions, and find stationary points - under construction5.2 (b) Find the equations of tangents and normals to a curve at a given point - under construction
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5.3 Stationary points and optimisation - under construction

Syllabus reference: 5.3 Local maximum and minimum points, optimisation

Lessons in this unit
5.3 (a) Stationary points: values of x where the gradient is zero, and local maximum and minimum points - under construction5.3 (b) Optimisation problems in context, using the gradient to find greatest and least values - under construction
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5.4 Integration - under construction

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

Lessons in this unit
5.4 (a) Anti-differentiation of terms of the form axⁿ, including a boundary condition to find the constant of integration - under construction5.4 (b) Definite integrals, using the GDC and by hand, and the area under a curve where f(x) is positive - under construction5.4 (c) Approximating the area under a curve using the trapezoidal rule - under construction
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