Skill plan for IB Diploma Programme - Applications and Interpretation SL
IXL provides skill alignments with recommended IXL skills for each topic. Find the IXL skills that are right for you below!
Topic
Print skill plan
1
Number and algebra
SL 1.1
SL 1.1
Operations with numbers in the form a × 10k where 1 ≤ a < 10 and k is an integer.
Operations with numbers in the form a × 10k where 1 ≤ a < 10 and k is an integer.
SL 1.2
SL 1.2
Arithmetic sequences and series.
Arithmetic sequences and series.
Use of the formulae for the nth term and the sum of the first n terms of the sequence.
Use of the formulae for the nth term and the sum of the first n terms of the sequence.
Use of sigma notation for sums of arithmetic sequences.
Use of sigma notation for sums of arithmetic sequences.
Applications.
Applications.
Analysis, interpretation and prediction where a model is not perfectly arithmetic in real life.
Analysis, interpretation and prediction where a model is not perfectly arithmetic in real life.
SL 1.3
SL 1.3
Geometric sequences and series.
Geometric sequences and series.
Use of the formulae for the nth term and the sum of the first n terms of the sequence.
Use of the formulae for the nth term and the sum of the first n terms of the sequence.
Use of sigma notation for the sums of geometric sequences.
Use of sigma notation for the sums of geometric sequences.
Applications.
Applications.
SL 1.4
SL 1.4
Financial applications of geometric sequences and series:
Financial applications of geometric sequences and series:
Compound interest
Compound interest
Annual depreciation
Annual depreciation
SL 1.5
SL 1.5
Laws of exponents with integer exponents.
Laws of exponents with integer exponents.
Introduction to logarithms with base 10 and e.
Introduction to logarithms with base 10 and e.
Numerical evaluation of logarithms using technology.
Numerical evaluation of logarithms using technology.
SL 1.6
SL 1.6
Approximation: decimal places, significant figures.
Approximation: decimal places, significant figures.
Upper and lower bounds of rounded numbers.
Upper and lower bounds of rounded numbers.
Percentage errors.
Percentage errors.
Estimation.
Estimation.
SL 1.7
SL 1.7
Amortization and annuities using technology.
Amortization and annuities using technology.
SL 1.8
SL 1.8
Use technology to solve:
Use technology to solve:
Systems of linear equations in up to 3 variables
Systems of linear equations in up to 3 variables
Polynomial equations
Polynomial equations
2
Functions
SL 2.1
SL 2.1
Different forms of the equation of a straight line.
Different forms of the equation of a straight line.
Gradient; intercepts.
Gradient; intercepts.
Lines with gradients m1 and m2.
Lines with gradients m1 and m2.
Parallel lines m1 = m2.
Parallel lines m1 = m2.
Perpendicular lines m1 × m2 = –1.
Perpendicular lines m1 × m2 = –1.
SL 2.2
SL 2.2
Concept of a function, domain, range and graph.
Concept of a function, domain, range and graph.
Function notation, for example f(x) , v(t) , C(n).
Function notation, for example f(x) , v(t) , C(n).
The concept of a function as a mathematical model.
The concept of a function as a mathematical model.
Informal concept that an inverse function reverses or undoes the effect of a function.
Informal concept that an inverse function reverses or undoes the effect of a function.
Inverse function as a reflection in the line y = x, and the notation f–1(x).
Inverse function as a reflection in the line y = x, and the notation f–1(x).
SL 2.3
SL 2.3
The graph of a function; its equation y = f(x).
Linear functions
Absolute value functions
Piecewise-defined functions
Quadratic functions
Polynomial functions
Exponential and logarithmic functions
Radical functions
Trigonometric functions
The graph of a function; its equation y = f(x).
Linear functions
Absolute value functions
Piecewise-defined functions
Quadratic functions
Polynomial functions
Exponential and logarithmic functions
Radical functions
Trigonometric functions
Creating a sketch from information given or a context, including transferring a graph from screen to paper.
Creating a sketch from information given or a context, including transferring a graph from screen to paper.
Using technology to graph functions including their sums and differences.
Using technology to graph functions including their sums and differences.
SL 2.4
SL 2.4
Determine key features of graphs.
Linear functions
Absolute value functions
Quadratic functions
Polynomial functions
Radical functions
Rational functions
Exponential and logarithmic functions
Trigonometric functions
Determine key features of graphs.
Linear functions
Absolute value functions
Quadratic functions
Polynomial functions
Radical functions
Rational functions
Exponential and logarithmic functions
Trigonometric functions
Finding the point of intersection of two curves or lines using technology.
Finding the point of intersection of two curves or lines using technology.
SL 2.5
SL 2.5
Linear models:
Linear models:
f(x) = mx + c.
f(x) = mx + c.
Quadratic models:
Quadratic models:
f(x) = ax2 + bx + c ; a ≠ 0. Axis of symmetry, vertex, zeros and roots, intercepts on the x-axis and y-axis.
f(x) = ax2 + bx + c ; a ≠ 0. Axis of symmetry, vertex, zeros and roots, intercepts on the x-axis and y-axis.
Exponential growth and decay models:
Exponential growth and decay models:
f(x) = kax + c

f(x) = ka–x + c (for a > 0)

f(x) = kerx + c
f(x) = kax + c

f(x) = ka–x + c (for a > 0)

f(x) = kerx + c
Equation of a horizontal asymptote.
Equation of a horizontal asymptote.
Direct/inverse variation:
Direct/inverse variation:
f(x) = axn, n is an integer.
f(x) = axn, n is an integer.
The y-axis as a vertical asymptote when n < 0.
The y-axis as a vertical asymptote when n < 0.
Cubic models:
Cubic models:
f(x) = ax3 + bx2 + cx + d.
f(x) = ax3 + bx2 + cx + d.
Sinusoidal models:
Sinusoidal models:
f(x) = asin(bx) + d.

f(x) = acos(bx) + d.
f(x) = asin(bx) + d.

f(x) = acos(bx) + d.
SL 2.6
SL 2.6
Modelling skills:
Modelling skills:
Use the modelling process described in the "mathematical modelling" section to create, fit and use the theoretical models in section SL2.5 and their graphs.
Linear models
Quadratic models
Exponential models
Use the modelling process described in the "mathematical modelling" section to create, fit and use the theoretical models in section SL2.5 and their graphs.
Linear models
Quadratic models
Exponential models
Develop and fit the model:
Develop and fit the model:
Given a context recognize and choose an appropriate model and possible parameters.
Given a context recognize and choose an appropriate model and possible parameters.
Determine a reasonable domain for a model.
Determine a reasonable domain for a model.
Find the parameters of a model.
Find the parameters of a model.
Test and reflect upon the model:
Test and reflect upon the model:
Comment on the appropriateness and reasonableness of a model.
Comment on the appropriateness and reasonableness of a model.
Justify the choice of a particular model, based on the shape of the data, properties of the curve and/or on the context of the situation.
Justify the choice of a particular model, based on the shape of the data, properties of the curve and/or on the context of the situation.
Use the model:
Use the model:
Reading, interpreting and making predictions based on the model.
Linear models
Quadratic models
Exponential models
Reading, interpreting and making predictions based on the model.
Linear models
Quadratic models
Exponential models
3
Geometry and trigonometry
SL 3.1
SL 3.1
The distance between two points in three-dimensional space, and their midpoint.
The distance between two points in three-dimensional space, and their midpoint.
Volume and surface area of three-dimensional solids including right-pyramid, right cone, sphere, hemisphere and combinations of these solids.
Surface area
Volume
Surface area and volume
Volume and surface area of three-dimensional solids including right-pyramid, right cone, sphere, hemisphere and combinations of these solids.
Surface area
Volume
Surface area and volume
The size of an angle between two intersecting lines or between a line and a plane.
The size of an angle between two intersecting lines or between a line and a plane.
SL 3.2
SL 3.2
Use of sine, cosine and tangent ratios to find the sides and angles of right-angled triangles.
Use of sine, cosine and tangent ratios to find the sides and angles of right-angled triangles.
The sine rule:
The sine rule:
a/sinA = b/sinB = c/sinC
a/sinA = b/sinB = c/sinC
The cosine rule:
The cosine rule:
c2 = a2 + b2 – 2abcosC; cosC = a² + b² – c²/2ab.
c2 = a2 + b2 – 2abcosC; cosC = a² + b² – c²/2ab.
Area of a triangle as 1/2absinC.
Area of a triangle as 1/2absinC.
SL 3.3
SL 3.3
Applications of right and non-right angled trigonometry, including Pythagoras's theorem.
Applications of right and non-right angled trigonometry, including Pythagoras's theorem.
Angles of elevation and depression.
Angles of elevation and depression.
Construction of labelled diagrams from written statements.
Construction of labelled diagrams from written statements.
SL 3.4
SL 3.4
The circle: length of an arc; area of a sector.
The circle: length of an arc; area of a sector.
SL 3.5
SL 3.5
Equations of perpendicular bisectors.
Equations of perpendicular bisectors.
SL 3.6
SL 3.6
Voronoi diagrams: sites, vertices, edges, cells.
Voronoi diagrams: sites, vertices, edges, cells.
Addition of a site to an existing Voronoi diagram.
Addition of a site to an existing Voronoi diagram.
Nearest neighbour interpolation.
Nearest neighbour interpolation.
Applications of the "toxic waste dump" problem.
Applications of the "toxic waste dump" problem.
4
Statistics and probability
SL 4.1
SL 4.1
Concepts of population, sample, random sample, discrete and continuous data.
Concepts of population, sample, random sample, discrete and continuous data.
Reliability of data sources and bias in sampling.
Reliability of data sources and bias in sampling.
Interpretation of outliers.
Interpretation of outliers.
Sampling techniques and their effectiveness.
Sampling techniques and their effectiveness.
SL 4.2
SL 4.2
Presentation of data (discrete and continuous): frequency distributions (tables).
Presentation of data (discrete and continuous): frequency distributions (tables).
Histograms.
Histograms.
Cumulative frequency; cumulative frequency graphs; use to find median, quartiles, percentiles, range and interquartile range (IQR).
Cumulative frequency; cumulative frequency graphs; use to find median, quartiles, percentiles, range and interquartile range (IQR).
Production and understanding of box and whisker diagrams.
Production and understanding of box and whisker diagrams.
SL 4.3
SL 4.3
Measures of central tendency (mean, median and mode).
Measures of central tendency (mean, median and mode).
Estimation of mean from grouped data.
Estimation of mean from grouped data.
Modal class.
Modal class.
Measures of dispersion (interquartile range, standard deviation and variance).
Measures of dispersion (interquartile range, standard deviation and variance).
Effect of constant changes on the original data.
Effect of constant changes on the original data.
Quartiles of discrete data.
Quartiles of discrete data.
SL 4.4
SL 4.4
Linear correlation of bivariate data.
Linear correlation of bivariate data.
Pearson's product-moment correlation coefficient, r.
Pearson's product-moment correlation coefficient, r.
Scatter diagrams; lines of best fit, by eye, passing through the mean point.
Scatter diagrams; lines of best fit, by eye, passing through the mean point.
Equation of the regression line of y on x.
Equation of the regression line of y on x.
Use of the equation of the regression line for prediction purposes.
Use of the equation of the regression line for prediction purposes.
Interpret the meaning of the parameters, a and b, in a linear regression y = ax + b.
Interpret the meaning of the parameters, a and b, in a linear regression y = ax + b.
SL 4.5
SL 4.5
Concepts of trial, outcome, equally likely outcomes, relative frequency, sample space (U) and event.
Concepts of trial, outcome, equally likely outcomes, relative frequency, sample space (U) and event.
The probability of an event A is P(A) = n(A)/n(U).
The probability of an event A is P(A) = n(A)/n(U).
The complementary events A and A' (not A).
The complementary events A and A' (not A).
Expected number of occurrences.
Expected number of occurrences.
SL 4.6
SL 4.6
Use of Venn diagrams, tree diagrams, sample space diagrams and tables of outcomes to calculate probabilities.
Use of Venn diagrams, tree diagrams, sample space diagrams and tables of outcomes to calculate probabilities.
Combined events:
Combined events:
P(A or B) = P(A) + P(B) − P(A and B)
P(A or B) = P(A) + P(B) − P(A and B)
Mutually exclusive events:
Mutually exclusive events:
P(A and B) = 0
P(A and B) = 0
Conditional probability:
Conditional probability:
P(A | B) = P(A and B)/P(B)
P(A | B) = P(A and B)/P(B)
Independent events:
Independent events:
P(A and B) = P(A)P(B)
P(A and B) = P(A)P(B)
SL 4.7
SL 4.7
Concept of discrete random variables and their probability distributions.
Concept of discrete random variables and their probability distributions.
Expected value (mean), E(X) for discrete data.
Expected value (mean), E(X) for discrete data.
Applications.
Applications.
SL 4.8
SL 4.8
Binomial distribution.
Binomial distribution.
Mean and variance of the binomial distribution.
Mean and variance of the binomial distribution.
SL 4.9
SL 4.9
The normal distribution and curve.
The normal distribution and curve.
Properties of the normal distribution.
Properties of the normal distribution.
Diagrammatic representation.
Diagrammatic representation.
Normal probability calculations.
Normal probability calculations.
Inverse normal calculations.
Inverse normal calculations.
SL 4.10
SL 4.10
Spearman's rank correlation coefficient, rs.
Spearman's rank correlation coefficient, rs.
Awareness of the appropriateness and limitations of Pearson's product moment correlation coefficient and Spearman's rank correlation coefficient, and the effect of outliers on each.
Awareness of the appropriateness and limitations of Pearson's product moment correlation coefficient and Spearman's rank correlation coefficient, and the effect of outliers on each.
SL 4.11
SL 4.11
Formulation of null and alternative hypotheses, H0 and H1 .
Formulation of null and alternative hypotheses, H0 and H1 .
Significance levels.
Significance levels.
p-values.
p-values.
Expected and observed frequencies.
Expected and observed frequencies.
The χ2 test for independence: contingency tables, degrees of freedom, critical value.
The χ2 test for independence: contingency tables, degrees of freedom, critical value.
The χ2 goodness of fit test.
The χ2 goodness of fit test.
The t-test.
The t-test.
Use of the p-value to compare the means of two populations.
Use of the p-value to compare the means of two populations.
Using one-tailed and two-tailed tests.
Using one-tailed and two-tailed tests.
5
Calculus
SL 5.1
SL 5.1
Introduction to the concept of a limit.
Introduction to the concept of a limit.
Derivative interpreted as gradient function and as rate of change.
Derivative interpreted as gradient function and as rate of change.
SL 5.2
SL 5.2
Increasing and decreasing functions.
Increasing and decreasing functions.
Graphical interpretation of f '(x) > 0, f '(x) = 0, f '(x) < 0.
Graphical interpretation of f '(x) > 0, f '(x) = 0, f '(x) < 0.
SL 5.3
SL 5.3
Derivative of f(x) = axn is f '(x) = anxn –1, n is an integer.
Derivative of f(x) = axn is f '(x) = anxn –1, n is an integer.
The derivative of functions of the form f(x) = axn + bxn – 1 … where all exponents are integers.
The derivative of functions of the form f(x) = axn + bxn – 1 … where all exponents are integers.
SL 5.4
SL 5.4
Tangents and normals at a given point, and their equations.
Tangents and normals at a given point, and their equations.
SL 5.5
SL 5.5
Introduction to integration as anti-differentiation of functions of the form f(x) = axn + bxn – 1 + …, where n is an integer, n ≠ – 1.
Introduction to integration as anti-differentiation of functions of the form f(x) = axn + bxn – 1 + …, where n is an integer, n ≠ – 1.
Anti-differentiation with a boundary condition to determine the constant term.
Anti-differentiation with a boundary condition to determine the constant term.
Definite integrals using technology.
Definite integrals using technology.
Area of a region enclosed by a curve y = f(x) and the x-axis, where f(x) > 0.
Area of a region enclosed by a curve y = f(x) and the x-axis, where f(x) > 0.
SL 5.6
SL 5.6
Values of x where the gradient of a curve is zero.
Values of x where the gradient of a curve is zero.
Solution of f '(x) = 0.
Solution of f '(x) = 0.
Local maximum and minimum points.
Local maximum and minimum points.
SL 5.7
SL 5.7
Optimisation problems in context.
Optimisation problems in context.
SL 5.8
SL 5.8
Approximating areas using the trapezoidal rule.
Approximating areas using the trapezoidal rule.
This document includes the IXL® skill alignments to International Baccalaureate's IB Diploma Programme curriculum. IXL provides skill alignments as a service to teachers, students, and parents. The skill alignments are provided by IXL and are not affiliated with, sponsored by, reviewed, approved or endorsed by International Baccalaureate or any other third party. IXL® and IXL Learning® are registered trademarks of IXL Learning, Inc. All other intellectual property rights (e.g., unregistered and registered trademarks and copyrights) are the property of their respective owners.