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Mathematics Analysis and Approaches (AA) Student Questions - Page 2 | RevisionDojo

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Student Questions

Mathematics Analysis and Approaches (AA)

SL 2.5-Composite functions, identity, finding inverse

What Is the Identity Function?

Learn what the identity function is, how composition leaves a function unchanged, and how it verifies inverse functions in IB Mathematics AA SL 2.5.

SL 2.6-Quadratic function

What Are the Three Forms of a Quadratic Function (Standard, Factored, Vertex)?

Learn the standard, factored and vertex forms of a quadratic function, what each form reveals, and how to convert between them for IB Math AA exams.

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SL 2.5-Composite functions, identity, finding inverse

How Do You Find a Composite Function f(g(x))?

Learn how to find a composite function f(g(x)) by substitution, simplify it correctly, check its domain, and avoid reversing the order in IB exams.

SL 2.7-Solutions of quadratic equations and inequalities, discriminant and nature of roots

How Do You Solve a Quadratic Equation by Factoring; Completing the Square; or the Quadratic Formula?

Learn three methods for solving quadratic equations with a worked IB Math AA example, method-selection guidance, common errors, and clear exam tips.

SL 2.6-Quadratic function

How Do You Convert Between Different Forms of a Quadratic Function?

Convert quadratic functions between general, factorized, and vertex forms using expansion, factorization, and completing the square for IB Math AA exams.

SL 2.5-Composite functions, identity, finding inverse

How Do You Find the Inverse Function Algebraically?

Learn how to find an inverse function algebraically using variable swapping, rearrangement, domain restrictions, and verification for IB Math AA SL exams.

SL 2.8-Reciprocal and simple rational functions, equations of asymptotes

How Do You Find the Vertical and Horizontal Asymptotes of a Rational Function?

Learn how to find vertical and horizontal asymptotes of simple rational functions, with an IB Math AA SL worked example and key exam errors explained.

SL 2.6-Quadratic function

How Do You Find the Y-Intercept, X-Intercepts, and Axis of Symmetry of a Parabola?

Learn to find a parabola's y-intercept, x-intercepts, and axis of symmetry from quadratic forms, with a worked IB Math AA exam-style example for SL.

SL 2.7-Solutions of quadratic equations and inequalities, discriminant and nature of roots

How Do You Know If a Quadratic Has Two Real Roots; One Real Root; or No Real Roots?

Learn how the discriminant determines whether an IB Math AA quadratic has two distinct real roots, one repeated real root, or no real roots.

SL 2.7-Solutions of quadratic equations and inequalities, discriminant and nature of roots

What Is the Discriminant and What Does It Tell You About the Roots?

Learn how the quadratic discriminant determines whether an equation has two distinct real roots, equal real roots, or no real roots in IB Math AA.

SL 2.8-Reciprocal and simple rational functions, equations of asymptotes

What Is the Reciprocal Function and Why Is It Self-Inverse?

Learn why the reciprocal function f(x) = 1/x is self-inverse and which domain, range, composition, and asymptotes matter for IB Math AA exams.

SL 2.8-Reciprocal and simple rational functions, equations of asymptotes

How Do You Graph a Rational Function of the Form (ax+b)/(cx+d)?

Learn how to graph a linear rational function by finding its asymptotes, intercepts, centre and branch positions for IB Mathematics AA SL exams.

SL 2.9-Exponential and logarithmic functions

Why Are Exponential and Logarithmic Functions Inverses of Each Other?

Learn why exponential and logarithmic functions undo each other through inverse compositions, swapped domains and ranges, and reflected graphs.

SL 2.9-Exponential and logarithmic functions

How Do You Graph an Exponential Function?

Learn how to graph an exponential function in IB Math AA by identifying growth or decay, plotting key points, and labelling the horizontal asymptote.

SL 2.9-Exponential and logarithmic functions

How Do You Graph a Logarithmic Function?

Learn how to graph logarithmic functions using intercepts, asymptotes, domain, range, transformations, and inverse relationships for IB Math AA exams.

SL 2.10-Solving equations graphically and analytically

How Do You Solve an Equation Like e^(2x) - 5e^x + 4 = 0?

Learn how to solve e^(2x) - 5e^x + 4 = 0 by substitution, factorization, and logarithms, with IB Math AA exam steps and common errors to avoid.

SL 2.10-Solving equations graphically and analytically

When Do You Need Technology to Solve an Equation With No Analytic Approach?

Learn when IB Math AA SL students should use a GDC for equations with no suitable analytic method, including key Paper 1 and Paper 2 exam technique.

SL 2.11-Transformation of functions

What's the Effect of a Vertical or Horizontal Translation on a Graph?

Learn how vertical and horizontal translations change a graph, including sign rules, point mappings, worked examples, and IB Mathematics AA exam tips.

SL 2.11-Transformation of functions

What's the Effect of a Reflection on a Graph (in the X-Axis or Y-Axis)?

Learn how reflections in the x-axis and y-axis transform a graph, with coordinate rules, worked examples, common errors, and IB Math AA exam advice.

AHL 2.12-Factor and remainder theorems, sum and product of roots

What's the Relationship Between the Zeros, Roots, and Factors of a Polynomial?

Learn how polynomial zeros, roots, and linear factors are linked by the factor theorem, with an IB Math AA HL example, multiplicity, and exam advice.

SL 2.11-Transformation of functions

What's the Effect of a Vertical or Horizontal Stretch on a Graph?

Learn how vertical and horizontal stretches transform graph coordinates, including scale factors, equations, examples, and common IB exam mistakes.

AHL 2.12-Factor and remainder theorems, sum and product of roots

What Is the Factor Theorem and the Remainder Theorem?

Learn the factor and remainder theorems for IB Math AA HL through proofs, worked examples, parameter problems, common errors, and exam technique.

AHL 2.13-Rational functions

How Do You Find an Oblique (Slant) Asymptote?

Learn how polynomial division finds an oblique asymptote of a rational function, with an IB Math AA HL example, degree test, common errors, and exam tips.

AHL 2.12-Factor and remainder theorems, sum and product of roots

How Do You Find the Sum and Product of the Roots of a Polynomial Equation?

Learn how to use polynomial coefficients and Vieta's formulas to find the sum and product of roots in IB Mathematics AA HL exam questions.

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