Grade 12 (DP2)

IB-DP Courses

Introduction

Welcome to Explorer Hop!

Explorer Hop's Financial Literacy Expertise

In The News

Why is Financial Literacy Important

Girls Left Behind When it Comes to Money

ℹ️ Frequently Asked Questions

Welcome!

How Does Explorer Math Work

Big Hello From Our Math Curriculum Director, Sara Chaudhry

How Does the Mini Challenge Work?

Let's Tinker!

All about Explorer Math

Introduction to Chapter 1

Introduction-2

Lesson 1: How can we represent a relation between two variables? (graphs, table of values, equation, etc)

Lesson 1 Quiz

Lesson 1 Power Math

Lesson 2: Review: Set notation and interval notation

Lesson 2 Quiz

Lesson 2 Power Math

Lesson 3: Review: Function vs. Relation (including one-to-one and vertical line test)

Lesson 3 Quiz

Lesson 3 Power Math

Lesson 4: Review: Linear Equations (use function notation, tables, equations)

Lesson 4 Quiz

Lesson 4 Power Math

Lesson 5: Finding the slope (Given two points AND finding the slope given a point and y intercept)

Lesson 5 Quiz

Lesson 5 Power Math

Lesson 6: Interpret and use any of the forms y = mx + b, y – y1 = m(x – x1), ax + by + c = 0 in solving problems

Lesson 6 Quiz

Lesson 6 Power Math

Lesson 7: Represent quadratic functions (using function notation, tables, equations)

Lesson 7 Quiz

Lesson 7 Power Math

Lesson 8: Identify the three forms of equations of quadratic functions: standard, factored, vertex

Lesson 8 Quiz

Lesson 8 Power Math

Lesson 9: Review: Converting from standard form to factored form (with and without coefficients)

Lesson 9 Quiz

Lesson 9 Power Math

Lesson 10: Review: Converting from standard form to vertex form (completing the square)

Lesson 10 Quiz

Lesson 10 Power Math

Lesson 11: Describe quadratic function features—degree, shape, concavity, intercepts, vertex, optimal value, and axis of symmetry—from the graph

Lesson 11 Quiz

Lesson 11 Power Math

Lesson 12: Sketching the graphs of quadratic functions: y= (x - p)^2 + q y= - (x - p)^2 + q y= (x - a) (x - b) y= - (x - a) (x - b)

Lesson 12 Quiz

Lesson 12 Power Math

Lesson 13: Determine the number of zeros (x-intercepts) of a quadratic function using graphs, factoring, and the discriminant

Lesson 13 Quiz

Lesson 13 Power Math

Lesson 14: Find the exact coordinates of the vertex of a quadratic function (in any form) using an appropriate algebraic method or techno...

Lesson 14 Quiz

Lesson 14 Power Math

Lesson 15: Determine the algebraic representation of a quadratic function from its real roots and a point on the function

Lesson 15 Quiz

Lesson 15 Power Math

Lesson 16: Find the y intercept of quadratic functions algebraically

Lesson 16 Quiz

Lesson 16 Power Math

Lesson 17: Solve quadratic inequalities

Lesson 17 Quiz

Lesson 17 Power Math

Lesson 18: Connect quadratic equations and graphs; use parameters a, c, and d to describe graph features of transformed quadratic functions.

Lesson 18 Quiz

Lesson 18 Power Math

Lesson 19: Solve problems involving quadratic functions arising from real-world applications and represented using function notation

Lesson 19 Quiz

Lesson 19 Power math

Lesson 20: Solve linear and quadratic equations algebraically

Lesson 20 Quiz

Lesson 20 Power Math

Lesson 21: Solve by substitution a pair of simultaneous equations of which one is linear and one is quadratic

Lesson 21 Quiz

Lesson 21 Power math

Lesson 22: Solve real-life problems involving the intersection of a linear function and a quadratic function graphically and algebraically

Lesson 22 Quiz

Lesson 22 Power Math

Lesson 23: Finding the point of intersection of two quadratics

Lesson 23 Quiz

Lesson 23 Power Math

Lesson 24 & 25: Review: graphs of f(x) = |x| , f(x) = √x, and f(x) = 1/x

Lesson 24 Quiz

Lesson 24&25 Power Math

Lesson 26: Revision of mathematical vocabulary and terms: function, domain, range, one-one function, inverse function and composition of ...

Lesson 26 Quiz

Lesson 26 Power Math

Lesson 27: Understand |x|, graph y = |ax + b|, and use absolute value relations to solve equations and inequalities.

Lesson 27 Quiz

Lesson 27 Power Math

Lesson 28: Find the inverse of a one-on-one function in simple cases

Lesson 28 Quiz

Lesson 28 Power Math

Lesson 29: Determine numeric or graphical representations of inverses of linear or quadratic functions; connect inverse graphs to reflection in y = x

Lesson 29 Quiz

Lesson 29 Power Math

Lesson 30: Comparing the domain and range of a function and its inverse function

Lesson 30 Quiz

Lesson 30 Power Math

Lesson 31: Roles of a, k, d, and c in y = af(k(x – d)) + c and Their Effects on Graph Transformations of Common Functions

Lesson 31 Quiz

Lesson 31 Power Math

Lesson 32: Continue on from previous lesson

Lesson 32 Quiz

Lesson 33: Sketch y = af(k(x − d)) + c using transformations of f(x) = x, x², √x, and 1/x; state domain and range

Lesson 33 Quiz

Lesson 32&33 Power Math

Lesson 34: Draw graphs of piecewise functions

Lesson 34 Quiz

Lesson 34 Power Math

Chapter 1: Characteristics of Functions

Introduction to Chapter 2

Lesson 1: Simplifying polynomial expressions by adding and subtracting

Lesson 2: Simplifying polynomial expressions by multiplying and dividing

Lesson 2: Division of polynomials

Lesson 2A Quiz

Lesson 2A Power Math

Lesson 3: Determine if two given algebraic expressions are equivalent (i.e., by simplifying; by substituting values)

Lesson 4: Exploration and understanding that √ab = √a x √b, a ≥ 0, b ≥ 0

Lesson 5: Stating restrictions on rational expressions

Lesson 6: Adding and subtracting rational expressions

Lesson 7: Multiplying rational expressions

Lesson 8: Partial Fraction Decomposition with Linear Factors, Repeated Factors, and Irreducible Quadratic Factors

Chapter 2 Mini Challenge

Math Check-In

Chapter 2: Polynomials and Rational Functions

Introduction to Chapter 3

Lesson 1/2: Graph y = bˣ (b > 0, b ≠ 1); define f(x) = bˣ as an exponential function and explain why it is a function.

Lesson 1/2 Quiz

Lesson 1/2 Power Math

Lesson 3: Determining the value of a power with a rational exponent

Lesson 4: Connections between the value of the base and the shape of the graph

Lesson 5: Converting from exponent form to radical form

Lesson 6: Simplifying and evaluating expressions with negative exponents

Lesson 7: Simplifying algebraic expressions containing integer and rational exponents

Lesson 8: Evaluating numeric expressions containing integer and rational exponents and rational bases

Lesson 9: Key Properties of Exponential Graphs: Domain, Range, Intercepts, Intervals, Asymptotes & End Behaviour

Lesson 9/14 Quiz

Lesson 9/14 Power Math

Lesson 10: The graph of y = e^kx for both positive and negative values of k

Lesson 11: Distinguishing exponential functions from linear and quadratic functions by making comparisons in a variety of ways

Lesson 12: Use technology to determine the roles of a, k, d, and c in y = af(k(x − d)) + c and describe their graph transformations

Lesson 13: Sketch y = af(k(x − d)) + c using transformations of f(x) = aˣ; state the domain and range of the transformed functions

Lesson 15: Use technology to determine that an exponential function can be expressed using different bases

Lesson 16: Solving exponential equations by expressing both sides of the equation as single powers of the same base and then equating the...

Lesson 17: Solving exponential equations using a graph

Lesson 18: Representing an exponential function with an equation, given its graph or its properties

Lesson 19: Collect and analyze primary-source data modeled by an exponential function, with and without technology, and graph the data

Lesson 19 Power Math

Lesson 20: Identify exponential functions, including real-world growth and decay models, from various representations

Lesson 21: Solving problems using given graphs or equations of exponential functions arising from a variety of real-world applications

Lesson 21 Power Math

Chapter 3 Mini Challenge

Chapter 3: Exponential Functions

Introduction to Chapter 4

Lesson 1: Review: Discrete functions vs. continuous functions

Lesson 2: Review and identify sequence as arithmetic, geometric or neither, given a numeric or algebraic representation

Lesson 3: Represent sequences using function notation

Lesson 4/9/10: Generating sequences given the initial terms

Lesson 4/9/10 Quiz

Lesson 4/9/10 Power Math

Lesson 5: Represent a sequence algebraically using a recursion formula

Lesson 6: Determine recursive patterns in the Fibonacci sequence and Pascal's triangle

Lesson 7: Explore the relationship between pascal's triangle and expansion of binomials

Lesson 8: Binomial Expansion: expansion of (1 + x) ^ n , where n is a rational number and |x| < 1

Lesson 9: Determine the formula for the general term of an arithmetic sequence or geometric sequence

Lesson 11/12: Derive formulas for arithmetic and geometric series and use them to calculate the sum of a given number of consecutive terms

Lesson 11/12 Quiz

Lesson 11/12 Power Math

Lesson 13: Review: Sequences vs. Series

Lesson 14/15: Expand and evaluate a series written in sigma notation; Express a series using sigma notation

Lesson 14/15 Quiz

Lesson 14/15 Power Math

Lesson 16: Use the formula for the nth term and for the sum of the first n terms to solve problems involving arithmetic or geometric prog...

Lesson 17: Introduce infinite series; use the convergence condition and sum-to-infinity formula for a convergent geometric progression

Lesson 18/19: Making connections between arithmetic sequences, simple interest, and linear growth

Lesson 18/19 Quiz

Lesson 18/19 Power Math

Lesson 20/21: Calculate A, P, or i using the compound interest formula A = P(1 + i)ⁿ (or FV = PV(1 + i)ⁿ)

Lesson 20/21 Quiz

Lesson 20/21 Power Math

Chapter 4 Mini Challenge

Chapter 4: Discrete Functions

Introduction to Chapter 5

Lesson 1: Labeling sides of a right triangle hypotenuse, opposite, and adjacent

Lesson 2: Drawing angles in standard position and recognizing coterminal angles

Lesson 3: Drawing and determining the size of the principle angle and of the related acute angle

Lesson 4: Understanding the concept of the unit circle and how to use it

Lesson 5: Using the x, y, r definitions to find the principal angle, given a point on the terminal arm

Lesson 5A: Determining the measures of two angles from 0º to 360º for which the value of a given trigonometric ratio is the same

Lesson 5A Quiz

Lesson 6: Calculating the primary and reciprocal trigonometric ratios given two sides of a right triangle

Lesson 7: Relating complementary trigonometric ratios

Lesson 8: Using trig ratios to find missing angles and sides in right angle triangles

Lesson 9: Using SOHCAHTOA to solve real-world problems

Lesson 10: Radians and arc length

Chapter 5: Trigonometric Functions

What will you learn?In this course, you will be taken through advanced mathematical concepts essential for building your foundation with advanced functions. In this course, you will be exploring features of various types of functions, like their domain and range, their end behaviour, and how to graph and analyze them in real life applications.This program goes into functions in a deeper level as compared to that required by Ontario for Grade 11 Math (MCR3U). This course covers all the content needed for IB, AP, British A levels and Singapore National Curriculum.This will allow you to develop a skillset of mathematical skills that are highly applicable in real life and in many careers. Subjects in this course include learning about various types of notation, representing functions in various manners, how to multiply and divide polynomial functions, and converting functions to different forms.Our Grade 11 Functions course covers topics needed for AP, IB, British A levels and Singapore Math.What is in the program?This online app will help you learn at your own pace covering a range of topics all simplified with:✅ GetCertificatesand Report Cards✅Continuous Feedbackas you go through the program✅ Easy to UnderstandInteractive Lessons✅ On Demand One-on-OneTeacher Support✅Gamified Learningwith Pop Quizzes, Mini Challenges and Practice ProjectsOur expertise in MathExplorer Math prepares all students from Grade 6-12 to learnadvanced international mathfrom the comfort of your home. Not only will your child be prepared to succeed from a global standpoint, but they will also bedeveloping an innate passion for math that they can actually apply!Our curriculums exceed the requirements ofMinistry of OntarioCanadian General Level (BC and other provinces)British (IGSE + A Levels)International Baccalaureate (IB)Singapore and Advance Placement (AP)AP Math curriculums (including AP Statistics &amp;amp; AP Calculus

Math Grade 11 Functions (AP + IB) (Level 6A): Master function notation, domain and range, graphing, end behavior, polynomial functions, and function transformations. Build deeper skills through interactive lessons, practice, quizzes, challenges, projects,

Math Grade 11 Functions (AP + IB) (Level 6A)

Math Grade 11 Functions (AP + IB) (Level 6A)

Hasina Lookman

Course Details

Course content

Includes