Preview Numbers and Algebra

Indices

BASIC LAWS OF EXPONENTS

Product Law

Quotient Law

Power Law

POWER LAW WITH COEFFICIENTS

Power Law with Coefficients

NEGATIVE EXPONENTS

Negative Exponents

Negative Exponents - Harder

EXPONENTS - COMBINATION

Combination (Product, Quotient, Power, Negative Exponents) - Non GDC

OPERATIONS ON INDICES

Operations Involving Exponents

EXPONENTS - WRITING WITHOUT FRACTIONS

Writing without fractions (Simplification)

EXPRESSING NUMBERS IN TERMS OF INDICES

Expressing Numbers in Terms of Indices

EXPONENTS INVOLVING FRACTIONAL POWER

Fractional Powers - Involving Constants

Fractional Powers - Involving Variables and Constants

HCF & LCM OF EXPONENTS

HCF & LCM with exponents

Solving Exponential Equations

Exponents involving fractional powers

Operations involving fractional powers

Operations Involving Fractional Powers

Exponents involving variable powers

Exponents involving Variable Powers

Simplification involving powers with variables

Simplification involving Powers with Variables

Standard Form

Standard Form - Concept & Determination

Determining for values in standard form (Non GDC)

Converting Numbers to Standard Form

Writing in standard form (Non GDC)

Converting Standard Form to Ordinary Numbers

Writing as an ordinary number (Non GDC)

Standard Form - Conversions

Conversions followed by standard form expressions (Non GDC)

Finding Missing Values

Finding missing values (Non GDC)

Comparing Numbers in Standard Form

Comparing Values (Non GDC)

Operations on Standard Form

Operations (Non GDC)

Word Problems

Surds

Concept of Surds

Writing in simplest form (Non GDC)

Finding Unknown Values

Find the value of k for simplest surd form (Non GDC)

Multiplying & Dividing Single Surds

Multiplying single surds (Non GDC)

Dividing single surds

Operations on surds

Operations on Surds (Addition and Subtraction)

Operation on Surds after simplification (Addition and Subtraction)

Multiplying single & binomial Surd Expressions

Multiplying single surds and binomial surd expression

Multiplying binomial surd expressions

Squaring Surds & Difference of Squares

Squaring single surd expressions

Squaring binomial surd expressions

Difference of squares of surd expressions

Rationalization of Single Surds

Lowest rationalizing factor

Rationalizing single surd denominators

Rationalisation of binomial expressions

Rationalizing denominators with binomial surd expressions (Non GDC)

Finding the values after rationalization

Simplify

Comparing Surd Values

Logarithms

Convert Exponential Statements to log statements

Converting Exponential statements to logarithmic expressions (using constant values) (Non GDC)

Converting Exponential statements to logarithmic expressions (using variable values)

Convert Log Statements to Exponential statements

Converting logarithmic expressions to exponential statement (using constant values)

Converting logarithmic expressions to exponential statement (using variable values) (Non GDC)

Finding values of log statements

Finding logarithmic values without a calculator (whole numbers) (Non GDC)

Finding logarithmic values without a calculator (surds/decimals/fractions) (Non GDC)

Changing subject of formula in log statements

Making x the subject of formula in logarithmic or exponential expressions (Non GDC)

Solving for the unknown value in log statements

Solving for the unknown value (Non GDC)

Finding Approximate values

Finding Values and Approximate Values (Non GDC)

Using the Calculator for Log Statements

Using GDC for different expressions (GDC)

Natural logs

Solving natural logarithmic expressions (Non GDC)

Simplifying with natural logs

Simplifying with natural logs (Non GDC)

Solving natural logs with a calculator

Using GDC for different expressions using natural logs (GDC)

Word Problems

Approximation and Estimation

Exact Value

Rounding Numbers

Rounding off to the nearest whole number

Rounding off based on number of decimal places

Rounding off based on significant figures

Calculating and then rounding off

Estimation

Estimation using a one figure approximation

Estimations by guessing (non GDC)

Estimations – Word Problems (non GDC)

Measurement & Bounds

Determining the accuracy

Determining the range or boundary values

Calculating values using bounds

Absolute & Percentage Error

Finding absolute and percentage error

Absolute and Percentage Error after Calculations

Maximum Percentage Error

Polynomial Equations

Quadratic Equations - Basics

Solving equations – Basic

Solving equations in factored form

Quadratic Equations - Factorization

Solving Quadratic Equations by factorization

Solving Quadratic Equations by factorization where coefficient of x2 is not equal to 1

Solving Quadratic Equations, rearrangement followed by factorization (non GDC)

Framing a Quadratic Equation

Framing the Quadratic Equation

Quadratic Equations - Solve using Technology

Quadratic Equations - Solve Graphically

Solving Higher Power Equations

Solving Power Equations

Solving Higher Power Equations using Technology

Solving Polynomial Equations using Technology

Linear Equation in 3 variables

Word Problems on Linear Equations in 3 variables

General Sequences

Forming Sequences

Forming the Sequence

Finding the terms of a Sequence

Finding the terms of the sequence

Identifying the next few terms

Identify the correct Sequence

Arithmetic Sequences

Arithmetic Sequence - Concept

Identifying the first term and common difference

Identify first term and common difference

Finding the general term

Finding the nth term

Finding the number of terms

Number of terms in sequence

Finding the term number

Checking if a term belongs

Using Inequalities in An Arithmetic Sequence

Using Inequalities

Miscellaneous

Using Unknowns in an Arithmetic Sequence

Using unknowns in an equation

Inserting Numbers in an Arithmetic Sequence

Insert numbers

Word problems

Approximations in an Arithmetic Sequence

Approximation

Sum of Series - Arithmetic

Concept of sum of Sum of an Arithmetic Series

Sum of terms in an Arithmetic Series

Sum of n terms

Finding the sequence and then finding the sum

Determining the sequence, then finding the sum

Finding the number of terms and then finding the sum

Determining the number of terms, then finding the sum

Finding the number of terms when the sum is given

Using Inequalities in Sum of Series

Using inequalities in a sum

Application type

Geometric Sequence

Geometric Sequences - Concept

Identify first term and common ratio

Finding the first term and common ratio

Finding the next few terms

Finding next few terms

Finding the sequence from random terms

General Term of a Sequence

Finding the general term of a sequence

Finding the particular term of a Sequence

Identifying the term number

Finding the term number of a sequence

Unknowns in a Geometric Sequence

Using unknowns in a sequence

Word Problems on Growth

Word problems - Growth

Word Problems on Decay

Word problems - Decay

Using Inequalities in Geometric Sequences

Using inequalities in sequences

Geometric Sequence - Sum of Finite Terms

Sum of Finite Terms in a Geometric Sequence

Finding the sum - rational numbers

Identifying First Term and Common ratio to find the sum of Geometric Series

Finding the sum by first identifying the first term and common ratio

Sum of Irrational Numbers in a Geometric Sequence

Finding the sum - irrational numbers

Finding Number of Terms in a Sum

Number of terms in a sum

Finding the general formula for a sum

Using Inequalities in a sum of Geometric Series

Using inequalities in a sum

Word Problems on Application of Sum of Series

Word problems - application

Arithmetic and Geometric Series - Use of Sigma

Expression of the term using sigma notation

Sum of Terms without Sigma Notation

Finding the sum of n terms without sigma notation (non GDC)

Sum Using Sigma Notation - terms starting from 1

Finding the sum of n terms using sigma notation (when terms start from 1)

Sum Using Sigma Notation - terms not starting from 1

Finding the sum of n terms using sigma notation (when terms do not start from 1)

Finding Unknowns when n starts from 1

Finding unknowns in a sigma series, when n starts from 1

Finding Unknowns when n does not start from 1

Finding unknowns in a sigma series, when n does not start from 1

Partial Sums - Geometric Sequence

Partial sums – Geometric Sequence

Partial Sums - Arithmetic Sequence

Partial sums – Arithmetic Sequence

Compound Interest

Concept of compound interest

Compound Interest and amount

Finding CI/amount for annual interest

Finding CI/amount for successive rates of interest

Half-Yearly and Quarterly Interest Calculations

Finding CI/amount compounded monthly/quarterly/semi-annually

Finding original Principal

Finding principal using amount

Comparing Interests

Comparing different interests

Finding the Rate Percent

Finding rate

Finding the Time Period

Finding the time period - using graphs

Finding Time

Inflation

Real Value of an investment

Real Value of an Investment

Concept of Depreciation

Depreciation

Financial Math - Loans and Annuities

Loans

Repayment

Repayments

Total Repayment & Interest charged

Total repayment and interest charged

Interest Difference between schemes

Finding interest differences between two schemes

Outstanding balance

Finding rate or time period of loan

Finding rate/time when repayment options are given

Total Interest paid in first year

Total interest in first year

Annuity

Time period for annuity

Finding time period of annuity

Amount drawn in annuity

Finding amount drawn in annuity

Compound interest rolled over into annuity

Compounding the amount and then rolling over into an Annuity fund

Outstanding balance in annuity

Difference in timings when repayments change

Finding difference in timings when repayments changed

Finding future values of deposits

Finding future values when deposits are made

Future values with different yearly interest rates

Finding future values when deposits are made with different yearly interest rates

Preview - Numbers and Algebra - AI SL