Counting to 10, Reading Numbers
Students become familiar with numbers up to 10 by counting pictures or dots and reading numbers. They should be able to read and easily recite numbers up to 10 and recognize the number of pictures or dots by counting.
Reading Numbers to 50, Sequence of Numbers
Students read numbers and number tables up to 50 by counting pictures or dots, reading numbers or number tables, and finding the missing numbers in number tables. They should be able to easily recite numbers up to 50 and become familiar with numbers up to 100.
Reading Numbers, Writing Numbers to 50
Students deepen their understanding of the number sequence through number reading and writing exercises in number tables, number boards, and complete-the-sequence problems. By the end of the level, students learn to write numbers up to 50 and read numbers up to 100.
Writing Numbers to 120, Adding up to 3
Students continue to enhance their understanding of the sequence of numbers as well as the number-writing skills that they developed in the previous level. Being introduced to addition, students master +1, +2, through to +3 individually. Students are challenged to answer random addition questions from +1 to +3.
Adding up to 10
Students further develop basic mental calculation skills in addition through a sequential study of adding 4 through adding 10. Students should master the contents of this level for smooth progress in subsequent levels. This level aims to develop the concentration ability and work skills necessary for higher level study.
Horizontal Addition, Subtraction from Numbers up to 20
Students study horizontal addition with larger numbers. Their addition skills will be strengthened before advancing to the horizontal subtraction exercises of this level. This level aims to develop mental calculations, while improving students’ concentration ability and their work skills.
Vertical Addition & Subtraction
Students learn vertical addition and subtraction, and encounter word problems. Students build advanced mental calculation skills as they "carry" in addition questions and "borrow" in questions involving subtraction. Understanding and mastering these concepts reduces errors in the future with multiplication and division.
Students study the multiplication tables up to 9. They continue by solving exercises up to 3 or more digits multiplied by 1 digit. Once multiplication is mastered, students begin studying division up to 3 digits divided by 1 digit.
Long Multiplication & Division, Introduction to Fractions
Students further develop the multiplication and division skills they acquired in the previous level by studying double-digit multiplication and long division. Students also become familiar with fractions and learn to reduce using the Greatest Common Factor.
Students learn to add, subtract, multiply, and divide fractions. Students also learn basic fraction/decimal conversions.
Four Operations, Decimals
Students use the order of operations to continue performing calculations with fractions and decimals.
Positive/Negative Numbers, Introduction to Algebra
Students use the four operations on positive and negative numbers, simplify algebraic expressions, and solve linear equations in one variable.
Linear Equations, Inequalities & Graphing
Students learn to solve simultaneous linear equations in two to four variables. Concepts of numerical and algebraic value are strengthened. Students are introduced to transforming equations, inequalities, functions and graphs.
Quadratic Equations, Factorization, Square Roots
Students further develop their algebraic skills through the study of quadratic equations, the multiplication of polynomials, factorization, calculation with square roots, and the Pythagorean Theorem.
Students are introduced to advanced factoring methods, complex numbers, the discriminant, and the Factor and Remainder theorems. Students conduct proofs of algebraic equalities and inequalities.
Functions—Quadratic, Fractional, Irrational, Exponential
After a thorough study of quadratic functions, students are introduced to various types of functions and their corresponding graphs. These functions include higher degree, fractional, irrational, and exponential. The skills developed here will help ease students into studying calculus.
Students begin by studying logarithmic functions. Then, students are led into the beginning of calculus, studying basic differentiation and integration. Students continue with an analysis of the applications of integration, including areas, volumes, velocity and distance.
Trigonometry, Addition Theorem, Circles
Students begin by studying the basics of trigonometric functions, followed by graphing trigonometric functions. Students also learn and use the formulas of the Addition Theorem. Finally, students study the equations of straight lines, circles, and tangent lines of circles.
Loci, Sequences and Series, Limits, Differentiation
Students begin by studying loci and quadratic inequalities. They then study arithmetic, geometric, infinite and other various types of sequences and series. Students continue by studying limits of functions and continuity and the basics of differentiation.
Advanced Differentiation, Integration, Differential Equations
Students study advanced differentiation and applications of differential calculus. They continue with an in-depth study of advanced integration and its applications. Finally, students study differential equations.
Triangles, Vectors, Matrices, Probability, Statistics
Students can choose to study elective topics from triangles, vectors, matrices, mapping and transformations, probability and statistics.
Level 6A: Counting to 10, Reading Numbers
Level 5A: Reading Numbers to 50, Sequence of Numbers
Level 4A: Reading Numbers, Writing Numbers to 50
Level 3A: Writing Numbers to 120, Adding up to 3
Level 2A: Adding up to 10
Level A: Horizontal Addition, Subtraction from Numbers up to 20
Level B: Vertical Addition & Subtraction
Level C: Multiplication, Division
Level D: Long Multiplication & Division, Introduction to Fractions
Level E: Fractions
Level F: Four Operations, Decimals
Level G: Positive/Negative Numbers, Introduction to Algebra
Level H: Linear Equations, Inequalities & Graphing
Level I: Quadratic Equations, Factorization, Square Roots
Level J: Advanced Algebra
Level K: Functions—Quadratic, Fractional, Irrational, Exponential
Level L: Logarithms, Calculus
Level M: Trigonometry, Addition Theorem, Circles
Level N: Loci, Sequences and Series, Limits, Differentiation
Level O: Advanced Differentiation, Integration, Differential Equations
Level X: Triangles, Vectors, Matrices, Probability, Statistics