Concepts in this chapter that link to other parts of the syllabus.
Chapter 2 — Logarithmic and exponential functions
The algebraic skills of solving equations and inequalities from Chapter 1, particularly those involving absolute values, are foundational for solving logarithmic and exponential equations and inequalities in Chapter 2. Understanding how to manipulate algebraic expressions is crucial before applying logarithmic and exponential laws.
Go to chapter →Chapter 4 — Differentiation
Polynomials, a key topic in Chapter 1, are frequently differentiated in Chapter 4. The algebraic manipulation skills developed in Chapter 1 are essential for simplifying expressions before and after applying differentiation rules like the product and quotient rules.
Go to chapter →Chapter 5 — Integration
Similar to differentiation, the integration of polynomial functions (from Chapter 1) is a fundamental skill introduced in Chapter 5. The algebraic techniques for manipulating expressions are prerequisite for successful integration.
Go to chapter →Chapter 6 — Numerical solutions of equations
The concept of finding roots of polynomial equations (from Chapter 1) is directly addressed in Chapter 6, where numerical methods are used to approximate these roots when exact algebraic solutions are not feasible. Students will apply iterative formulae to find roots of polynomial functions.
Go to chapter →Chapter 7 — Further algebra
Chapter 7 builds directly on the polynomial division and factor/remainder theorems from Chapter 1, extending these concepts to improper algebraic fractions and partial fractions. The ability to factorise polynomials is crucial for decomposing fractions into partial fractions.
Go to chapter →Chapter 11 — Complex numbers
The modulus function from Chapter 1 is directly extended in Chapter 11 to define the modulus of a complex number, representing its distance from the origin in the complex plane. This shows a conceptual link between absolute value in real numbers and magnitude in complex numbers.
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