The LWB Level 2 Mathematics and Statistics Externals Learning Workbook is a high-impact, write-on resource designed to prepare students for the three most common external examinations. This workbook streamlines the revision process by combining Algebraic Methods, Calculus, and Probability into a single, cohesive guide, providing the scaffolding needed for students to move from basic procedures to complex problem-solving.
AS 91261 (2.6): Apply Algebraic Methods in Solving Problems
Manipulating Expressions: Intensive practice in expanding, factoring, and simplifying complex algebraic fractions.
Equations and Inequalities: Solving linear, quadratic, and simple exponential equations (2x=32).
The Discriminant (b2−4ac): Mastering the tool used to determine the nature of roots (two real, one real, or no real solutions) and applying it to find unknown coefficients.
Logarithms: Introduction to log laws (log(ab)=loga+logb) and their use in solving equations where the variable is an exponent.
Rearranging Formulas: Developing the skill to change the subject of a formula, a critical skill for Physics and higher-level Calculus.
Achievement to Excellence: Progresses from routine equation solving to solving multi-step "word problems" that require students to form their own equations from a context.
AS 91262 (2.7): Apply Calculus Methods in Solving Problems
Differentiation (Finding the Gradient): Mastering the power rule to find the derivative (f′(x)) of polynomial functions.
Gradient and Tangents: Using the derivative to calculate the gradient at a specific point and finding the equations of tangent lines.
Turning Points and Optimisation: Identifying local maximums and minimums where f′(x)=0. Students learn to solve real-world problems, such as finding the maximum volume of a container or the minimum cost of materials.
Integration (Anti-differentiation): Learning to reverse the process of differentiation to find the original function (f(x)) from a gradient function, including solving for the constant +C.
Kinematics: Analyzing the relationship between Displacement (s), Velocity (v), and Acceleration (a). Students learn to differentiate to find velocity and integrate to find displacement.
AS 91267 (2.12): Apply Probability Methods in Solving Problems
Probability Trees and Tables: Using visual tools to calculate probabilities for multi-stage events and conditional probability scenarios.
Risk and Relative Risk: Comparing probabilities between different groups (e.g., comparing the risk of an event occurring for Group A vs. Group B).
The Normal Distribution: Mastering the "bell curve."
Standardizing (Z-scores): Calculating how many standard deviations a value is from the mean.
Inverse Normal: Finding a value given a probability (e.g., "What is the cutoff for the top 5%?").
Statistical Literacy: Learning to critique claims made in the media by understanding sampling variability and the limits of probability models.
Workbook Features
NCEA-Style Practice: Every section concludes with "Check Your Progress" tasks that mirror the format and difficulty of the end-of-year NCEA exams.
Step-by-Step Worked Examples: Provides clear templates for how to set out mathematical working to ensure students don't lose marks on "minor errors."
Graphics Calculator Hints: Includes specific tips for using Casio or TI calculators to solve equations and find Normal Distribution values quickly.
Full Answer Appendix: Every question has a fully worked solution at the back of the book, allowing for independent study and immediate feedback.
Formula Reminders: Key formulas are highlighted throughout the text to reinforce the "Formula Sheet" provided in the actual exam.