IGCSE Mathematics

Sequences and Functions

Build algebraic rules before studying transformations.

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IGCSE Sequences and nth Term

🎯 Key idea: A sequence is a list with a rule. First ask whether the same amount is added each time or the same multiplier is used each time. The notation $u_n$ means the term in position $n$. 🔢 1. Arithmetic sequences An arithmetic sequence has a constant difference. For example, $7, 11, 15, 19, […]

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IGCSE Functions and Transformations

🎯 Key idea: $f(x)$ is an output, not multiplication. Read it as “the function $f$ of input $x$”. 🔁 1. Function notation If $f(x)=2x+5$, substitute the input inside the rule. Worked example: Find $f(-3)$. $f(-3)=2(-3)+5=-1$. 🔗 2. Composite and inverse functions For a composite, apply the inside function first: $fg(x)$ means $f(g(x))$. Worked example: $f(x)=x+4$ […]

Graphs and Coordinate Geometry

Interpret linear and non-linear graphs using their defining features.

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IGCSE Linear Graphs and Coordinate Geometry

🎯 Key idea: In $y=mx+c$, $m$ tells you the vertical change for every one step right; $c$ tells you where the line crosses the $y$-axis. 📈 1. Gradient and equations A positive gradient rises left to right; a negative gradient falls. Use $m=[[frac{change in y}{change in x}]]$. Worked example: A line rises $6$ when it […]

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IGCSE Graph Families Investigation

🎯 Key idea: Do not identify a graph only by a rough picture. Use features: intercepts, symmetry, turning points, whether it crosses an axis, and whether it approaches an asymptote. ⌣ 1. Quadratic $y=x^2$ is a quadratic. It is a U-shape, symmetric about the $y$-axis, with a minimum at $(0,0)$. Investigation: Compare $y=x^2$, $y=x^2+3$ and […]

Number and Proportion

Use exam-ready ratio and proportion methods.

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IGCSE Ratio and Proportion: Exam Methods

🎯 Key idea: Ratio and proportion questions are usually won by setting up the parts correctly before calculating. You will meet these ideas in recipes, maps, scale drawings, rates, geometry, and word problems. 🔢 1. Simplifying Ratios A ratio compares quantities in the same unit. To simplify a ratio, divide every part by the highest […]

Statistics

Interpret spread in a data set with confidence.

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Standard Deviation Without Fear

Master Standard Deviation without the headache. Learn what it measures, decode the formula, and use a simple table method to calculate it step-by-step.