Mathematics - 0580 CIE

Sketching Curves

Muhtasari

Every type of equation has a signature shape when you draw it: a straight line, a smooth U-shaped parabola, a wave, a curve that races away. Recognising these shapes lets you picture an equation at a glance and sketch it quickly without plotting dozens of points.

In this lesson you will recognise, sketch and interpret the graphs of linear and quadratic functions, and (at Extended) cubic, reciprocal and exponential functions, picking out their key features such as intercepts and turning points.

Malengo

Recognise, sketch and interpret graphs of the following functions: (a) linear (b) quadratic.
Recognise, sketch and interpret graphs of the following functions: (a) linear (b) quadratic (c) cubic (d) reciprocal (e) exponential. (Extended only)

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Maelezo ya Somo

A sketch shows the behaviour of a function instantly: where it crosses the axes, where it turns, and how it grows. This visual understanding supports solving equations and reading real data.

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Hongera kwa kukamilisha somo la Sketching Curves. Sasa kwa kuwa umechunguza dhana na mawazo muhimu, ni wakati wa kuweka ujuzi wako kwa mtihani. Sehemu hii inatoa mazoezi mbalimbali maswali yaliyoundwa ili kuimarisha uelewaji wako na kukusaidia kupima ufahamu wako wa nyenzo.

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Tumia sehemu hii ya tathmini kama fursa ya kuimarisha uelewa wako wa mada na kubaini maeneo yoyote ambapo unaweza kuhitaji kusoma zaidi. Usikatishwe tamaa na changamoto zozote utakazokutana nazo; badala yake, zitazame kama fursa za kukua na kuboresha.

What shape is the graph of y = x^2 - 4? A. A straight line B. A parabola C. An S-shape D. A circle Answer: B
Where does y = x^2 - 4 cross the x-axis? A. x = -4 and x = 4 B. x = -2 and x = 2 C. x = 0 only D. x = 4 only Answer: B
What is the vertex of y = x^2 - 4? A. (0, 0) B. (0, 4) C. (0, -4) D. (-4, 0) Answer: C
The graph of y = mx + c is always: A. a parabola B. a straight line C. an S-shape D. a curve Answer: B
If a is negative in y = ax^2 + bx + c, the parabola: A. opens upwards B. opens downwards C. is a straight line D. has no vertex Answer: B

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Vitabu Vinavyopendekezwa

Cambridge IGCSE Mathematics Core and Extended Coursebook

Manukuu: Second edition

Mchapishaji: Cambridge University Press

Mwaka: 2018

ISBN: 978-1-108-43718-9

Maelezo: Endorsed coursebook with full coverage of the 0580/0980 syllabus, worked examples and practice exercises.

Cambridge IGCSE Core and Extended Mathematics

Manukuu: Fifth edition

Mchapishaji: Hodder Education

Mwaka: 2023

ISBN: 978-1-398-37391-4

Maelezo: Endorsed textbook with worked examples and graded questions across Core and Extended content.

Jifunze zaidi kutoka vyanzo huria

Sehemu ya kitabu Graph Quadratic Functions Using Properties OpenStax · Intermediate Algebra
Recognize the graph of a quadratic function

"Intermediate Algebra: Graph Quadratic Functions Using Properties" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/intermediate-algebra/pages/9-6-graph-quadratic-functions-using-properties. Access for free at https://openstax.org/books/intermediate-algebra/pages/1-introduction
Sehemu ya kitabu Linear Functions OpenStax · Algebra and Trigonometry
Represent a linear function.

"Algebra and Trigonometry: Linear Functions" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/algebra-and-trigonometry/pages/4-1-linear-functions. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction

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