Mathematics (9-1) - 0980 CIE

Compound Shapes And Parts Of Shapes

Muhtasari

Real objects are rarely a single neat rectangle or circle. An L-shaped room, a running track, a washer with a hole in it: these are compound shapes, built from simpler shapes joined together or cut apart. The good news is that you already know all the formulas you need. The skill is deciding how to split the shape and whether to add or subtract.

In this lesson you will find the area of compound shapes by splitting them into known shapes and adding the parts, and the area of shapes with a piece removed by subtracting. The same add-and-subtract thinking extends to compound solids and their volumes. Master the splitting strategy and even awkward-looking shapes become a short, tidy calculation.

Malengo

  1. Carry out calculations and solve problems involving perimeters and areas of: compound shapes parts of shapes.
  2. Carry out calculations and solve problems involving surface areas and volumes of: compound solids parts of solids.

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Maelezo ya Somo

Almost no real surface is a perfect single shape. Floor plans, garden layouts, machine parts and sports pitches are all compound shapes. Being able to break a complicated outline into rectangles, triangles and circles, then add or subtract their areas, turns a daunting figure into a few simple calculations and is one of the most practical skills in the whole section.

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Tathmini ya Somo

Hongera kwa kukamilisha somo la Compound Shapes And Parts Of Shapes. 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.

Utakutana na mchanganyiko wa aina mbalimbali za maswali, ikiwemo maswali ya kuchagua jibu sahihi, maswali ya majibu mafupi, na maswali ya insha. Kila swali limebuniwa kwa umakini ili kupima vipengele tofauti vya maarifa yako na ujuzi wa kufikiri kwa makini.

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.

  1. An L-shape splits into a rectangle 8 cm by 2 cm and a rectangle 3 cm by 4 cm. What is its total area? A. 17 cm^2 B. 24 cm^2 C. 28 cm^2 D. 48 cm^2 Answer: C
  2. A circle of radius 3 cm is cut from a square of side 10 cm. Using pi = 3.142, what is the area remaining to 2 d.p.? A. 28.28 cm^2 B. 71.72 cm^2 C. 90.58 cm^2 D. 100.00 cm^2 Answer: B
  3. A compound solid is a cuboid 5 cm by 4 cm by 3 cm with a cuboid 2 cm by 2 cm by 3 cm on top. What is its volume? A. 60 cm^3 B. 72 cm^3 C. 84 cm^3 D. 120 cm^3 Answer: B
  4. What is the best first step when finding the area of a compound shape? A. Square the longest side B. Split it into simpler shapes you can calculate C. Multiply all the given lengths together D. Add up every length given Answer: B
  5. A washer is a circle of radius 5 cm with a circle of radius 2 cm removed from its centre. Using pi = 3.142, what is its area to 2 d.p.? A. 12.57 cm^2 B. 65.98 cm^2 C. 78.55 cm^2 D. 91.12 cm^2 Answer: B

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Vitabu Vinavyopendekezwa

Cambridge IGCSE Mathematics Core and Extended Coursebook
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
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.

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