Mathematics Specification B - 4MB1 PearsonEdexcel

Vectors

Muhtasari

A delivery drone needs more than a distance to reach its target: it needs a direction too. Fly 4 km the wrong way and you are further from the parcel than when you started. Vectors are the tool mathematics uses to carry size and direction together, and they turn awkward geometry problems, where a diagram only gets you so far, into clean algebra.

This topic builds vector notation and column vectors from the ground up, covers addition, subtraction, scalar multiplication and magnitude, and finishes with the technique examiners favour most: using vectors to prove that lines are parallel, that points are collinear, and that several lines meet at a single point.

Malengo

  1. Understand scalar and vector quantities in two dimensions
  2. Understand and use vector notation including column vectors
  3. Represent a vector by a directed line segment
  4. Understand and use parallel vectors, unit vectors and position vectors
  5. Find the sum and difference of two vectors
  6. Calculate the modulus (magnitude) of a vector
  7. Multiply a vector by a scalar
  8. Find the resultant of two or more vectors
  9. Apply vector methods to simple geometrical problems including collinearity, parallel lines and concurrency

Ramani ya mawazo

Mada hii imechorwa ili uone jinsi mawazo yanavyounganika.

Fungua ramani ya mawazo kwenye programu

Kadi za kumbukumbu

Mazoezi ya haraka ya kumbukumbu kuhusu kinachopimwa katika mada hii.

Fanya mazoezi ya kadi hizi kwenye programu

Maelezo ya Somo

Some measurements are complete once you state a single number: a mass of 4 kg, a temperature of 20°C, an area of 15 m². These are scalars. Others are incomplete without a direction attached: a displacement of 4 km only makes sense once you also say which way, and a force of 10 N pulling left has a completely different effect from a force of 10 N pulling right. Quantities like these, with both size (magnitude) and direction, are vectors.

Dokezo Kamili la Somo Linapatikana kwenye Programu ya Green Bridge

Pata programu ya Green Bridge CBT kwenye simu au kompyuta yako kwa maktaba kamili ya IGCSE: mitihani ya miaka iliyopita, miongozo ya usahihishaji, ramani za mawazo, kadi za marudio na masomo ya sauti.

Maelezo kamili ya masomo yenye michoro
Msaidizi wa kujifunza wa AI
Mitihani ya majaribio yenye muda, husahihishwa mara umalizapo
Pakua programu ya simu Pakua programu ya kompyuta
Inapatikana kwa Android, Windows, macOS, na Linux Programu ya iOS inakuja hivi karibuni

Tathmini ya Somo

Hongera kwa kukamilisha somo la Vectors. 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. Which of these is a vector quantity? A) Mass B) Temperature C) Velocity D) Area Answer: C
  2. What is the magnitude of the vector (8, -6)? A) 2 B) 10 C) 14 D) 100 Answer: B
  3. If a = (5, -2) and b = (-3, 6), what is a - b? A) (2, 4) B) (8, -8) C) (-8, 8) D) (2, -4) Answer: B
  4. Multiplying a vector by -3 will: A) triple its magnitude and keep the same direction B) triple its magnitude and reverse its direction C) divide its magnitude by 3 and reverse its direction D) keep the magnitude the same and reverse its direction Answer: B
  5. P, Q and R have position vectors such that PQ = 2(PR). What can you conclude? A) P, Q and R are collinear B) PQ is perpendicular to PR C) Q is the midpoint of PR D) Nothing can be concluded Answer: A

Fanyia kazi maswali haya kwenye programu

Fanyia kazi maswali haya kwenye programu

Vitabu Vinavyopendekezwa

Pearson Edexcel International GCSE (9-1) Mathematics B Student Book
Pearson Edexcel International GCSE (9-1) Mathematics B Student Book
Manukuu: First edition
Mchapishaji: Pearson Education
Mwaka: 2017
ISBN: 978-0-435-18316-9
Maelezo: Endorsed student book for the 4MB1 specification with worked examples and graded exercises.

Jifunze zaidi kutoka vyanzo huria

Vimechapishwa na mashirika mengine chini ya leseni huria na vinatajwa kama wanavyoomba. Viungo hufungua tovuti zao.

Fanya Mazoezi ya Maswali ya Majaribio

Ungependa kufanya mazoezi ya maswali ya majaribio kuhusu Vectors? Pakua programu ya Green Bridge CBT ili kupata maswali ya majaribio na tathmini kamili za mazoezi kuhusu mada hii.

Pakua Programu Kwenye Google Playstore

Kila kitu unachohitaji ili kufaulu katika JAMB, WAEC & NECO.

Green Bridge CBT Mobile App
Msaidizi wa Gumzo wa Kujifunza wa AI Uliobinafsishwa
Maswali ya mtihani zaidi ya 200,000 ya IGCSE, JAMB, WAEC na NECO
Zaidi ya Madaftari ya Masomo 1200
Msaada Nje ya Mtandao - Jifunze Wakati Wowote, Popote Pale
Ratiba ya Daraja la Kijani
Muhtasari wa Fasihi na Maswali Yanayoweza Kutokea
Fuata Utendaji na Maendeleo Yako
Maelezo ya Kina kwa Kujifunza kwa Kina