Further Pure Mathematics - 4PM1 PearsonEdexcel

Inequalities

Muhtasari

Equations tell you exactly where two expressions are equal, but in mathematics and real life you often need to know where one quantity is larger or smaller than another. Inequalities give you a way to describe entire ranges of values, not just single solutions, and they appear throughout the 4PM1 specification whenever a question asks for a set of values rather than a point.

You will learn to solve linear and quadratic inequalities algebraically, represent linear inequalities in two variables on a coordinate grid, and tackle introductory linear programming problems. Every technique builds on algebra you already know, with a few critical sign rules that catch out even confident students.

Malengo

  1. Solve simple linear and quadratic inequalities
  2. Represent linear inequalities in two variables graphically
  3. Solve simple problems on linear programming

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Maelezo ya Somo

A manufacturer needs at least 200 units of raw material but can store no more than 500. A student needs a mark above 60% to pass but below 90% for a merit. These are everyday inequality problems, and the algebraic tools you build here let you solve them precisely, whether the relationship is linear, quadratic, or a combination of constraints on a coordinate plane.

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Tathmini ya Somo

Hongera kwa kukamilisha somo la Inequalities. 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. Solve 3x - 5 > 7. A) x > 4 B) x > 2 C) x < 4 D) x > 12 Answer: A
  2. Which values of x satisfy x^2 - 4x - 5 < 0? A) x < -1 or x > 5 B) -1 < x < 5 C) x < -5 or x > 1 D) -5 < x < 1 Answer: B
  3. When solving an inequality, what must you do if you divide both sides by a negative number? A) Nothing changes B) Reverse the inequality sign C) Square both sides D) Add 1 to both sides Answer: B
  4. In a linear programming problem, the optimal value of the objective function occurs at: A) The centre of the feasible region B) Any point on a boundary line C) A vertex of the feasible region D) The origin Answer: C
  5. The boundary line for the inequality 2x + y < 6 should be drawn as: A) A solid line B) A dashed line C) A dotted line with arrows D) A double line Answer: B

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Vitabu Vinavyopendekezwa

Pearson Edexcel International GCSE (9-1) Further Pure Mathematics Student Book
Pearson Edexcel International GCSE (9-1) Further Pure Mathematics Student Book
Manukuu: First edition
Mchapishaji: Pearson Education
Mwaka: 2017
ISBN: 978-0-435-18831-7
Maelezo: Endorsed student book covering the full 4PM1 specification.

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Msaada Nje ya Mtandao - Jifunze Wakati Wowote, Popote Pale
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