Further Pure Mathematics - 4PM1 PearsonEdexcel

Inequalities

Gbogbo ọrọ náà

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.

Ebumnobi

Solve simple linear and quadratic inequalities
Represent linear inequalities in two variables graphically
Solve simple problems on linear programming

Akọmọ Ojú-ẹkọ

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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Ayẹwo Ẹkọ

Ekele diri gi maka imecha ihe karịrị na Inequalities. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.

Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.

Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.

Solve 3x - 5 > 7. A) x > 4 B) x > 2 C) x < 4 D) x > 12 Answer: A
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
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
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
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