Mathematics - 9260 OxfordAQA

Solving Equations And Inequalities

Aperçu

An equation is a question about a number: which value makes these two expressions agree? Solving it is the process of stripping away everything that has been done to the unknown until it stands alone. That is the mechanical half of this topic. The other half is harder and worth more marks: turning a situation described in words, or drawn as a shape, into the equation in the first place.

You will solve linear equations, including those with brackets and with the unknown on both sides, solve quadratic equations by factorising, solve two linear simultaneous equations in two variables, find approximate solutions from a graph, translate simple situations or procedures into algebraic expressions or formulae, derive and solve equations from geometrical problems and problems set in context, and solve linear inequalities and represent the solution set on a number line. On the Extension Tier you will add completing the square and the quadratic formula, simultaneous equations where one is quadratic, inequalities in two variables and quadratic inequalities, and the graphical representation of a solution set.

Objectifs

  1. [Core] solve linear equations in one unknown algebraically
  2. [Core] find approximate solutions using a graph (Notes: including use of brackets and those with the unknown on both sides of the equation)
  3. [Core] solve quadratic equations algebraically by factorising
  4. [Core] find approximate solutions using a graph
  5. [Extension] including completing the square and by using the quadratic formula
  6. [Core] solve two linear simultaneous equations in two variables algebraically
  7. [Core] find approximate solutions using a graph
  8. [Extension] including one linear and one quadratic
  9. [Core] translate simple situations or procedures into algebraic expressions or formulae
  10. [Core] derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution (Notes: including the solution of geometrical problems and problems set in context)
  11. [Core] solve linear inequalities in one variable
  12. [Core] represent the solution set on a number line
  13. [Extension] solve linear inequalities in one or two variable(s), and quadratic inequalities in one variable
  14. [Extension] represent the solution set on a number line and on a graph (Notes: students should know the conventions of an open circle on a number line for a strict inequality and a closed circle for an included boundary. In graphical work the convention of a dashed line for strict inequalities and a solid line for an included inequality will be required)

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Note de cours

Take a number, multiply it by 6 and subtract 12, and you get 0. What was the number? Nobody solves this by algebra: you add 12 back, then divide by 6, and get 2. That is the entire principle. An equation records a sequence of operations applied to an unknown, and solving it means applying the inverse operations in the reverse order. The formal rule, do the same thing to both sides, is a way of keeping that honest when the sequence gets complicated.

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Évaluation de la leçon

Félicitations, vous avez terminé la leçon sur Solving Equations And Inequalities. Maintenant que vous avez exploré le concepts et idées clés, il est temps de mettre vos connaissances à lépreuve. Cette section propose une variété de pratiques des questions conçues pour renforcer votre compréhension et vous aider à évaluer votre compréhension de la matière.

Vous rencontrerez un mélange de types de questions, y compris des questions à choix multiple, des questions à réponse courte et des questions de rédaction. Chaque question est soigneusement conçue pour évaluer différents aspects de vos connaissances et de vos compétences en pensée critique.

Utilisez cette section d'évaluation comme une occasion de renforcer votre compréhension du sujet et d'identifier les domaines où vous pourriez avoir besoin d'étudier davantage. Ne soyez pas découragé par les défis que vous rencontrez ; considérez-les plutôt comme des opportunités de croissance et d'amélioration.

  1. Circle the equation with roots 4 and -8. A. 4x(x - 8) = 0 B. (x - 4)(x + 8) = 0 C. x^2 - 32 = 0 D. (x + 4)(x - 8) = 0 Answer: B
  2. A number line shows a closed circle at -7, an open circle at 6, and the values between them shaded. Which inequality does it show? A. -7 < x < 6 B. -7 is less than or equal to x, and x < 6 C. -7 < x, and x is less than or equal to 6 D. -7 is less than or equal to x, and x is less than or equal to 6 Answer: B
  3. Solve 5(x + 4) = 3(x + 7) + 2. A. x = 0.5 B. x = 1.5 C. x = 3 D. x = 21.5 Answer: B
  4. How many solutions does x^2 = 5x have? A. none B. one C. two D. infinitely many Answer: C
  5. Which method must be used to solve the pair 4x + y = -3 and y = x^2 + 2x + 5? A. adding the two equations B. subtracting the two equations C. substitution D. trial and improvement Answer: C

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Livres recommandés

OxfordAQA International GCSE Mathematics Core (9260)
OxfordAQA International GCSE Mathematics Core (9260)
Sous-titre: Student Book
Éditeur: Oxford University Press
Année: 2016
ISBN: 978-0-19-837586-9
Description: The endorsed student book for the Core Tier of the 9260 specification, written for first teaching in September 2016. 520 pages covering every Core content statement with graded practice and worked model answers.
OxfordAQA International GCSE Mathematics Extension (9260)
OxfordAQA International GCSE Mathematics Extension (9260)
Sous-titre: Student Book
Éditeur: Oxford University Press
Année: 2016
ISBN: 978-0-19-837587-6
Description: The endorsed student book for the Extension Tier. 560 pages: it carries the whole Core content plus every Extension statement, so it is the one book to own if you are entered for Papers 1E and 2E.
Alex's Adventures in Numberland
Alex's Adventures in Numberland
Sous-titre: Dispatches from the Wonderful World of Mathematics
Éditeur: Bloomsbury
Année: 2011
ISBN: 978-1-4088-0959-4
Description: Where the mathematics on this specification came from and what it is for: counting systems, the golden ratio, probability paradoxes and the people who argued about them. Read it for the reason behind the rule.

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