Mathematics - 9260 OxfordAQA

Structure And Calculation

Overzicht

Every other topic in this course is standing on this one. Solve a quadratic and you are factorising; find the area of a circle and you are rounding; work with a bearing and you are reading a calculator display correctly. The eleven specification references gathered here, N1 to N11, are the machinery the rest of the subject runs on, and a candidate who is shaky on any of them will lose marks in questions that look nothing like arithmetic.

You will order numbers and use the six comparison symbols precisely; apply the four operations to negatives, decimals and mixed numbers; break a number into its prime factors and use that to find a highest common factor in seconds; handle powers, roots and index laws; write and read standard form; use set notation and Venn diagrams; round sensibly and estimate quickly; and, on the Extension Tier, work exactly with surds, rationalise a denominator and calculate with upper and lower bounds. The single most profitable habit in this topic is refusing to round until the very last line.

Doelstellingen

  1. [Core] order positive and negative integers, decimals and fractions
  2. [Core] use the symbols =, ≠, <, >, ≤, ≥ (Notes: including use of a number line)
  3. [Core] apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers - all both positive and negative
  4. [Core] understand and use place value (eg when working with very large or very small numbers, and when calculating with decimals) (Notes: including questions set in context)
  5. [Core] recognise and use relationships between operations, including inverse operations (eg cancellation to simplify calculations and expressions)
  6. [Core] use conventional notation for priority of operations, including brackets, powers, roots and reciprocals
  7. [Core] use the concepts and vocabulary of even, odd and prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation (Notes: prime factor decomposition including product of prime factor written in index form)
  8. [Core] use positive integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5
  9. [Core] index laws for multiplication and division using integer powers
  10. [Extension] including fractional powers
  11. [Core] calculate exactly with fractions
  12. [Extension] calculate exactly with surds
  13. [Extension] manipulation and simplification of surds including rationalising a denominator
  14. [Core] calculate with and interpret standard form A × 10ⁿ, where 1 ≤ A < 10 and n is an integer (Notes: interpret calculator displays)
  15. [Core] use language and notation of sets including n(A), A′, A ∩ B, A ∪ B, ξ
  16. [Core] understand and use Venn diagrams to solve problems
  17. [Core] use calculators effectively and efficiently including trigonometrical functions
  18. [Core] round numbers and measures to an appropriate degree of accuracy (eg to a specified number of decimal places or significant figures)
  19. [Core] apply and interpret limits of accuracy
  20. [Core] use estimation to work out approximate answers to calculations
  21. [Extension] calculate and use upper and lower bounds

Mindmap

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Flashcards

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Lesnotitie

There is a question on the specimen Core paper that asks you to work out \( 19.42^2 - \sqrt[3]{1006} \div 4.95 \) on a calculator and write down the full display. It is worth one mark. The very next part asks you to check that your answer is sensible by using approximations, and that is worth two. The board is telling you something with that arrangement: pressing the buttons is the cheap part. Knowing whether the number that came back is plausible is the skill worth paying for, and it is built out of exactly the ideas in this topic.

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Lesevaluatie

Gefeliciteerd met het voltooien van de les op Structure And Calculation. Nu je de sleutelconcepten en ideeën, het is tijd om uw kennis op de proef te stellen. Deze sectie biedt een verscheidenheid aan oefeningen vragen die bedoeld zijn om uw begrip te vergroten en u te helpen uw begrip van de stof te peilen.

Je zult een mix van vraagtypen tegenkomen, waaronder meerkeuzevragen, korte antwoordvragen en essayvragen. Elke vraag is zorgvuldig samengesteld om verschillende aspecten van je kennis en kritisch denkvermogen te beoordelen.

Gebruik dit evaluatiegedeelte als een kans om je begrip van het onderwerp te versterken en om gebieden te identificeren waar je mogelijk extra studie nodig hebt. Laat je niet ontmoedigen door eventuele uitdagingen die je tegenkomt; beschouw ze in plaats daarvan als kansen voor groei en verbetering.

  1. Which of these numbers is the smallest? A. -8 B. -3 C. 0.65 D. 0.7 Answer: A
  2. 672 = 2^5 x 3 x 7 and 252 = 2^2 x 3^2 x 7. What is the highest common factor of 672 and 252? A. 21 B. 84 C. 168 D. 2016 Answer: B
  3. Write 2 500 000 in standard form. A. 25 x 10^5 B. 2.5 x 10^5 C. 2.5 x 10^6 D. 0.25 x 10^7 Answer: C
  4. Work out 24 divided by 6 multiplied by 2. A. 2 B. 8 C. 12 D. 288 Answer: B
  5. A length is 24 cm to the nearest centimetre. Which statement is correct? A. The length is between 23 cm and 25 cm inclusive B. The length is at least 23.5 cm and less than 24.5 cm C. The length is greater than 23.5 cm and at most 24.5 cm D. The length is exactly 24 cm Answer: B

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Aanbevolen Boeken

OxfordAQA International GCSE Mathematics Core (9260)
OxfordAQA International GCSE Mathematics Core (9260)
Ondertitel: Student Book
Uitgever: Oxford University Press
Jaar: 2016
ISBN: 978-0-19-837586-9
Beschrijving: 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)
Ondertitel: Student Book
Uitgever: Oxford University Press
Jaar: 2016
ISBN: 978-0-19-837587-6
Beschrijving: 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
Ondertitel: Dispatches from the Wonderful World of Mathematics
Uitgever: Bloomsbury
Jaar: 2011
ISBN: 978-1-4088-0959-4
Beschrijving: 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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