Mathematics - 9260 OxfordAQA

Ratio And Proportion

Gbogbo ọrọ náà

Mix white paint and blue paint in the ratio 3 to 2, then work out what 20 litres of the mixture costs. Buy a 400 gram jar for $3.20 or a 650 gram jar for $5.07 and say which is better value. Work out how many cards you can cut from a thousand centimetres of ribbon. These three questions look like three different subjects and they are all the same idea: quantities that keep a fixed relationship to one another as they change.

You will write ratios and reduce them to their simplest form, see how a ratio connects to a fraction, divide a quantity in a given ratio, and apply ratio to problems that do not announce themselves as ratio problems. You will use common measures of rate, including rates of pay and best-buy comparisons, and solve problems involving direct and inverse proportion, including repeated proportional change. On the Extension Tier you will meet exponential growth and decay, where the multiplier itself is the model.

Ebumnobi

  1. [Core] use ratio notation, including reduction to simplest form and links to fraction notation
  2. [Core] divide a quantity in a given ratio
  3. [Core] apply ratio to solve problems
  4. [Core] use common measures of rate, including calculating rates of pay and best-buy problems
  5. [Core] solve problems involving direct and inverse proportion including repeated proportional change
  6. [Extension] exponential growth and decay

Maapụ uche

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Akwụkwọ Ọmụmụ

Proportional reasoning is the single most useful piece of school mathematics outside school, and it is also the piece candidates most often get wrong by attacking it with addition. If 40 cubic centimetres of copper has a mass of 354 grams, the instinct to reach for 354 plus something has to be replaced by the instinct to ask what number multiplies 40 to give 100. That number is 2.5, and it multiplies the mass too. Everything in this topic is a variation on finding the multiplier and applying it to the right quantity.

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Nnyocha Ọmụmụ

Ekele diri gi maka imecha ihe karịrị na Ratio And Proportion. 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.

  1. White paint and blue paint are mixed in the ratio 3 : 2. What fraction of the mixture is blue? A. 2/3 B. 3/2 C. 2/5 D. 3/5 Answer: C
  2. 6 workers build a wall in 10 days. How long would 4 workers take, working at the same rate? A. 6.7 days B. 8 days C. 15 days D. 24 days Answer: C
  3. The mass of 40 cubic centimetres of copper is 354 grams. What is the mass of 100 cubic centimetres? A. 141.6 g B. 414 g C. 885 g D. 1416 g Answer: C
  4. In the model N = 12 000 a^t with a = 0.8, what is the value of N when t = 0? A. 0 B. 0.8 C. 9600 D. 12 000 Answer: D
  5. Coffee costs $3.20 for 100 g, $7.75 for 250 g or $22.80 for 750 g. Which is the best value? A. the 100 g jar B. the 250 g jar C. the 750 g jar D. they are all the same value Answer: C

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