Mathematics Specification A - 4MA1 PearsonEdexcel

Proportion

Gbogbo ọrọ náà

When two quantities are linked so that changing one always changes the other in a predictable way, we say they are in proportion. This Higher-tier topic builds on the ratio and proportion work from Foundation by introducing algebraic equations for direct and inverse relationships.

You will learn to set up proportionality equations using a constant of proportionality, solve problems involving direct and inverse proportion (including squared and cubed relationships), and connect the algebra to the shape of the corresponding graph.

Ebumnobi

[Higher] Set up problems involving direct or inverse proportion and relate algebraic solutions to graphical representation of the equations

Akọmọ Ojú-ẹkọ

The fuel cost for a journey doubles when the distance doubles. The time to fill a pool halves when you use twice as many hoses. These two patterns, direct and inverse proportion, have distinct algebraic forms that examiners test at Higher tier.

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Ayẹwo Ẹkọ

Ekele diri gi maka imecha ihe karịrị na 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.

If y is directly proportional to x, which graph shows this? A) A straight line through the origin B) A curve through the origin C) A straight line not through the origin D) A horizontal line Answer: A
y is inversely proportional to x. When x = 5, y = 4. What is y when x = 10? A) 8 B) 2 C) 20 D) 1 Answer: B
y is proportional to x squared. When x = 3, y = 18. What is k? A) 6 B) 2 C) 9 D) 3 Answer: B
Which equation represents inverse proportion? A) y = kx B) y = k/x C) y = kx + c D) y = k + x Answer: B
y is inversely proportional to the square root of x. When x = 4, y = 6. Find y when x = 16. A) 3 B) 12 C) 1.5 D) 24 Answer: A