Mathematics Specification B - 4MB1 PearsonEdexcel

Calculus

Gbogbo ọrọ náà

The last topic estimated the gradient of a curve using a tangent drawn by eye, or two points squeezed close together. Calculus turns that estimate into an exact answer: a single formula, the derivative, that gives the gradient at any point on a curve instantly, with no drawing and no approximation.

You will use differentiation to locate the highest and lowest points on a curve, to find the equation of a tangent, and to move between displacement, velocity and acceleration in problems about moving objects.

Ebumnobi

Differentiate integer powers of x using dy/dx notation
Determine gradients, rates of change, maxima, minima, stationary points and turning points
Apply calculus to linear kinematics and other simple practical problems, including distance/time and speed/time graphs
Understand the relationship between displacement or distance, velocity and speed, and acceleration

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Akwụkwọ Ọmụmụ

Estimating a gradient from two nearby points on a curve gets more accurate the closer those two points sit together. Differentiation is what happens when that closing gap is taken all the way to zero: it produces a formula for the exact gradient at any single point on a curve, called the derivative, written \(\frac{dy}{dx}\).

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Nnyocha Ọmụmụ

Ekele diri gi maka imecha ihe karịrị na Calculus. 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.

What is dy/dx when y = 5x^4? A) 5x^3 B) 20x^3 C) 20x^4 D) 4x^3 Answer: B
Differentiate y = 3x^2 - 7x + 2. A) 6x - 7 B) 3x - 7 C) 6x + 2 D) 6x^2 - 7 Answer: A
At a stationary point of a curve, dy/dx equals: A) 1 B) undefined C) 0 D) the y-value Answer: C
The curve y = x^2 - 4x + 3 has a stationary point at: A) (2, -1) B) (4, 3) C) (-2, -1) D) (2, 1) Answer: A
If displacement s = t^2 - 4t, the velocity ds/dt equals: A) t - 4 B) 2t - 4 C) 2t D) t^2 - 4 Answer: B

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