Mathematics Specification B - 4MB1 PearsonEdexcel

Calculus

Bayani Gaba-gaba

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.

Manufura

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

Takardar Darasi

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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Nazarin Darasi

Barka da kammala darasi akan Calculus. Yanzu da kuka bincika mahimman raayoyi da raayoyi, lokaci yayi da zaku gwada ilimin ku. Wannan sashe yana ba da ayyuka iri-iri Tambayoyin da aka tsara don ƙarfafa fahimtar ku da kuma taimaka muku auna fahimtar ku game da kayan.

Za ka gamu da haɗe-haɗen nau'ikan tambayoyi, ciki har da tambayoyin zaɓi da yawa, tambayoyin gajeren amsa, da tambayoyin rubutu. Kowace tambaya an ƙirƙira ta da kyau don auna fannoni daban-daban na iliminka da ƙwarewar tunani mai zurfi.

Yi wannan ɓangaren na kimantawa a matsayin wata dama don ƙarfafa fahimtarka kan batun kuma don gano duk wani yanki da kake buƙatar ƙarin karatu. Kada ka yanke ƙauna da duk wani ƙalubale da ka fuskanta; maimakon haka, ka kallesu a matsayin damar haɓaka da ingantawa.

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