Mathematics Specification A - 4MA1 PearsonEdexcel

Calculus

Bayani Gaba-gaba

Calculus is the mathematics of change. It gives you a precise way to find the gradient of a curve at any point, locate maximum and minimum values, and describe how quantities such as speed and acceleration are related.

This Higher-tier topic introduces differentiation of polynomial functions, finding stationary points, and applying calculus to kinematics and optimisation problems. It is one of the most powerful tools in the specification.

Manufura

[Higher] Understand the concept of a variable rate of change
[Higher] Differentiate integer powers of x
[Higher] Determine gradients, rates of change, stationary points, turning points (maxima and minima) by differentiation and relate these to graphs
[Higher] Distinguish between maxima and minima by considering the general shape of the graph only
[Higher] Apply calculus to linear kinematics and to other simple practical problems

Takardar Darasi

On a straight line, the gradient is constant. On a curve, the gradient changes from point to point. Calculus lets you calculate that changing gradient exactly, without drawing a tangent by hand.

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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.

Differentiate y = 5x^3. A) 15x^2 B) 5x^2 C) 15x^3 D) 3x^2 Answer: A
What is the gradient of y = x^2 - 4x at x = 3? A) -3 B) 2 C) 6 D) 0 Answer: B
A stationary point occurs when: A) y = 0 B) x = 0 C) dy/dx = 0 D) dy/dx = 1 Answer: C
If s = 4t^2 + 3t, what is the velocity? A) 4t + 3 B) 8t + 3 C) 8t D) 4t^2 Answer: B
Differentiate y = 7. A) 7 B) 0 C) 1 D) 7x Answer: B