Calculus
Akopọ
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.
Awọn Afojusun
- [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
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Oriire fun ipari ẹkọ lori Calculus. Ni bayi ti o ti ṣawari naa awọn imọran bọtini ati awọn imọran, o to akoko lati fi imọ rẹ si idanwo. Ẹka yii nfunni ni ọpọlọpọ awọn adaṣe awọn ibeere ti a ṣe lati fun oye rẹ lokun ati ṣe iranlọwọ fun ọ lati ṣe iwọn oye ohun elo naa.
Iwọ yoo pade adalu awọn iru ibeere, pẹlu awọn ibeere olumulo pupọ, awọn ibeere idahun kukuru, ati awọn ibeere iwe kikọ. Gbogbo ibeere kọọkan ni a ṣe pẹlu iṣaro lati ṣe ayẹwo awọn ẹya oriṣiriṣi ti imọ rẹ ati awọn ogbon ironu pataki.
Lo ise abala yii gege bi anfaani lati mu oye re lori koko-ọrọ naa lagbara ati lati ṣe idanimọ eyikeyi agbegbe ti o le nilo afikun ikẹkọ. Maṣe jẹ ki awọn italaya eyikeyi ti o ba pade da ọ lójú; dipo, wo wọn gẹgẹ bi awọn anfaani fun idagbasoke ati ilọsiwaju.
- 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
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