Ultimate Multiple Choice Questions on Calculus (Derivatives) : Grade 12
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Mastering calculus is essential for students because it develops powerful problem-solving and analytical thinking skills that are valuable across many fields. Calculus, particularly concepts like derivatives, helps students understand change, motion, and real-world relationships, forming the foundation for advanced study in science, engineering, economics, medicine, and technology. In education, it prepares learners for higher-level mathematics and critical reasoning, while in careers it is widely used in areas such as data analysis, construction, finance, and computer programming. By learning calculus, students gain the ability to think logically, model real-life situations, and make informed decisions—skills that are increasingly important in a modern, knowledge-based economy.
QUESTION 1 OF 20
Using the power rule, what is the derivative of f(x) = x⁵?
Find the derivative of f(x) = 3x² + 2x - 1.
Determine dy/dx for y = 4x³ - ½x² + 7.
What is the derivative of f(x) = √x?
Differentiate y = 5/x³ with respect to x.
The gradient of the tangent to the curve y = x² - 4x + 3 at x = 3 is:
For the curve f(x) = x³ - 6x, the gradient at x = 2 is:
The equation of the tangent line to y = x² at (2, 4) is:
If the gradient of the tangent is 2, the gradient of the normal is:
The normal to a curve is:
Stationary points occur where:
f(x) = x² - 6x + 5 has a:
To determine nature of stationary point use:
If f'(a)=0 and f''(a)<0, then:
Number of stationary points of x³ - 3x + 1:
Maximum area width for A = w(50 - w):
Maximum height of h(t)=20t-5t²:
Rate of change is found by:
Derivative of sin x:
Derivative of cos x:
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