Question bank

TMUA-P1-MM6-001

Differentiate $y = x^5$ with respect to $x$.

TMUA-P1-MM6-002

Let $f(x) = 3x^2 + 2x - 7$. What is the value of $f'(1)$?

TMUA-P1-MM6-003

Let $f(x) = x^3$. What is the value of $f''(2)$?

TMUA-P1-MM6-004

Differentiate $y = \sqrt{x^3}$ (for $x > 0$) with respect to $x$.

TMUA-P1-MM6-005

Let $f(x) = \frac{x^2 + 4x}{x}$ for $x \neq 0$. What is $f'(x)$?

TMUA-P1-MM6-006

Find the equation of the tangent to $y = x^2$ at the point where $x = 2$.

TMUA-P1-MM6-007

Find the equation of the normal to $y = x^3$ at the point $(1, 1)$.

TMUA-P1-MM6-008

The curve $y = x^3 - 3x$ has a local maximum. What is its $y$-value?

TMUA-P1-MM6-009

The area of a circle is $A = \pi r^2$. The radius increases at $2$ cm/s. At what rate is the area increasing when $r = 5…

TMUA-P1-MM6-010

For which values of $x$ is $f(x) = x^3 - 6x^2 + 9x + 1$ strictly increasing?

TMUA-P1-MM6-012

Differentiate $y = x^5$ with respect to $x$.

TMUA-P1-MM6-013

Find the gradient of $y = 3x^2$ at the point where $x = 2$.

TMUA-P1-MM6-014

Find $\frac{dy}{dx}$ given $y = 4x^3 - 2x + 7$.

TMUA-P1-MM6-015

Differentiate $y = (2x + 3)^4$ with respect to $x$.

TMUA-P1-MM6-016

Find $\frac{dy}{dx}$ given $y = x^2(3x - 1)$.

TMUA-P1-MM6-017

Differentiate $y = \frac{5}{x^2}$ with respect to $x$.

TMUA-P1-MM6-018

What is the gradient of the tangent to $y = x^2$ at the point $(3, 9)$?

TMUA-P1-MM6-019

Find the $x$-coordinate of the stationary point of $y = x^2 - 4x + 3$.

TMUA-P1-MM6-020

For $f(x) = x^3 - 3x$, on which interval is $f$ strictly decreasing?

TMUA-P1-MM6-021

Given $y = x^4$, find $\frac{d^2y}{dx^2}$.

TMUA-P1-MM6-022

A rectangle has perimeter $40$. What is its maximum possible area?

TMUA-P1-MM6-023

Differentiate $y = x(2x+1)^3$ with respect to $x$.

TMUA-P1-MM6-024

For $y = x^3 - 3x^2$, which statement is true?

TMUA-P1-MM6-025

The line $y = 2x + c$ is tangent to $y = x^2 + 1$. Find $c$.