Question bank

TMUA-P1-MM7-001

Evaluate $\int 2x\,dx$.

TMUA-P1-MM7-002

Evaluate $\int_0^1 3x^2\,dx$.

TMUA-P1-MM7-003

The curve $y = 2x - 6$ lies below the $x$-axis between $x = 1$ and $x = 3$. What is the area enclosed by the curve, the…

TMUA-P1-MM7-004

Suppose $F'(x) = f(x)$ with $F(5) = 20$ and $F(2) = 8$. What is $\int_2^5 f(x)\,dx$?

TMUA-P1-MM7-005

Given $\int_1^3 f(x)\,dx = 7$ and $\int_1^5 f(x)\,dx = 4$, what is $\int_3^5 f(x)\,dx$?

TMUA-P1-MM7-006

Values of $f$ at $x = 0, 1, 2, 3$ are $2, 5, 6, 9$. What is the trapezium-rule estimate of $\int_0^3 f(x)\,dx$ with $3$…

TMUA-P1-MM7-007

A curve satisfies $\frac{dy}{dx} = 6x^2 - 4x + 1$ and passes through $(1, 3)$. What is its equation?

TMUA-P1-MM7-008

The trapezium rule with $4$ strips is used to estimate $\int_0^2 x^2\,dx$. Which statement is correct?

TMUA-P1X-MM7-01

Evaluate $\int (3x^2 + 2x)\,dx$.

TMUA-P1X-MM7-02

Evaluate $\int_1^2 (2x + 1)\,dx$.

TMUA-P1X-MM7-03

The curve $y = x^2 - 4$ lies below the $x$-axis between $x = 0$ and $x = 2$. What is the area enclosed by the curve, the…

TMUA-P1X-MM7-04

Suppose $F'(x) = f(x)$ with $F(4) = 15$ and $F(1) = 6$. What is $\int_1^4 f(x)\,dx$?

TMUA-P1X-MM7-05

Values of $f$ at $x = 0, 1, 2, 3$ are $1, 4, 6, 5$. What is the trapezium-rule estimate of $\int_0^3 f(x)\,dx$ with $3$…

TMUA-P1X-MM7-06

A curve satisfies $\frac{dy}{dx} = 3x^2 + 2x - 1$ and passes through $(2, 5)$. What is its equation?

TMUA-P1X-MM7-07

The trapezium rule with $4$ strips is used to estimate $\int_0^2 (4 - x^2)\,dx$. Which statement is correct?

TMUA-P2-MM7-001

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