NCEA Level 2 Curve Sketching — Practice Questions with Answers

Question Bank

Gradients Tangents Increasing/Decreasing Stationary Points Antidifferentiation Sketching Optimisation Rates of Change Kinematics

Achieved

Shown below is the graph of a function $y=f(x)$. Sketch the graph of the derivative $y=f'(x)$.

$y = f(x)$

Achieved

Shown below is the graph of a function $y = f(x)$.

Sketch the graph of the gradient function $y = f'(x)$.

$y = f(x)$

Achieved

Shown below is the graph of a function $y = f(x)$.

Sketch the graph of the gradient function $y = f'(x)$.

$y = f(x)$

Merit

Shown below is the graph of a function $y=f(x)$. Sketch the graph of the derivative $y=f'(x)$.

$y = f(x)$

Merit

Shown below is the graph of a function $y=f(x)$. Sketch the graph of the derivative $y=f'(x)$.

$y = f(x)$

Merit

Shown below is the graph of a function $y=f'(x)$. Sketch the graph of the antiderivative $y=f(x)$ that passes through the point shown.

$y = f'(x)$

Merit

Shown below is the graph of a function $y=f'(x)$. Sketch the graph of the antiderivative $y=f(x)$ that passes through the point shown.

$y = f'(x)$

Merit

Shown below is the graph of a function $y=f'(x)$. Sketch the graph of the antiderivative $y=f(x)$ that passes through the point shown.

$y = f'(x)$

Merit

Shown below is the graph of a function $y = f(x)$.

Sketch the graph of the gradient function $y = f'(x)$.

$y = f(x)$

Merit

Shown below is the graph of a function $y=f'(x)$. Sketch the graph of the antiderivative $y=f(x)$ given $f(x)$ passes through the origin.

$y = f'(x)$

Merit

Shown below is the graph of a function $y = f(x)$.

Sketch the graph of the gradient function $y = f'(x)$.

$y = f(x)$

Excellence

The graph of the gradient function $y = f'(x)$ is shown below. The graph of $y = f(x)$ passes through the point $(0, 2)$.

$y = f'(x)$

(a) Find the equation of $y = f(x)$.

(b) Find the coordinates of the turning points of $y = f(x)$, and justify the nature of each one.