Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

of a random cubic spline

of a random cubic spline

of a random cubic spline

of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

This question plots a general amplitude modulated carrier signal defined by $v_s(t) = (V_{DC} + V_m \cos(2\pi f_m t))\cos(2\pi f_c t)$, where $V_{DC}$ is a DC offset, $V_m$ is the message amplitude, $f_m$ is the message frequency and $f_c$ is the carrier frequency ($f_c = 20f_m$ in this question). The student must identify the values of $V_{DC}$ and $V_m$ and enter these values into the appropriate gaps in the equation of the AM signal.

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Students enter equation and turning point

Students enter equation and turning point

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Find the equation of a line given a point and a parallel line.

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Find the equation of a line given a point and a parallel or perpendicular line.

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Drag points on an axis to plot a linear graph (integer gradient and intercept only)

Calculate the length of a line segment given two points

Drag points on an axis to plot a linear graph (rational gradient and intercept)

Customised for the Numbas demo exam

Motion under gravity. Object is projected vertically with initial velocity $V\;m/s$. Find time to maximum height and the maximum height. Now includes an interactive plot.

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An applied example of the use of two points on a graph to develop a straight line function, then use the t estimate and predict. MCQ's are also used to develop student understanding of the uses of gradient and intercepts as well as the limitations of prediction.

The data is fitted by linear and quadratic regression.  First, find a linear regression equation for the $n$ data points, $20 \le n \le 35$.

They then are shown that the quadratic regression is often a better fit as measured by SSE. Also users can experiment with fitting polynomials of higher degree.

Given a graph of a line of the form $y=ax+b$ where $a$ and $b$ are integers, find the equation of the line. The y-intercept is given.

Method of undermined coefficients:

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+a^2y=0,\;y(0)=c$ and $y(1)=d$.  (Equal roots example). Includes an interactive plot.

rebelmaths

Given a graph of a line of the form $y=ax+b$ where $a$ and $b$ are integers, find the equation of the line. The y-intercept is given.