159 results authored by Julie Crowley - search across all users.

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• Recurrence relations
Exam (5 questions)

First- and second order recurrence equations, homogenous and nonhomogenous

• Question

Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

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• Regression 3
Question

Find a regression equation given 12 months data on temperature and sales of a drink. Includes an interactive diagram for experimenting with fitting a regression line.

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• Question

No description given

• Question

Graph Limits

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• Pearson1
Question

Calculate the Pearson correlation coefficient on paired data and comment on the significance.

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• Poisson (sales)
Question

Application of the Poisson distribution given expected number of events per interval.

Finding probabilities using the Poisson distribution.

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• Question

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.

• Question

Solve: $\displaystyle \frac{d^2y}{dx^2}+2a\frac{dy}{dx}+(a^2+b^2)y=0,\;y(0)=1$ and $y'(0)=c$.

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• Question

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.

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• Question

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

• Question

Compute a table of values for a quadratic function. A JSXgraph (the graph paper) plot shows the curve going through the entered values. The student input is now disconnected from the graph so that they slide the points usually after they input the values and the answer fields are not updated.

• Question

Compute a table of values for a quadratic function. The student input is now disconnected from the graph so that they slide the points on the graph after they input the values and the answer fields are not updated. Now includes a graph in advice.

• Question

No description given

• Question

Compute a table of values for an exponential function. The student input is now disconnected from the graph so that they slide the points on the graph after they input the values and the answer fields are not updated. Now includes a graph in advice.

• Question

Calculate the Pearson correlation coefficient on paired data and comment on the significance.

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• Question

No description given

• Question

Indices

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• TLU Workshop
Draft
Exam (12 questions)

No description given

• Question

Splitting an algebraic fraction into partial fractions

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• Matrices
Draft
Exam (5 questions)

Matrix addition, multiplication. Finding inverse. Determinants. Systems of equations.

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• Summation notation 3
Question

Practice use of summation notation for regression question.

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• Question

$X \sim \operatorname{Binomial}(n,p)$. Find $P(X=a)$, $P(X \leq b)$, $E[X],\;\operatorname{Var}(X)$.

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• Integration
Draft
Exam (25 questions)

Basic indefinite integrals, Basic definite integrals, integration by substitution

Missing: Area type question, solving diff eq application

• Exam (12 questions)

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

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• Question

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Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

• Question in JP

Find the stationary points of the function: $f(x,y)=a x ^ 3 + b x ^ 2 y + c y ^ 2 x + dy$ by choosing from a list of points.

• Exam (12 questions)

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

Missing: Application with bacteria, turning points, difficult chain rule

• Exam (18 questions)

Transposition of formulae. Changing the subject of an equation.

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• Stem and Leaf plot