Xiaodan Leng

Graphing $y=a\log_{b}(x)+c$

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

Graphing $y=a\log_{b}(\pm x+d)+c$

determine the least residue mod n of a given number.

Construct a line through two points in a GeoGebra worksheet. Change the line by setting the positions of the two points when the worksheet is embedded into the question.

Applied questions that could be done with modulo arithmetic.

Applied questions that could be done with modulo arithmetic.

Showing off the part types.

Given the gradient of a slope and the coefficient of friction for a mass resting on it, use the equations of motion to calculate how it moves.

Includes a GeoGebra rendering of the model.

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multiple choice testing sin, cos, tan of  random(0,90,120,135,150,180,210,225,240,270,300,315,330) degrees

Unit circle definition of sin, cos, tan using degrees

multiple choice testing sin, cos, tan of  random(pi/6, pi/4, pi/3) radians

multiple choice testing csc, sec, cot  of  random(pi/6, pi/4, pi/3) radians

multiple choice testing csc, sec, cot of random(30, 45, 60) degrees

multiple choice testing sin, cos, tan of  random(30, 45, 60) degrees

Use $\cos^2\theta+\sin^2\theta=1$ and/or an understanding on the unit circle definitions to determine $\cos\theta$ given $\sin\theta$ and the quadrant theta is in.

Use $\cos^2\theta+\sin^2\theta=1$ and/or an understanding on the unit circle definitions to determine $\sin\theta$ given $\cos\theta$ and the quadrant theta is in.

Using $\cos^2\theta+\sin^2\theta=1$ to evaluate expressions.

Given a geometric sequence, find the common ratio (negative in this question), write down the formula for the nth term and use it to calculate a given term.

Present some given data in a frequency table.

Given results from a survey about what people eat for breakfast, where some people eat one or both of cereal and toast. Student is asked to pick the probability of eating either one or the other from a list. Distractors pick out common errors.

Given descriptions of some pairs of random events, pick the ones which are mutually exclusive.

Given the probability that a basketball shot misses the hoop, find the probability that it's on target - use the law of total probability.

Given the probabilities that each of four out of five friends will win a round of mini-golf, work out the probability that the fifth friend won't win, then use that to find the probability that they will win.

Previous throws don't affect the probability distribution of subsequent throws. Believing otherwise is the gambler's fallacy.

This question aims to assess the student's understanding of the difference between biased and unbiased events and also to assess the student's understanding of the fact that the experimental probability tends towards the theoretical probability as the number of trials increases.

Compute the experimental probability of a particular score on a die given a sample of throws, and compare it with the theoretical probability.

The last part asks what you expect to happen to the experimental probability as the sample size increases.

A bag contains balls of three different colours. You're told how many there are of each, and asked the probability of picking a ball of a particular colour.

Choose the probability of getting a tails, from four options.