Ace of diamonds. Graphing worksheet

Transcription

1 Ace of diamonds Produce a screen displaying a the Ace of diamonds Open University A silver-level, graphing challenge. Reference number SG1 Graphing worksheet Choose one of the following topics and write a graphics calculator worksheet to teach the topic to a pupil younger than yourself. Coordinates; Solving equations; Shading. Try your worksheet out on a younger pupil and find out its strengths and weaknesses Open University A silver-level, graphing challenge. Reference number SG2

2 Highway code From a recent copy of the Highway Code find the shortest stopping distances for various speeds. These are made up of thinking distances and braking distances. Using regression facilities of your machine, or otherwise, find two equations to represent the thinking and braking distances, given the speed. Enter the two equations and plot their graph, together with one representing the total stopping distances. Write an explanation of how to obtain the stopping distance for any given speed and also the speed given any stopping distance Open University A silver-level, graphing challenge. Reference number SG3 OU logo The Open University logo consists, basically, of a white circle in the top left-hand corner of a black shield. Draw this logo on your screen and explain how you did it Open University A silver-level, graphing challenge. Reference number SG4

3 Parametric investigation In parametric mode, investigate what happens when you draw the graph of X1 T =COS NT, Y1 T =SIN MT for various wholenumber values of N and M. Write a report of your findings Open University A silver-level, graphing challenge. Reference number SG5 Trajectory The trajectory of a ball thrown through the air depends upon its speed and the initial angle with the horizontal. Draw a graph which represents the trajectory for any given speed and angle Open University A silver-level, graphing challenge. Reference number SG6

4 Parabolas An equation has the form Y = A(X B) 2 + C. Investigate what happens to the graph when: A=1, C=0 and B varies; B is fixed, C=0 and A varies; A is fixed, B is fixed and C varies. Make sure you consider negative as well as positive values. Produce a clear explanation of the effect that changing A, B and C has on the graphs Open University A silver-level, graphing challenge. Reference number SG7 Palindrome Enter ten numbers into each of two lists, say L1 and L2, so that: all twenty numbers are different; the mean of the values in L1 with corresponding frequencies in L2, is equal to the mean of the values in L2 with corresponding frequencies in L Open University A silver-level, statistics challenge. Reference number SS1

5 Statistics worksheet Choose one of the following topics and write a worksheet to teach the topic (using a calculator or computer) to a pupil younger than yourself. Boxplots; Averages; Frequency diagrams; Scatterplots. Try your worksheet out on a younger pupil and find out its strengths and weaknesses Open University A silver-level, statistics challenge. Reference number SS2 Boxed in Draw a boxplot representing twelve values in a list. The boxplot should be skewed to the right and the median should be exactly half of the value of the upper quartile. Write a short explanation of how you did it and give a real-life situation which your results might represent Open University A silver-level, statistics challenge. Reference number SS3

6 Design a game Devise a game which makes use of one or more of the random number generating commands. The game should support or help to teach a particular skill (not necessarily a mathematical skill). It should be fun, easy to understand and play, and clearly designed to develop the particular skill Open University A silver-level, statistics challenge. Reference number SS4 Some explaining to do Write a short explanation, suitable for someone of your own age, of how to plot a variety of statistical graphs on your calculator or computer. Try it out on a friend and then improve your explanation accordingly. Both drafts should be submitted Open University A silver-level, statistics challenge. Reference number SS5

7 Three coins If three coins are tossed, what is the chance that all of them will turn up alike (i.e. either all heads or all tails)? Below is a possible solution to this question. Use your machine to test whether it is true. If it is not true, give the correct solution and explain why the reasoning below is incorrect.. "At least two of the coins must turn up alike and, as there is an even chance that a third coin is heads or tails, the chance of all three being alike is 1 2 " Open University A silver-level, statistics challenge. Reference number SS6 Dice product The game 'Dice Product' is played as follows. Any number of people can play this game. Each player chooses a target number between 1 and 36. Two dice are rolled and the product of their scores is the winning number. For example, if the scores are 5 and 3, the winning number is 15 (i.e. 5x3). The player who had chosen a target number of 15 is then the winner. Find a way of simulating the game Dice Product a large number of times and identify the most frequently-occurring target number. What is the theoretically most likely target number? Explain, briefly, why Open University A silver-level, statistics challenge. Reference number SS7

8 Really random? Choose one of the commands on your machine which produces random numbers. Devise a statistical test to check whether any of the digits from 0 to 9 appears more frequently than the others when your chosen command is used Open University A silver-level, statistics challenge. Reference number SS8 Bank roll Devise a gambling game for 2 people and create a suitable program or spreadsheet. Investigate experimentally whether the player with the larger initial bank-roll tends to win more often Open University A silver-level, algorithms challenge. Reference number SA1

9 The 107% rule Find out about the 107% rule in Grand Prix Motor racing. Create a program or spreadsheet to let you input practice lap times and which then outputs the lap times that qualify Open University A silver-level, algorithms challenge. Reference number SA2 Guess the number Create a program or spreadsheet to allow two players to play the game of 'Guess the number'. Rules. Player A secretly inputs any whole number in the range 0 to 100. Player B now has to guess the number A has chosen by repeatedly entering a guess. After every guess the machine displays the guess divided by the secret number. Sample play. Player A selects 67 as the hidden number. Player B records the following guesses. Guess Display Comment is too small is too big is just too small is the hidden number Open University A silver-level, algorithms challenge. Reference number SA3

10 Algorithms worksheet Choose one of the following topics and write a programming or spreadsheet worksheet to teach the topic to a pupil younger than yourself. Using the IF command; Creating a frequency table from a list of data; Try your worksheet out on a younger pupil and find out its strengths and weaknesses Open University A silver-level, algorithms challenge. Reference number SA4 Practice makes perfect Create a program or spreadsheet that allows the user to practice and improve one of the following skills: estimating numbers of dots; estimating lengths on the graphing screen; estimating angles on the graphing screen; estimating and comparing areas; comparing ratios; estimating means or medians Open University A silver-level, algorithms challenge. Reference number SA5

11 Bar-code Create a program or spreadsheet to test out the final digit 'check sum' on any 13 digit bar-code Open University A silver-level, algorithms challenge. Reference number SA6 Horse race A simple version of the board-game "Horse race" is played as follows. Each of up to four players chooses a horse, named A, B, C and D. Players in turn roll a die and move their horse forward the number of squares shown on the die. The winner is the first to reach 50. Adapt the game for the calculator or computer. Pay particular attention to what appears on the screen try to make the race as exciting as possible to watch Open University A silver-level, algorithms challenge. Reference number SA7

12 One hundred up A simple version of the board-game 'One hundred up' is played as follows. This is a dice game for two or more players with the aim of being the first to reach 100. Player A rolls the die as many times as she likes, adding each new score to the total in that round. However, if a 1 is thrown, A's score for the round becomes zero and her turn ends. Otherwise A decides when to stop and the turn passes to B. Adapt the game for a calculator or computer Open University A silver-level, algorithms challenge. Reference number SA8