Application to generate math tests

Create an **architecture** for a web application that generates math tests similar to? <[login to view URL]>? . A user will visit a web interface, select the options of the test he wants to generate, and click enter. The software will select the types of problems to show up on the test, the order that they'll appear, the numbers used in the problems, etc. ? Most of those decisions will be the results of random numbers generated within certain parameters. ? The software will also format the test in a manner consistent with the test at the above link and will generate an answer key. We prefer software developers that: * Provide an **expert guarantee** * Will develop extensible, object-oriented code * Will develop in PHP (not a hard requirement, but a preference) The deliverables of this project are: 1. Architecture for a web application that generates the math tests. ? **You do not have to write the web application itself.** 2. Detailed class definitions for things such as Test, Problem, Estimation Problem, etc. 3. Example of how the Problem class can be extended to cover Estimation Problems. 4. Example of how the Problem class can be extended to cover "Multiplying by 11" and to "Multiplying by 11 without carry". 5. Simple UI that allows the user to specify the variables of the test he wants to create 6. Example of how to add new problem types to the system. ## Deliverables The math tests the software will generate have two pages made up of several components: 1. A static text block on the upper 1/3 of the first page. ? (From where it says "The University Interscholastic League" down to where it says "Stop Wait for Signal" . ? this text will not change, but it must occupy exactly 1/3 of the first page. 2. A list of 80 problems in two column format. ? The problems are mainly in 11pt Times font and there is a margin of just under 1/2 inch between the columns. ? The first page contains as many problems as will fit on its bottom 2/3. ? The second page contains the rest of the problems. 3. Each problem begins with its problem number, enclosed in parentheses, such as (3). 4. Problems 10, 20, 30...80 are preceeded by an asterisk, so their numbers look like *(10). 5. The problem numbers are aligned right. 6. The math problem is then presented and is followed by a solid line where the test taker will write in the answer. ? The solid line should end with a period. ? There may be an instruction preceding the period that tells the test taker how the answer should be written. ? Example: ? (decimal). 7. Many mathematical symbols will by used, so the software needs to support some way of displaying these symbols. ? These include but are not limited to ? fractions (with smaller font sizes for the numerator and denominator), square root symbols, cube root symbols, exponents, absolute value symbols (vertical lines), integration symbols, and summation symbols (Greek capital letter sigma). Each problem tests a certain type of math skill and the software will need to generate a problem that tests that skill. For example, suppose the problem type is "Multiplying a two digit number by 11 without a carry". ? For this problem type, we will want to generate problems such as 24 x 11 = ______ or 11 x 53 = _________. ? We will call the numbers like 24 and 53 the "operands". ? For this problem type, we would specify that the operand must have two digits and that the digits of the operand must add to 9 or less. ? Therefore 24 and 53 would be valid operands, but 124 would not since it has 3 digits and 55 would not, since 5+5 is greater than 9. Once the operand is calculated, the software would need to determine whether to present the problem as 11 x 24 or as 24 x 11. ? This can be randomly determined. The software would need to calculate (or randomly generate) acceptable operands for a given problem type and then prepare the problem in a way that can be printed to an output file that looks like the sample tests linked to above. Note that some problem types should only be allowed to show up in some areas of the test. ? So, for example, we may want to define the "multiplying a two digit number by 11 without a carry" problem type so that it can only show up in problems 5-25. ? Outside of that range, that problem type can't be used. Examples of other problem types will include: * Multiplying an even, two-digit number by 50 * Multiplying an odd, two-digit? number by 50 * Multiplying an even, two digit number by 15 * Multiplying an odd, two digit number by 15 * Squaring a two digit number that ends in 5 (as in 35 x 35 or 452) * Squaring a number between 13 and 30 (as in 17 x 17 or 232) Every 10th problem on the test is marked with an asterisk and will be an estimation problem. ? The only difference between this and a regular problem has to do with the answer key. ? On estimation problems, the answer key needs to print out a range that is +/- 5% of the exact answer. ? So on an estimation problem, if the real answer is 1000, the answer key will print out "950 - 1050" instead of 1000. The answer key and the math test itself should be created as PDF's. ? Alternatively, the software could create an intermediate format, such as LaTex that can easily be compiled to PDF. Again, the objective of this project is to design the software architecture and a prototype, but not to develop the full-fledged application. ? Please respond with any questions and I'll be glad to answer them as best I can.