| Forum Home | ||||
| PC World Chat | ||||
| Thread ID: 75000 | 2006-12-13 02:48:00 | Ncea Maths | Dally (6292) | PC World Chat |
| Post ID | Timestamp | Content | User | ||
| 506354 | 2006-12-13 07:17:00 | Such a question is open to so many interpretations. I put a deposit for 1 year in a bank but when i terminate it 6-months earlier, I was paid interest for the 6 months. Some banks impose a penalty. They take away half of the interest they pay you. So it varies from bank to bank. As long as no conditions of deposit are given, how will one expect the young kids to know. Blame it on the person who sets the question. Obviously, not much thought is given when setting questions. Just like implementing NCEA and a number of legislations passed in NZ. They implement it and then amend them as they go along. In the meantime, many innocent people suffered along the way. Sad to say but this the way NZ is run nowadays. |
Taurus (9579) | ||
| 506355 | 2006-12-13 07:25:00 | Come on, this is a fairly straightforward question. It relies on students knowing that interest on a bank account is compound interest, but this is not unreasonable. A more unreasonable aspect is the use of the word "better". Unless told otherwise, you should never consider complications that might appear in real-life conditions. You are not working out how to invest money - you are demonstrating competence in mathematics. To work out the better deal you simply have to convert the second scheme to an annual rate. Each time you add interest you are multiplying by one plus the interest rate. For the first scheme, this is 1.0325 (once in the year). For the second scheme, this is 1.013 * 1.013 (twice in the year) = 1.013 ^ 2 = 1.026169. At the end of any given year the end-year balance under the first scheme is 3.25% greater than its balance at the start and for the second scheme it would be roughly 2.62% greater. The first scheme is clearly better over any reasonably long period. P.S. This is nothing to do with NCEA. There are plenty of problems with NCEA itself but this happened under the old system just as much. I sat mathematics in the old system during the final year it was running and this level of vagarity doesn't surprise me at all. |
TGoddard (7263) | ||
| 506356 | 2006-12-13 07:34:00 | Here is another question from this years NCEA maths. It is simply put and straightforward. How they should be The difference between two positive numbers is 3 The difference between their reciprocals is 1/90 What are the two numbers? |
Dally (6292) | ||
| 506357 | 2006-12-13 08:25:00 | You can produce two equations from this, using x to represent the higher number and y for the lower. x - y = 3 |1/x - 1/y| = 1/90 we can simplify the second equation using our knowledge of the properties of reciprocals: x > y so 1/y > 1/x 1/y - 1/x = 1/90 Replace the x in this equation with the equivalent in terms of y taken from the first equation. Convert this to the standard quadratic form and solve for y using the quadratic formula. Since x and y are both positive, the negative solution can be discarded. You can then get x by adding 3. The end result should be x = 18, y = 15. Try doing this for yourself to ensure that you understand the process - you will need it next year. Make sure when answering a question like this to answer the original question in writing at the end. This lets the examiner know that you understand what you needed to do and have done it. |
TGoddard (7263) | ||
| 506358 | 2006-12-13 08:36:00 | TGoddard, Nice working. I did without looking at your solution and our methods were identical. Getting back to the interest question, I think that the wording of the 3.25 % was a bit unfortunate. It would have been much more straightforward if the 3.25 % was "per annum". Then the calculation could have allowed for 2.5 years instead of waiting until the end of the third year. I wonder whether that is what the unfortunate examiner was actually aiming at. In my opinion after 43 years teaching high school mathematics, the question was poorly set. It is supposed to determine each student's knowledge of mathematics and not trying to second guess the examiner's poor instructions. Jim |
Hhel (8073) | ||
| 506359 | 2006-12-13 08:57:00 | The question asked which would be the best scheme? There were two alternatives and they were asked for the "best" one? Obviously, the exam setter failed pretty basic English. Shouldn't it have been "which is the better one"? But I suppose in these days when kids can use text language in English exams, it's immaterial. |
TideMan (4279) | ||
| 506360 | 2006-12-13 09:10:00 | You can produce two equations from this, using x to represent the higher number and y for the lower. x - y = 3 |1/x - 1/y| = 1/90 we can simplify the second equation using our knowledge of the properties of reciprocals: x > y so 1/y > 1/x 1/y - 1/x = 1/90 Replace the x in this equation with the equivalent in terms of y taken from the first equation. Convert this to the standard quadratic form and solve for y using the quadratic formula. Since x and y are both positive, the negative solution can be discarded. You can then get x by adding 3. Make sure when answering a question like this to answer the original question in writing at the end. This lets the examiner know that you understand what you needed to do and have done it. Come on, this is what you would have done in the old proper exams. This is NCEA, the "achieved or not" pretend exams. They sure wouldn't be expected to even comprehend an equation like that. Whats quadratic? Can I do it uisng my fingers? I only have 10.....(sarcasm) |
pctek (84) | ||
| 506361 | 2006-12-13 21:30:00 | Drat! I stand corrected. I totally forgot about compund interest... Then again, there are schemes around that dont compound the interest.. Methinks they should have made it clear whether the interest was compounded or not. [QUOTE]only at the end of each year[/QUOT0] Oops My brain must have turned off. I didn't take notice of that part. |
Sherman (9181) | ||
| 506362 | 2006-12-13 22:19:00 | The interest is not compounded. It would have said in the question. You need to answer maths questions with only the information given and do not assume something like compounding. | KiwiTT_NZ (233) | ||
| 506363 | 2006-12-13 23:40:00 | Deduct tax on the interest, subtract the bank fees, and the question should be "Why save?" | R2x1 (4628) | ||
| 1 2 3 | |||||