Just a quick look at this question.
(d) (ii) By using the discriminant ( Δ ), find the largest possible whole number value that a could take in this context.
Use this value of a to find the dimensions of both the cube and the cuboid.
Explain your reasoning clearly.
To put it plainly, using the discriminant is not enough to find the required value of a. All the discriminant will give is a possible range of values. Based on the wording of the question it is reasonable for students to believe the required answer has been found, but that is not the case. The contenders for the largest possible whole number have to be tested using the quadratic formula.
It is implied that simply using a fancy calculator which can solve quadratic equations will not be adequate because the student is instructed on the front page of the exam to "Show ALL working."
The discriminant gives a range of values, but the largest of those values fails to pass testing with the quadratic formula. The value doesn't work because one side of the cuboid ends up with a negative length.
Remember the 2019 exam? That was just two years earlier, and testing one particular answer revealed a rectangle height of -1. The failure of that exam should not mislead students into giving up at this point; this time it's deliberate!
The next lower whole numbered value must be tested as well. It passes the test. (At least, it will if the student has enough time to complete the working!) It is this second whole numbered value which is the actual largest possible whole number value of a which can be used to find the dimensions of the cube and cuboid.
The marking scheme starts with the discriminant > 0 instead of ≥ 0. This is a mistake, since having the discriminant = 0 would possibly give a solution.
Comment:
The instructions are misleading and simply wrong. Much more work is required than the instructions indicate. The discriminant is not enough to find the required value of a.
What part of the Level 2 syllabus indicates that misleading students in an exam is a necessary part of the course? Or is this a kickback against the embarrassment of the -1 rectangle height in the 2019 exam? It's almost as if the exam is mocking anyone who complained about the 2019 exam.
Because of the misleading instructions the actual work required is not at all clear, and will be very time consuming if a calculator is not used. But if a calculator is used, full working would not be shown.
The requirement to "Explain your reasoning clearly" is another example of literacy skills displacing numeracy skills in NCEA Mathematics. This is a maths exam, and should test particular numeracy skills. It should not test the ability of students to teach mathematics.
Testing is not normally required – or needed – for NCEA Mathematics problems. Indeed, the infamous 2019 exam with the -1 rectangle height clearly showed that NCEA exam checkers(!) did not check answers.
This time, testing of solutions – something only the best students generally have time for – will reveal a negative side length to the cuboid which is deliberate. Or is this a psychology test to see which students give up, assuming NCEA has stuffed up yet another exam? Guess what? It has stuffed up another exam.
It would not have been hard to make the question clear and correct.
