Half a million teenagers could be expected to study a new approach to maths up to the age of 18 in a drive to make Britain a more numerate nation.
Mathematicians have drawn up plans for a higher maths qualification aimed at sixth formers who avoid the subject at AS or A level.
Ministers are expected to embrace the plan, which may become a centrepiece of the new Advanced Baccalaureate, to spur teenagers to choose a broader mix of post-16 subjects.
Maths experts have spent a year designing the new qualification, which some sixth formers may begin studying from 2015
Q1: Circumstantial evidence links Alice to a murder scene; there is also a DNA link but this has a 1 in 1,000 chance of being a false match. Bob is not linked with the crime scene, but was identified from a DNA database as almost a perfect fit: a 1 in a million chance of a false DNA match. Which suspect (probably) did it?
A1: Alice (probably). On a database of one million there will be one false match like Bob with no connection to the murder. Alice is chosen from a small group, probably no more than ten, certainly fewer than 100, linked to the murder scene.
Q2: You must design a multistorey car park for 300 cars with six floors. The cost of each floor increases with its area. What dimensions would you recommend to minimise the costs?
A2: This is an open-ended question to test methodology. A student should i) estimate the typical area of a car; ii) estimate the area of a parking space; and iii) use ergonomics, geometry, estimation and observation to test models, eg, square or rectangle, allowing space for access and exits, calculate aspect ratios, etc
Q3: You buy a digital camera for £75. The same camera five years ago cost £160. The salesman offers a three-year guarantee costing £15 to replace the camera if there is a technical fault but not if you break or lose it. A magazine says that 1 per cent of digital cameras malfunction. Should you buy the guarantee too?
A3: Almost certainly not. The chance of the camera going wrong over three years is small. The fee would require the rate of malfunction to be around 20 per cent over three years to be worthwhile. Costs of cameras are dropping dramatically, making this an even worse deal.
Q4: A rare, deadly, latent disease affects one in 1,000 of the population. A new screening test for it is 99 per cent accurate. Should the test be offered to everyone?
A4: Probably not. If 1,000 random people took the test one will have the disease but there will be about ten false positives. It may be reasonable to wait until a patient presents with initial symptoms and will depend on what further tests can be done, what treatment is available and its side effects.