A1 New undergraduates

The first example concerns a test given to 55 incoming honours mathematics students at one English university in October 1994. The students' mathematics A-level grades were: A 12, B 13, C 16, D 6, other qualification 8. We choose some of the questions to indicate particular concerns, but other examples could also have been used. After the statement of each question appears the percentage of students who answered the question correctly.

1.

Solve the equation . (75%)

2.

Factorise the following expressions as far as possible:

(a)

(78%)

(b)

(73%)

[Note: Of the 6 students who managed to factorise neither of these quadratics, 3 had achieved a Grade B at A-level.]

3.

Calculate the areas shaded in the diagrams, leaving your answer in terms of where appropriate.

(a)

(78%)

(b)

(84%)

(c)

(5%)

[Note: the lack of success on the third part of this question underlines the dangers of a system which

(a)

sets questions which lead the candidate, step by step and

(b)

rewards superficial knowledge of those items listed in the `levels' of the National Curriculum.

This question needs no mathematics beyond `level 7'; but it asks students to use and apply this knowledge in a mathematical way. For they must draw together knowledge from different areas and undertake, without instruction, the extra steps required.]

4.

In the diagram below:

(a)

Express h in terms of b and . (91%)

(b)

Express h in terms of c and . (91%)

(c)

Express h in terms of a, and . (18%)

[Note: Again, there is a substantial drop in success when the question requires additional, unsignalled steps.]