# "Show that" Questions

For a "show that" question, would you have to tackle it as a proof by induction or just show it works for a certain set of values? (Assignment 3 STEP Question)

### Show that

If the question says "show that" then it is asking you to completely justify the given answer (no gaps allowed!). In the case you need to show that there are 15 five-digit numbers that satisfy the given digit sum AND no others (you cannot just stop once you have found 15, you must show that a 16th is not possible!)

### Show that

In the case of this question you will want to consider it in general. When it says show that it means show it for all values so showing its true for several examples wont suffice. For example in this case you know that the area increases as a summation of a geometric progression, so by saying the area is the summation up to 2^(a-1) you can show its true for all values of a. Drawing a sketch might help.

Underground Mathematics: Selected worked STEP questions

STEP Question database

University of Cambridge Mathematics Faculty: What do we look for?

University of Cambridge Mathematics Faculty: Information about STEP

University of Cambridge Admissions Office: Undergraduate course information for Mathematics

Stephen Siklos' "Advanced Problems in Mathematics" book (external link)

MEI: Worked solutions to STEP questions (external link)

OCR: Exam board information about STEP (external link)

AMSP (Advanced Maths Support programme): Support for University Admission Tests (external link)