IB Maths AA SL 1.6 Deductive Proof

IB Mathematics: analysis and approaches guide, first assessment 2021

Practise proving identities, divisibility and inequalities through justified algebraic transformations, with clear equality notation and contradiction where required.

How this is tested

transform one side of an identity by factoring, expanding or combining fractions until it matches the other
express integers algebraically and factor the result to prove a stated divisibility property
state the negated assumption in a contradiction proof and derive an explicit impossibility

[Maximum number: 3]

Rectangular playing cards are stacked in the shape of a pyramid with n rows, where $n \geq 1$ .
Some cards are placed horizontally and some cards are stacked at an angle of $60^{\circ}$ to the horizontal.
The following diagrams represent pyramid stacks for n=1, n=2 and n=3.

Figure for Question 8(c) — IB Maths AA SL

Let $t_{n}$ represent the number of cards used to create a pyramid stack with n rows.

Show that $t_{n}=\frac{n(3 n+1)}{2}$ .

There are 52 cards in a full pack of playing cards.

How this is tested

Question 8(c)