IB Maths AA HL Topic 1: Number and algebra questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Paper

Paper 1, no calculator Paper 2, calculator

Difficulty

Easy Medium Hard

Question 1

Paper 1, no calculatorHard6 marks

For real numbers $u,v,w$ it is given that $u+v+w=0$ and $uvw=5$

(a)

Write down the value of $u+v+w$

[1]

(b)

For arbitrary real numbers $u,v,w$ starting with the left-hand side, prove that

u^3+v^3+w^3-3uvw \equiv (u+v+w)(u^2+v^2+w^2-uv-vw-wu).

In your final line, use $\equiv$ to indicate an identity.

[4]

(c)

Hence determine $u^3+v^3+w^3$ for the numbers in the stem.

[1]

Question 2

Paper 1, no calculatorHard6 marks

(a)

Use mathematical induction to prove that $5$ divides $2^n+3^n$ for every positive odd integer $n$

[4]

(b)

A student conjectures that $2^n+3^n$ is prime for every positive integer $n$ Use your result from part (a) to disprove this conjecture, explaining why your example is a counterexample.

[2]

The best questions are still waiting

Unlock every question in this topic, then type, photograph or draw your answer and have it marked against the markscheme. Find out where you are dropping marks.

Unlock all questions Compare Student and Student Plus