IB Maths AA SL 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

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Question 1

Paper 1, no calculatorMedium6 marks

A geometric sequence has nth term $u_n$ where $u_3=18$ and $u_6=486$

(a)

Determine the first term and the common ratio of the sequence.

[3]

(b)

Hence, write $S_6$ the sum of the first six terms, in sigma notation and determine its value.

[3]

Question 2

Paper 1, no calculatorMedium6 marks

Let $p=\log_2 3$ and $q=\log_2 5$ Consider the equation

4^{x+\frac12}=\frac{5\times81^{\frac34}}{3},\qquad x\in\mathbb R.

(a)

Find the value of $81^{\frac34}$

[1]

(b)

Show that

\log_2\left(\frac{5\times81^{\frac34}}{3}\right)=2p+q.

[2]

(c)

Hence solve the equation, giving your answer in terms of $p$ and $q$

[3]

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