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Exam-Style Questions.

Problems adapted from questions set for previous Mathematics exams.

1.

IB Standard

(a) Expand the following as the sum of six terms:

$$ \sum_{r=3}^{8} 2^r$$

(b) Find the value of:

$$ \sum_{r=3}^{25} 2^r$$

(c) Explain why the following cannot be evaluated:

$$ \sum_{r=3}^{\infty} 2^r$$

2.

IB Studies

Consider the number sequence where \(u_1=500, u_2=519, u_3=538\) and \(u_4=557\) etc.

(a) Find the value of \(u_{30}\)

(b) Find the sum of the first 12 terms of the sequence:

$$\sum_{n=1}^{12} u_n $$

Another number sequence is defined where \(w_1=4, w_2=8, w_3=16\) and \(w_4=32\) etc.

(c) Find the exact value of \(w_{10}\).

(d) Find the sum of the first 9 terms of this sequence.

\(k\) is the smallest value of \(n\) for which \(w_n\) is greater than \(u_n\).

(e) Calculate the value of \(k\).


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The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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