## 1.12 Complex number Introduction (Not for AA SL)

Calculator Allowed: No Question Answer Transcription of this question: [Maximum mark: 4]In the following Argand diagram the point A represents the complex number —1 + 4i andthe point B represents the complex number —3 + Oi. The shape of ABCD is a square.Determine the complex numbers represented by the points C and D.

## 1.10 Counting principles, permutations and combinations (Not for AA SL)

Calculator Allowed: Yes Question Answer Transcription of this question: 3.[Maximum mark: 71A team Of 6 players is to be selected from 10 volleyball players, Of whom 8 are boysand 2 are girls.(a)(b)(c)In how many ways can the team be selected

## 1.15.1 Proof by mathematical induction (Not for AA SL)

Calculator Allowed: No Question Answer Transcription of this question: 12.[Maximum mark: I OI(a)(b)Find the sum Of the infinite geometric sequence 27 , —9, 3Use mathematical induction to prove that for n e ,[3 marks][7 marks]

## 5.18.2 Differential Equations – Variables Separable (Not for AA SL)

Calculator Allowed: Yes Question Answer Transcription of this question: 9.[Maximum mark: 81The population of mosquitoes in a specific area around a lake is controlled by pesticide.The rate Of decrease Of the number Of mosquitoes is proportional to the number Ofmosquitoes at any time t. Given that the population decreases from 500 000 to 400 000in […]

## 1.5 Laws of exponents, Intro to logs with base 10 and base e

Calculator Allowed: No Question Answer Transcription of this question: 4.[Maximum mark: 6](a)(b)Write the expression 31n2—ln4 in the form Ink , where k e Z.Hence or otherwise, solve 31n2 — In 4 = —Inx.[31[31

## 1.2 Arithmetic sequence and series

Calculator Allowed: No Question Answer Transcription of this question: 2.[Maximum mark: 7]In an arithmetic sequence, the third term is 10 and the fifth term is 16.(a)(b)(c)Find the common difference.Find the first term.Find the sum Of the first 20 terms Of the sequence.[2][2][31

## 2.3 Graph of Functions

Calculator Allowed: No Question Answer Transcription of this question: 3.[Maximum mark: 61The following diagram shows the graph Of y f (x) , for —4 x 5 .(a)(b)(c)-4Write down the value Of(ii) f -1(1)Find the domain Of642-2-2624.6On the grid above, sketch the graph Of f -[21[21[21

## 4.1 Sampling Techniques

Calculator Allowed: No Question Answer Transcription of this question: [Maximum mark: 51The cumulative frequency curve below represents the marks obtained by 100 students.10095857565504535302515o10203040 50 60Mark708090 100(a) Find the median mark(b) Find the interquartile range.[2 marks]

## 3.12 Introduction to Vectors. (Not for AA SL)

Calculator Allowed: Yes Question Answer Transcription of this question: 8.[Maximum mark: 161The following diagram shows the cuboid (rectangular solid) OABCDEFG, where O isthe origin, and OA=4i, OC=3j , OD=2k(i)(ii)(iii)Find 0BFind OFShow that AG—4i + 3j + 2k[5 marks](b)(c)Write down a vector equation for(i) the OF;(ii) the line AG.Find the obtuse angle between the lines OF […]

## 5.5 Integration

Calculator Allowed: No Question Answer Transcription of this question: 4.[Maximum mark: 6]Let +2. Given that f(2) = 5 , find f (x)