## 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 […]

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

Calculator Allowed: Yes Question Answer Transcription of this question: [Maximum mark: 8]Eight boys and two girls sit on a bench. Determine the number of possible arrangements,given that(a)(b)(c)the girls do not sit together;the girls do not sit on either end;the girls do not sit on either end and do not sit together.[2]

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

Calculator Allowed: Yes Question Answer Transcription of this question: [Maximum mark: 6]Consider the complex number z(a)(b)(c)6+2iExpress z in the form a + ib, where a, b eQ.Find the exact value of the modulus of z.Find the argument of z, giving your answer to 4 decimal places.[2][2][2]

## 2.2 Concept of Function & Inverse of a Function

Calculator Allowed: No Question Answer Transcription of this question: 4.[Maximum mark: 6]Consider the function f, where f (x) arcsin (In x).(a)(b)Find the domain OfFind r[3 marks][3 marks]

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

Calculator Allowed: Yes Question Answer Transcription of this question: [Maximum mark: 18]oLet A =11011 and B:001o(a)(b)(c)Given that X and Y -B(i)(ii)find X and Y;does x-i +Yhave an inverse

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

Calculator Allowed: Yes Question Answer Transcription of this question: 6.[Maximum mark: 6]The acceleration in Ins-2 Of a particle moving in a straight line at time t seconds,t 20, is given by the formula a v. When t —O, the velocity is 40 Ins-I2Find an expression for v in terms Of t.

## 5.2 Increasing decreasing Functions

Calculator Allowed: No Question Answer Transcription of this question: [Maximum mark: 7]Consider the function defined by f (x) = x’— 3×2+ 4.(a) Determine the values of x for which f(x) is a decreasing function.There is a point of inflexion, P, on the curve y = f(b) Find the coordinates of P.