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Colegio ALPAMAYO Asesora deMatemtica

Lima Per Programa del Diploma

Gua de Repaso 01- Prueba Tipo 1Alumno: ___________________________________________________ Fecha: ___ / ___ / ___

Profesor: Ciro Tuo!ue "rado ##

1. In the diagram the shaded region represents a circular track with centre O, within a square fieldPQRS. The outer edge of the track touches the sides of the field. The radii of the inner and outeredges of the track arexm andym respectivel.

P Q

S R

Oy

x

Diagram not to scale

!a" #rite down an e$pression for the area of the track.

!%" The area of the field PQRS is &'(( m).

!i" *indy.

!ii" +iven thatx )-, find the area of the track.

Working:

Answers

!a" ////////////////..

!%" !i" //////////////...

!ii" //////////////...

(Total 4 marks)

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2. The universal set Uis defined as the set of positive integers less than -(. The su%setsAandBaredefined as

A 0integers that are multiples of 12B 0integers that are factors of 1(2

!a" 3ist the elements of

!i" A4

!ii" B.

!%" Place the elements ofAandBin the appropriate region in the 5enn diagram %elow.

U

A B

Working:

Answers

!a" !i" ///////////////

!ii" ............................................................

(Total 4 marks)

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4. On a certain game show, contestants spin a wheel to win a pri?e, as shown in the diagram. Thelarger angles are 40!the shaded sectors", and the smaller angles are 20.

@ o P r i ? e

@ o P r i ? e

@ o P r i ? e

@ o P r i ? e

@ o P r i ? e

@ o P r i ? e+ A

+ A

# B

# B

# B

C D R

*ind the pro%a%ilit that a contestant

!a" will notwin a pri?e4

!%" will win a holida in +reece !+A"4

!c" will win a washerEdrer !#B", given that he knows that he has won a pri?e4

!d" will win a holida in +reece ora washerEdrer.

Working:

Answers

!a" ////////////////..

!%" ////////////////..

!c" ////////////////..

!d" ////////////////..

(Total 4 marks)

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5. F!p q" pG q

!a" Complete the truth ta%le %elow for the compound statement a%ove.

p q p q !p q" p F!p q" pGq

T T

T F

F T

F F

!%" H$plain the significance of our result.

Working:

Answers

!%" ////////////////..

..................................................................

(Total 4 marks)

6. Of a group of five students, two will %e selected to visit the >nited @ations. The five studentsare ohn, Jaria, Raul, Aenri and Susan.

!a" #ith the aid of a tree diagram or a ta%le of outcomes, find the num%er of differentpossi%le com%inations of students that could go to the >nited @ations.

!%" *ind the pro%a%ilit that %oth Jaria and Susan will go on the trip.

Working:

Answers

!a" ////////////////..

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!%" ////////////////..

(Total 4 marks)

7. !a" *ory (.; cos (.;x, find

!i" the amplitude4

!ii" the period.

!%" 3ety 61 sinx8 ), where '(7 9x9 )=(7.

K drawing the graph ofyor otherwise, complete the ta%le %elow for the givenvalues ofy.

x y

6-

)

LWorking:

Answers

!a" !i" //////////////..

!ii" //////////////..

(Total 4 marks)

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. >nder certain conditions the num%er of %acteria in a particular culture dou%les ever -( secondsas shown % the graph %elow.