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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.