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PQS is right-angled at Q.. Which of the folloowing numbers is not a possible perimeter of the triangle?. Question 9: The value of x... The diagram beside shows the isosceles trapesiod

PEOPLE COMMITTEE OF

NGO QUYEN DISTRICT

NGOQUYEN EDUCATION AND

EDUCATION DEPARTMENT

NGO QUYEN ENGLISH MATHEMATICS AND SCIENCE COMPETITION FOR GRADE 8 STUDENTS

SCHOOL YEAR: 2021 – 2022

Time allowance: 120 minutes

PART 1: MULTIPLE – CHOICE (100 mark)

Question 1: If 2 3

p

p q 

 then

p

q equals

E None of the above.

Question 2: If  2  2

x  y y  x and x y What is the value x2y2?

Question 3: How many zerof are there in the last digits of the following number

11 12 13 88 89

Question 4 : What is the smallest possible value of M x2y2 – – –x y xy

 A 1;  B 1;  C 2;  D 2;  E None of the above

Question 5: Find the unit digit of 3 2021

Question 6: In the diagram, PS5,PQ3. PQS is right-angled at Q. QSR·  30 and

QR RS The length of RS is:

(E) None of the above.

Question 7: Calculate 19992 19982 19972 19962    32 22 1 2

Question 8: Two of the three side of a triangle are 25 and 15 Which of the folloowing

numbers is not a possible perimeter of the triangle?

Question 9: The value of x

45 ; 

A  B 60 ;   C 90 ;   D 105

Question 10 The diagram beside shows the isosceles trapesiod ABCD, which is with 7

BD cm, ·ABD 45 Determine the area of the one

A 24,5cm2 B. 22.5cm2 C 49cm2 D 28.5cm2 E None of the above

PART II: COMPOSE (200 mark)

Problem 1 Given a33ab2 9;b33a b2  46. Find the value of P a 2 b2

Problem 2 Let n be a prime numbe n2  Prove that the value of expression

2

2021 3

A n  which is divisible by 8.

Problem 3 Find all pairs  x y,

of integers such that x xy y – 8

Problem 4 Let ABCD be a rectangular, ·BDC 30 Draw the straight line through point C, perpendicular to BD, intersects BD at E and intersects the bisector of angle ADB at M.

a) Prove that AMBD is an isosceles trapezoid

b) Let N and K be the projections of point M on DA and AB respectively Prove that N K, and E are collinear

-THE

END -PART 1: MULTIPLE – CHOICE (100 mark)

ANSWERS AND MARKS Questio

PART II: COMPOSE (200 mark)

1(50

mark)

We have a33ab2 9;b33a b2  46.

Therefore ( a3 – 3ab2)2 + (b3 – 3a2b)2 = 2197 20

2(50

mark)

We have 2021n2 3 2016n25n1 n 1 8 20

And n be the prime number n2 , so 5n1 n M1 8

Therefore 2021n2  M 3 8 Where n P n ; 2.

20

3(50

mark)

We have x + xy – y = 8

20

So (x; y) (8;0);(2;6);( 6; 2);(0;8)   10

4

( 50 mark)

a, Easily proved µA1B¶2 300

so AM is parallel to BD

10 10

easily proved we have ·ADB MDB· 60o

Hence AMBD is an isosceles trapezoid

1 0

NME so ·MNE30o

Have quadrilateral MNAK is a rectangle, so

1 30o MNK A 

So three points N, K, E are collinear.

10 10