CAN THO EDUCATION AND TRAINING
DEPARTMENT
LY TU TRONG HIGH SCHOOL
FOR THE GIFT
ENGLISH MATH CONTEST SCHOOL
YEAR 2019
DATE OF TEST:
SUBJECT: MATH - GRADE 10
Time allotted: 150 minutes (not including delievery time)
(The test has 02 page)
Full name:………………………………………….......... Class:………………………….
Problem 1. (3,0 marks) Among the school seniors the top grade was received by 48 students in
mathematics, 37 in physics, 42 in chemistry, 75 in mathematics and physics, 76 in mathematics
and chemistry, 66 in physics and chemistry and 4 students in all three subjects. How many
students got more than one excellent mark? How many of them got only one excellent mark?
Problem
2.
(3,0
marks)
In
the
plane
with
Oxy
coordinate,
given
parabola
( P) : y  x2  (m  2) x  m and line d : y  2 x  3 , where m is a parameter. Suppose that the
intersection of d and ( P) is two distinct points A and B. Find the value of m such that A and B
are on the same side as the vertical axis.
Problem 3. (2,0 marks) Andy, a member of the Bigstone Cree First Nation, has a contract as a
fire lookout at the Sandy Lake lookout tower near South Wabasca Lake, Alberta. He sights smoke
at a bearing of 1400 to the tower, and reports it over the radio. The Rock Island Lake lookout near
Calling Lake reports the smoke at a bring of 200. The Rock Island Lake lookout tower is 62 km
away from the Sandy Lake lookout tower, at a bearing of 1650 from Sandy Lake. The layout is
shown in the diagram below.
Calculate the distance of the smoke from each of the two towers.
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Problem 4. (2,5 marks) Suppose Lindsay’s mom invests 10,000,000 VND, part at 3%, and the
rest at 2.5%, in interest bearing accounts. The totally yearly investment income is 283,000 VND.
How much did Lindsay’s mom invest at each rate?
Problem 5. (2,0 marks) A motorboat is moving with a speed of 25 kilometers per hour, relative
to the water. It is going from A to B, moving with the constant current. At a certain moment, it
has travelled 42% of the total distance. From that point on, it takes the same amount of time to
reach B as it would to travel back to A. What is the speed of current (in kilometers per hour)?
Problem 6. (3,0 marks) The cost of one kilogram of chocolate is x USD and one kilogram of
potatoes is y USD, x and y are positive integers and have not more than two digits. Mother said to
Mary to buy 200 grams of chocolates and 1 kilogram of potatoes that cost exactly N USD. Mary
to confuses all and bought 200 grams of potatoes and 1 kilogram chocolates. She had to pay
exactly M USD (M > N). It turned out that the numbers M, N have no more than two digits and
are formed of the same digits, but in a different order. How much are one kilogram of potatoes
and one kilogram of chocolates cost?
Problem 7. (3,0 marks) On the Oxy coordinate plane, given triangle ABC. M  2;0  is the
midpoint of the line segment AC. The general equations of the altitude AH and the median AN
respectively are 7 x – 2 y – 3  0 and 6 x – y – 4  0. Find the coordinate of point B.
Problem 8. (1,5 marks) For a, b, c  0 and if a  b  c  1. Find maximum value of
P  3 a  b  3 b  c  3 c  a.
-----------------THE END-------------Candidates are not allowed to use references
Invigilators are not allowed to explain anything.
Candidate’s full name…………………………….... Identification number…………………
1st invigilator’s signature…………………… 2st invigilator’s signature………………………
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