# Grade 8 Olympiad – Tuyển chọn câu hỏi Olympiad lớp 8

Table Of Contents

Grade 8 Olympiad

## Week 1

### Choose correct answer(s) from the given choices

(1) If ● + ♥ = 2♠ and ♠ + ♦ = 2● , which of the following is correct?

a. ● + ♠ = 2♦ b. ● + ♦ = ♥ + ♠

c. ● + ♠ = ♥ + ♦ d. ● + ♠ = 2♥

(2) Kaylee and Alyssa start from the same point. Kaylee walks 4 km in West direction, then turn left and walks for 7 km. Alyssa walks 7 km in South direction, and turn left and walks for 3 km. Find the distance between Kaylee and Alyssa now.

a. 7 km b. 5 km

c. 8 km d. 6 km

(3) Coin A is flipped 4 times and coin B is flipped 5 times. What is the probability that the number of heads obtained from flipping the two coins is the same?

a. \frac{65}{258}

b. \frac{{61}}{{256}}

a. \frac{{63}}{{256}}

a. \frac{{65}}{{256}}

(4) Brandon selects 3 numbers randomly from the following set of 5 numbers 2, 1, 5, 6 and 7. He puts them in the form of a proper fraction of the type a\frac{{b}}{{c}}

What is the probability that you will get a fraction greater than 2\frac{21}{22}

a. \frac{18}{30}

b. \frac{12}{36}

ca. \frac{24}{30}

a. \frac{24}{36}

### Fill in the blanks

(5) Clock’s hour and minute hands overlap ……….. times in a day

### Answer the questions

(6) If p + \frac{1}{p} = \sqrt 2 , find the value of {p^2} + \frac{1}{{{p^2}}}

(7) Find the value of A and B, from following summation.

(8) Matthew’s roll number is a two digit number. His friend David’s roll number has the same digits as Matthew’s roll number, but with digits interchanged. If they add their roll number, and divide the sum by 11. Find the remainder of this division.

(9) The number of days left in the month of December are 11 more than the number of days already passed. How many days have already passed in the month?

(10) If Austin drives at three fourth of his usual speed, he covers a certain distance in 2 hours more than the time he takes while driving at his usual speed. Find the time taken by him to cover this distance with his usual speed.

## Week 2

### Choose correct answer(s) from the given choices

(1) If diagonals of a rhombus-shaped park are 10 and 21 meters, find the cost of fencing the park boundary at the rate of $5 per meter.

a. $68 b. $268 c. $272 d. $260

(2) Anthony is solving a question, where a given number has to be multiplied by 32. Anthony did not read the question carefully, and multiplied the number by 2 (instead of 32). If his answer is 480 less than the correct answer, find the given number.

a. 19 b. 13

c. 16 d. 14

(3) If you plot following set of points on a graph, which set of points will form a straight line?

a. (2,4) (4,8) (5,11) (6,12) (8,16)

b. (0,1) (1,2) (3,3) (3,4)

c. (0,2) (1,4) (2,6) (4,10)

d. (1,3) (2,3) (4,6) (6,8) (7,9)

(4) An express train from Atlanta to San Francisco runs every 5th day. If the train went on Wednesday, after how many days will the train run on a Saturday?

a. 14 days b. 10 days

c. 9 days d. 11 days

(5) Let p be a prime number such that the next larger number is a perfect square. Find the sum of all such prime numbers. For example, if you think 11 and 13 are two such prime numbers, then the sum is 24)

a. 3 b. 7 c. 1 d.9

### Fill in the blanks

(6) The perimeter of a trapezoid with height 10 cm is 37 cm. If the sum of non-parallel sides is 25 cm, the area of the trapezoid is ……….. cm2.

(7) The number of even digits in the product 88888888 x 99999999 are …………

### Answer the questions

(8) Kevin writes all the numbers from 4 to 72, which are divisible by 4. What will be the number at the 8th position?

(9) Nicole wants to print some brochures for her business. If she goes for style 1, it will cost her $89 plus $0.2, per brochure. If she goes for style 2, it will cost her $5 plus $0.4, per brochure. For how many brochures will the price for both the styles be the same?

(10) If a polygon has its sum of interior angles smaller than 2060^{0} what is the maximum number of sides of the polygon?

## Week 3

### Choose correct answer(s) from the given choices

(1) If x^{2} + y^{2} = 25 and xy = 12, find the value of 3(x + y)^{2} – 2(x – y)^{2}.

a. 142 b. 149

c. 152 d. 145

(2) There are a total of 9 chocolates – 3 each in the flavors of coffee, mango and grape. There are also 4 children. If each child is allowed to choose their own favorite flavor, what is the probability that all of them will get flavors of their choice?

a. 26/27 b. 26/26

c. 25/28 d. 5/27

### Fill in the blanks

(3) The smallest perfect square that can be divided by 15 and 55 is .

### Answer the questions

(4) In a trapezoid of area 70 cm2, the length of two parallel sides are in ratio 4:3. If the height of trapezoid is 10 cm, find the length of smaller of the two parallel sides.

(5) Anthony was asked by his teacher to subtract 4 from a number and to divide the result by 8. However, he subtracted 8 from that number and divided the result by 4 to get 25. If he had done it correctly, what answer would he have gotten?

(8) Find the missing number.

(9) If there are numbers of which one is latex] \left( {1 – \frac{1}{{{n^4}}}}\right)[/latex] and all the others are then by how much is the arithmetic mean of these numbers less than 1.

(10) There are 3 hats belonging to 3 students. The hats were put into a box, and each student pulls out a hat one after the other. What is the probability that each student gets his or her own hat?

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