Luyện Toán seamo cho học sinh lớp 7, 8

Nội dung text: Luyện Toán seamo cho học sinh lớp 7, 8

1. Phần 3: Q1. 24 4- digit number can be formed by using 1,3,5 and 7, with each digit being used exactly one each time. Find the average of these 24 numbers? 1 1 1 1 Q2. Evaluate 1 3 3 5 5 7 19 21 Q3. Simplify x 2 3 2x 5 x 2 2x 5 Phần 4: Paper A: How many 5- digit numbers are greater than 40000 that ues the digits 1,2,3,4 and 5, and the digits cannot be repeated? Paper B: At an exhibition, an adult entry ticket costs $4 while 2 child entry tickets cost $1. If 100 tickets were sold and a total of $120 was collected, how many children attended the exhibition? 2021 Paper C: Evaluate 20212 2020.2022 2 Paper D: Factorize x 4 2 a 2 b 2 x 2 a 2 b 2 Paper E: Let a,b and c be real numbers such that a 8 b and c 2 ab 16 . Find the value of a c Phần 5: Paper B: 739abc is divisible 3, 4 and 5. Find the smallest value of 739abc Paper C: Find the missing number of the sequence is 4,6,10,14,22,26,34,( ),46, x n x m m Paper D: Solve the equation given that mn 0 m n n Phần 6:
2. Paper B:In a new operation 3  4 13 5  9 24 7  7 28 Find value of 13  8 Paper C: A new operetion is defined as 4  2 4 5 9 5  6 5 6 7 8 9 10 45 Find the value of m in m  7 49 c a b Paper D: Given that a,b,c >0, and , arrange a,b,c in ascending order a b b c a c
3. Phần 7: Paper B: Find the value of 200 198 196 194 8 6 4 2 Paper C: n denotes smallest whole number that is not a factor of n. For example 7 2, 12 5 . Find the value of 23 40 Paper D: If the positive numbers a,b,c satisfy a.b.c 1 , solve the equation in x: 2ax 2bx 2cx 1 ab a 1 bc b 1 ca c 1 Phần 8: Paper A: When we write 72 as a product of two whore numbers, A and B, what is the smallest value of A +B? Paper B: In the pentagon below, AB = BC = CD = DE = AE, find ABC ? B AC y ED 1 1 1 1 Paper C: Evaluate: 1 1 1 1 22 32 42 20212 a Paper D: a,b are positive integers. Given that b takes the minimum value, find the fraction b 8 a 9 satisfying 9 b 10 Phần 9: Paper A: Jordan has 37 apples and Jonathan has 15 apples. How many apples does Jordan at teast have to give to Jonathan to make them have a 4-apple difference? Paper B: Whats is the sum of first 68 digits 358421358421358421 Paper C: Find the number of 4-digit palindromes which are a multiple of 11 Paper D: Given that a night- angled triangle has a perimeter of 56cm and anarea of 84 cm 2 , find the lengths of its 3 sides
4. Phần 10: Paper A: The letters A, B, C and D represent elther 1,2,3,4 or 5, which cnnot be repeated. What is the number that is not used? Paper B: Find the missing number 5 4 ? 4 6 3 5 2 4 7 12 14 Paper C: At a movie premiere, a queue starts forming at the box office before it opened at 1p.m. From 1p.m onwards, a fixed number of people joined the queue every minute. If 7 counters opens at the box office, the queue could be cleared in 14 minutes. If 9 countes were open, the queue would be cleared in 10 minutes. It 12 counters open. How lonh wouid it take to clear the queue? Paper D: In ABC,C 900 , and the point D lies on the midpoint of AC. Prove that AB 2 3BC 2 4BD 2
5. Phần 11: Paper A: Stady the pattern 1+2+1=4 12+3+2+1=9 1+2+3+4+3+2+1=16 1+2+3+4+5+4+3+2+1=25 Then, use a simple method to compute 1+2+3+ +7+8+7+ +3+2+1 Paper C: The following figure shows a circle inscribed with in a right- angled triangle. Determine the radius of the circle 5cm 12cm Paper D: Solve the quadratic equation: x 2 x 3 x 3 24 0 Phần 12: Paper A: Observe the sequence below. How many digits have been used altogether? 1,2,2,3,3,3,4,4,4,4, ,10,10,10,10,10,10,10,10,10,10 Paper C: It is known 0 x 1 , y x x and z x y . Arrange the 3 number in increasing order 1 4 2 1 3 3 3 3 Paper D: Simplify the expresion 3 9 9 9 1 Note: 3 a x x 3 a;a 1 a Phần 13: Paper A: If 6 children can construct 2 lego houses in one day,how many children would it take to construct 9 lego houses in three days?
6. 1 1 1 1 1 1 Paper B: Evaluate 2 4 8 16 128 256 Paper C: There were 200 students in TCAprimary school, numbered 1 to 200. Those with numbers which are multiple of 4 are in choir, those with numbers which are multiples of 7 are in dance and those with square numbers are in band. How many students are in none of these 3 CCAs? 2 3 3 5 Paper D: Simplify 2 3 2 3 5 Phần 14: Paper A: A school recucles paper cups for use in its canteen, 3 used cups are needed ta make up 1 new cup. If the school only has 15 unused cups. What is the maximum number of cups the school can use in total? Paper B: Jack adds up the sum of 1+2+3+ on a calculator. When he reaches the sum of 331, he realizes that he has forgotten to add one number. What is that number? Paper D: Given that a,b,c >0, and the quadratic equation c a x 2 2bx c a 0 has 2 equal roots, detemine if 3 segments of lenhths a,b,c cau form a triangle. If so, show what type of triangle is formed Paper E: Suppose ABCD is a rectangle. M and N are points on BC and CD respectively such that area of ABM , CMN and AND an 3, 4 and 5 respectively. Find the area of AMN N DC M AB Phần 15: Paper B: How many 5- digit numbers can be formed from the digits 1,2,3,4 and 5 if there are no repetition of numbers and the one’s digit muts be greater than the ten’s digit? Paper C: Compare the following 3111 and 1714 which is larger? 1 Paper D: Detemine the various values of k such that the following system: kx y 3 3y 1 6x Has a unique solution, no solutions, and infinitely many solutions respectively
7. Phần 16: Paper A: Evalute 101 102 103 109 110 Paper B: ABCD is a square of side length 4cm. E is the midpoint of AD, and F is the midpoint of EC. Find the erea of BFD? A E D F BC Paper C: Find the values of a,b,c and d, given that 15! 1,3a7,674,b68,0cd 1 1 1 x y z 2 1 1 1 Paper D: Solve the following system of equations: y z x 3 1 1 1 z x y 4 1 1 1 1 Q2. Evaluate 1 2 32 64 128 128 64 32 2 Q3. Given that p q 198 , find the intiger solutions to the equation x 2 px q 0