Time : 60 minutes Passing mark : 70%
Answer : Please click the end of problem <Answer>
Problem 1
Problem 2
(2) As shown in a figure, right triangle ABC is clockwise rotated around C as the center of the rotation until the side CA overlaps with the straight line L for the first.
(3) Taro and Jiro do a certain work.
(4) There is a certain integer A and even if either 119 or 176 or 328 is divided by A, the remainder is B in any division.
(5) The ratio of the number of boy students and girl students of a certain junior high school is 7 : 8.
Problem 3
Problem 4
Problem 5
Problem 6
Problem 2
Find X, Y, Z
(1) 4 × 4 × 5.14 - 51.4 × 0.75 + 0.257 × 30 = X
(2) 5.2 / (Y + 6.5) - 2/15 = 0.4
(3) 7 - { 26/5 - ( 5/4 - 11/20) × Z } = 2
Problem 2
Answer the following questions.
(1) In a figure, the point O is the center of a circle and A, B, C, E are points on the circumference.
In case OA = DE, find the angle of X and Y. (2) As shown in a figure, right triangle ABC is clockwise rotated around C as the center of the rotation until the side CA overlaps with the straight line L for the first.
In this case, find the area of the portion where the side AB passes.
Pi is assumed to be 3.14.
Pi is assumed to be 3.14.
(3) Taro and Jiro do a certain work.
It will take 5 hours when Taro and Jiro do this work together.
When Taro does this work alone for 4 hours first, it will take 7 hours for Jiro to do the remaining work alone after that.
Find the time when each of them complete this work by one person, respectively.
(4) There is a certain integer A and even if either 119 or 176 or 328 is divided by A, the remainder is B in any division.
B is one or more integers.
Find A and B.
Find A and B.
(5) The ratio of the number of boy students and girl students of a certain junior high school is 7 : 8.
The ratio of the number of students who go to school by bicycle and on foot is 4 : 5.
Noted that there is no student other than going to school by bicycle and on foot.
The number of boys who go to school by bicycle is 90 persons.
The number of girls who go to school on foot is 126 persons.
Find the number of all the students of this school.
Problem 3
Taro left P point at 9:00 a.m. and went to Q point with a fixed speed. He rested for 6 minutes on the way at R point.
Then, he walked with the same speed as before and he arrived at Q point at 10:42 a.m.
On the other hand, Jiro left P point at 9:13 a.m. and went to Q point with a fixed speed.
Jiro passed Taro at R point when Taro began to rest and he arrived at Q point at 10:25 a.m.
Answer the following questions.
(1) Find the ratio of the distance between PR and between RQ by the least integer.
(2) Find the time when Jiro passed Taro.
Problem 4
In accordance with the following rule, a number is lined up from the left to the right in order in a row.
<Rule>
① Both the 1st number and the 2nd number from the left is 1.
② From the third number, it is the sum of previous two numbers.
However, when the sum is 3, it turned to 0 to be written and when the sum is 4, it turned to be 1 to be written 4.
The figure shows that numbers are written in order until the 5th number.
Answer the following questions.
(1) Write down additional 10 numbers in order following 1, 1, 2, 0, 2.
(2) How many times is 2 written by the 500th number from the 1st?
(3) Find the sum of numbers from the 1st number to the 500th.
<Rule>
① Both the 1st number and the 2nd number from the left is 1.
② From the third number, it is the sum of previous two numbers.
However, when the sum is 3, it turned to 0 to be written and when the sum is 4, it turned to be 1 to be written 4.
The figure shows that numbers are written in order until the 5th number.
Answer the following questions.
(1) Write down additional 10 numbers in order following 1, 1, 2, 0, 2.
(2) How many times is 2 written by the 500th number from the 1st?
(3) Find the sum of numbers from the 1st number to the 500th.
Problem 5
As for trapezoid ABCD in a figure, AD : BC = 2 : 3 and AD and BC are parallel.
Point P is the point on the side AB and point Q is the point on the side CD.
The area of the triangle ADQ, the triangle APQ, the triangle CPQ, and the triangle BCP is 3 cm2, 5 cm2, 4 cm2, 3 cm2, respectively.
The intersection of AC and PQ is set to R.
Answer the following questions.
(1) Find the area of the triangle APC.
(2) Find the area of the triangle APR.
Point P is the point on the side AB and point Q is the point on the side CD.
The area of the triangle ADQ, the triangle APQ, the triangle CPQ, and the triangle BCP is 3 cm2, 5 cm2, 4 cm2, 3 cm2, respectively.
The intersection of AC and PQ is set to R.
Answer the following questions.
(1) Find the area of the triangle APC.
(2) Find the area of the triangle APR.
Problem 6
Answer the following questions.
(1) As for the cube whose side is 4 cm, find the volume of the solid made after hollowing out a rectangular prism with rectangle ABCD as a bottom.
(2) As for the solid made in (1), find the volume of the solid made after hollowing out a rectangular prism with rectangle EFGH as a bottom further.
(3) Draw the cut surface in the Fig.2 with hatched lines made when the solid made in (2) is cut by the plane which passes along three point P, Q, and R.
Moreover, find the ratio of the area of the cut surface to the area of the triangle PQR by the least integer.
(1) As for the cube whose side is 4 cm, find the volume of the solid made after hollowing out a rectangular prism with rectangle ABCD as a bottom.
(2) As for the solid made in (1), find the volume of the solid made after hollowing out a rectangular prism with rectangle EFGH as a bottom further.
(3) Draw the cut surface in the Fig.2 with hatched lines made when the solid made in (2) is cut by the plane which passes along three point P, Q, and R.
Moreover, find the ratio of the area of the cut surface to the area of the triangle PQR by the least integer.
Find X, Y, Z
(1) 4 × 4 × 5.14 - 51.4 × 0.75 + 0.257 × 30 = X
(2) 5.2 / (Y + 6.5) - 2/15 = 0.4
(3) 7 - { 26/5 - ( 5/4 - 11/20) × Z } = 2
Answer
(1) 51.4
(2) 13/4
(3) 2/7
Problem 2
Answer the following questions.
(1) In a figure, the point O is the center of a circle and A, B, C, E are points on the circumference.
In case OA = DE, find the angle of X and Y.
Answer
(2) As shown in a figure, right triangle ABC is clockwise rotated around C as the center of the rotation until the side CA overlaps with the straight line L for the first.
X = 17,
Y = 34
Y = 34
(2) As shown in a figure, right triangle ABC is clockwise rotated around C as the center of the rotation until the side CA overlaps with the straight line L for the first.
In this case, find the area of the portion where the side AB passes.
Pi is assumed to be 3.14.
Pi is assumed to be 3.14.
Answer
(3) Taro and Jiro do a certain work. It will take 5 hours when Taro and Jiro do this work together.
12.56 cm2
Reference
(3) Taro and Jiro do a certain work. It will take 5 hours when Taro and Jiro do this work together.
When Taro does this work alone for 4 hours first, it will take 7 hours for Jiro to do the remaining work alone after that.
Find the time when each of them complete this work by one person, respectively.
Answer
Taro 7.5 hours
Jiro 15 hours
(4) There is a certain integer A and even if either 119 or 176 or 328 is divided by A, the remainder is B in any division.
(5) The ratio of the number of boy students and girl students of a certain junior high school is 7 : 8.
Problem 3
Problem 4
(4) There is a certain integer A and even if either 119 or 176 or 328 is divided by A, the remainder is B in any division.
B is one or more integers.
Find A and B.
Find A and B.
Answer
A = 19, B = 5
(5) The ratio of the number of boy students and girl students of a certain junior high school is 7 : 8.
The ratio of the number of students who go to school by bicycle and on foot is 4 : 5.
Noted that there is no student other than going to school by bicycle and on foot.
The number of boys who go to school by bicycle is 90 persons.
The number of girls who go to school on foot is 126 persons.
Find the number of all the students of this school.
Answer
405 persons
Problem 3
Taro left P point at 9:00 a.m. and went to Q point with a fixed speed.
He rested for 6 minutes on the way at R point.
Then, he walked with the same speed as before and he arrived at Q point at 10:42 a.m.
On the other hand, Jiro left P point at 9:13 a.m. and went to Q point with a fixed speed.
Jiro passed Taro at R point when Taro began to rest and he arrived at Q point at 10:25 a.m.
Answer the following questions.
(1) Find the ratio of the distance between PR and between RQ by the least integer.
(2) Find the time when Jiro passed Taro.
Answer
(1) 13 : 11
(2) 9:25 AM
(2) 9:25 AM
Problem 4
In accordance with the following rule, a number is lined up from the left to the right in order in a row.
<Rule>
① Both the 1st number and the 2nd number from the left is 1.
② From the third number, it is the sum of previous two numbers.
However, when the sum is 3, it turned to 0 to be written and when the sum is 4, it turned to be 1 to be written 4.
The figure shows that numbers are written in order until the 5th number.
Answer the following questions.
(1) Write down additional 10 numbers in order following 1, 1, 2, 0, 2.
(2) How many times is 2 written by the 500th number from the 1st?
(3) Find the sum of numbers from the 1st number to the 500th.
Problem 5
<Rule>
① Both the 1st number and the 2nd number from the left is 1.
② From the third number, it is the sum of previous two numbers.
However, when the sum is 3, it turned to 0 to be written and when the sum is 4, it turned to be 1 to be written 4.
The figure shows that numbers are written in order until the 5th number.
Answer the following questions.
(1) Write down additional 10 numbers in order following 1, 1, 2, 0, 2.
(2) How many times is 2 written by the 500th number from the 1st?
(3) Find the sum of numbers from the 1st number to the 500th.
Answer
(1) 2, 1, 0, 1, 1, 2, 0, 2, 2, 1
(2) 187 times
(3) 562
(2) 187 times
(3) 562
Problem 5
As for trapezoid ABCD in a figure, AD : BC = 2 : 3 and AD and BC are parallel.
Point P is the point on the side AB and point Q is the point on the side CD.
The area of the triangle ADQ, the triangle APQ, the triangle CPQ, and the triangle BCP is 3 cm2, 5 cm2, 4 cm2, 3 cm2, respectively.
The intersection of AC and PQ is set to R.
Answer the following questions.
(1) Find the area of the triangle APC.
(2) Find the area of the triangle APR.
Point P is the point on the side AB and point Q is the point on the side CD.
The area of the triangle ADQ, the triangle APQ, the triangle CPQ, and the triangle BCP is 3 cm2, 5 cm2, 4 cm2, 3 cm2, respectively.
The intersection of AC and PQ is set to R.
Answer the following questions.
(1) Find the area of the triangle APC.
(2) Find the area of the triangle APR.
Answer
Problem 6
(1) 6 cm2
(2) 10/3 cm2
Reference
Problem 6
Answer the following questions.
(1) As for the cube whose side is 4 cm, find the volume of the solid made after hollowing out a rectangular prism with rectangle ABCD as a bottom.
(2) As for the solid made in (1), find the volume of the solid made after hollowing out a rectangular prism with rectangle EFGH as a bottom further.
(3) Draw the cut surface in the Fig.2 with hatched lines made when the solid made in (2) is cut by the plane which passes along three point P, Q, and R.
Moreover, find the ratio of the area of the cut surface to the area of the triangle PQR by the least integer.
(1) As for the cube whose side is 4 cm, find the volume of the solid made after hollowing out a rectangular prism with rectangle ABCD as a bottom.
(2) As for the solid made in (1), find the volume of the solid made after hollowing out a rectangular prism with rectangle EFGH as a bottom further.
(3) Draw the cut surface in the Fig.2 with hatched lines made when the solid made in (2) is cut by the plane which passes along three point P, Q, and R.
Moreover, find the ratio of the area of the cut surface to the area of the triangle PQR by the least integer.
Answer
11 : 16
(1) 56 cm3
(2) 50 cm3
(3)
(2) 50 cm3
(3)
Reference
