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Japanese 8th grade achievement test
Posted:
Mar 23, 1995 2:25 PM
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While back, I posted a couple of questions from Japense senior
high school entrance exam. Here are some questions from an
achievement test for 8th graders in Japan. This is not a
national exam, but unique to a prefecture adjacent to Tokyo. In
that particular prefecture, the score from this test, along with
students transcripts and their entrance test scores determine
whether or not students will be accepted to a particular school
(public). So, it is an "SAT" for junior high kids. The
achievement test, however, cover 9 subjects: math, science,
social studies, language (Japanese), foreigh language (English),
music, art, health, shop/home econonmics (both boys and girls
take both sections). I'm not sure how much time is given, but they take
all 9 tests in two days. So, I would guess somewhere around 60 - 90 minutes
************************************************************************
* Tad Watanabe e-mail *
* Dept. of Mathematics watanabe-t@toe.towson.edu *
* Towson State University watanabe-t@towsonvx.bitnet *
* Towson, MD 21204 tad@midget.towson.edu *
* (410) 830 - 3585 (410) 830 - 4149 FAX *
************************************************************************
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1 Simplify.
a) 3a - b + 4a - 2b b) 5(a^2 - a)- (2a^2 - 3a)
c) 8x^2y / (-4x)^2 * 6y d) omitted
2 i) Which of the following is the correct solution to the
inequality: -6x - 13 < 5.
a) -6x-13<5 b) -x-13<5 c) -6x-13<5 d) -6x-13<5
-6x>5+13 -6x>5+13 -6x<5+13 -6x<5+13
-6x>18 -6x>18 -6x<18 -6x<18
x>-3 x<-3 x<-3 x>-3
ii) What is the smallest value of x that satisfies the
inequality: 3(x-6)>= -x + 1
iii) Solve:
3x + y = 7
x - 2y = 7
iv) Which of the following represent 30 expressed in base
2?
a) 1110 b) 1111 c) 10111 d) 11011 e) 11110
3 At a junior high school, they are planning to have a
"sports-day." All 106 boys in the eighth grade must select
either basketball or soccer (but not both). Each soccer
team has 11 members and each basketball team has 5 members.
When all boys have selected a sport, there were exactly 14
teams (combined) total. Answer the following questions:
i) In order to find the number of students who selected
soccer and basketball, two students set up systems of
equations as shown below. Fill in the blank for each
student's reasoning.
Student A
Let x be the number of students who chose soccer, and y
be the number of students who chose basketball.
____________ = 106
____________ = 14
Student B
Let x be then umber of soccer team and y be the number
of basketball team.
____________ = 14
____________ = 106
ii) Find the number of students who chose basketball and
the number of students who chose soccer.
4 (In actual problem, a graph is included). In the graph,
line l is a linear function, y = -2/3 x - 2. Lable the x-
intercept A, y-intercept B. Line m goes through the point
C(0,6) and it is a decreasing line. Label its x-intercetp
D. Answer the following questions.
i) Find the coordinate of point B.
ii) Express the equation of the line that goes throuh
points A and C in the form, y = ax+b.
iii) If the area of triangle ABC and the area of triangle
ABC are equal, find the slope of line m.
5 There are two candles, A & B. A is 26 cm long and it burns
at the rate of 0.6 cm per minute. B is 20cm long and burns
at the rate of 0.2 cm per minute. Two candles were lit at
the same time.
i) When will A be 20 cm long. Answer in minutes after the
it was lit.
ii) Will the two candles be equal in length anytime? If
so, find that length.
6 (Again, there is a diagram included, but I can't do that
here.)
In paralellogram ABCD below, E and F are on the diagonal BD
and m(BE) = m(DF). Drop a perpendicular from E to AB and a
perpendicular from F to CD. Let the points of intersection
be labeled G and H, respectively. The proof below shows
that quadrilateral GEHF is a parallelogram. Fill in the
blank. For i and ii select from Group A, for a and b,
select from Group B.
In triagles BEG and DFH, BE = DF (given) (1)
<EGB=<FHD=90 (given) (2)
Since AB // DC, _____a______ (3)
By (1), (2), (3), tirangles BEG and DFH are contgruent
(_____i_____) (4)
Therefore, EG = FH (5)
Also, <GEF = 180-<BEG (6)
<HFE=180 - <DFH (7)
By (4), < BEG = <DFH (8)
(6), (7), (8) imply <GEF = < HFE
Therefore,______b_______ (9)
From (5) and (9), because of _____ii_______, quadrilateral GEHF is a parallelgram.
Group A
1 <CBE = <ADF 2 <EGF=<FHE
3 <GBE = <HDF 4 GF = EH
5 BG = DH 6 AD // BC
7 GE // FH 8 GF // EH
Group B
1 AAA
2 SAS
3 ASA
4 Two right triangles are congruent if their hypoteneus are congruent and one
corresponding angles are congruent.
5 Two right triangles are congruent if their hypoteneus are congruent and one
corresponding leg are congruent.
6 If both pairs of opposite angles are congruent, then the quadrilateral is a
parallelogram.
7 If both pairs of opposite sides are congruent, then the quadrialteral is a
parallelogram.
8 If both pairs of opposite sides are parallel, then the quadrilateral is a
parallelogram.
9 If one pair of opposite sides are parallel and congruent, the quadrilateral is a
parallelogram.
7 (Actual problem with a diagram)
In triangle ABC below, point D is such taht AD:DB = 1:2. From D, a line parallel
to AC and a line parallel to BC were drawn. The point where these lines meet AC
and BC are labeled E and F, respectively. Connect E and F, B and E. Let the
intersection of DF and BE be G. Finally, from G construct a line parallel to BC, and
let the ponint of intersection between this line and AB be H.
Answer the following questions.
i) Express the ratio of DE to BC in the simplest form.
ii) If DH = 2cm, find AB.
iii) If the area of triangle EGF is 4 cm^2, find the area of triangle ABC.
8 The table below shows the records of 40 8th grade students' vertical leap and high
jump. Answer the question using the table.
vertical leap -> 25 30 35 40 45 50 (included)
high jump | | | | | |
V 30 35 40 45 50 55 (not included)
120 - 130 1 1 1
110 - 120 2 8 2 1
100 - 110 3 A 5 3
90 - 100 1 2 1
80 - 90 1 1
i) Find A
ii) How many students high jumped better than 110cm and vertical leap of more
than 40 cm?
iii) what percentage of students high jumped between 80cm and 90 cm?
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