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SundarSTEM
Admission Test for Class – 9
Year 2024 Phase-1
(Part-II)
Duration: 90 Minutes
Part-II contains 6 subjective questions.
Total marks for Part-II are 100. Individual marks are mentioned for each question.
Attempt all the questions. There will be no negative marking.
Part-II has 10 pages including this one. There is enough space for you to solve a question
in its designated space. Last 3 pages are left blank for extra work.
Extra sheet is not allowed.
Please fill the below details before proceeding to test.
Test ID: ___________________ Date of Birth (dd/mm/yyyy): _______________
Name: _____________________________________________________________
Father’s Name_______________________________________________________
Test Center: ________________________________________________________
Test center City:_____________________________________________________
Invigilator’s signature:________________________________________________
Instructions:
All answers should be exact. Never use approximations. For example:
o DO NOT approximate √𝟐 = 𝟏. 𝟒𝟏𝟒𝟐. Just leave it as √𝟐 in the formula.
𝟐𝟐
o DO NOT approximate 𝝅 ≈ 𝒐𝒓 𝝅 ≈ 𝟑. 𝟏𝟒. Just leave it as 𝝅.
𝟕
Simplify your answers.
Calculator is not allowed in the test. If a student is making long, time-consuming
calculations, he is probably on the wrong track.
The working of candidate will be used in assessment of his problem solving approach.
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Problem 1.
Ammar is given 27 standard dice and asked to glue them together into a
larger 3 × 3 × 3 cube, so that the adjacent faces (i.e. the faces glued
together) have the same number of dots. What is the maximal number
of dots that Ammar can leave visible on the outside of his 3 × 3 × 3
cube?
Note: Two views of the standard dice are shown below. The faces are
arranged so that opposite sides add to 7.
[15]
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Problem 2.
A rectangle with sides of the length 3 and 4 is inscribed into a circle.
Moreover, four half – circles are glued to its sides from outside as in the
picture. What is the area of the shaded region, which consists of region
of the half – circles not lying inside the circle?
[15]
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Problem 3.
All the even numbers from 2 to 98 inclusive, excluding those ending in 0,
are multiplied together. What is the rightmost digit (the unit digit) in
this multiplication?
[15]
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Problem 4.
The numbers 1, 2, 3, . . . , 16 must be placed in the 16 squares in such a
way that the sum of the numbers in each of the four rows and columns
is the same. What is the smallest possible sum of the four numbers in
the corner squares?
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Problem 5.
In the figure shown, and are line segments each of length 2,
and . Arcs and are each one-sixth of a circle with
radius 2. What is the area of the region shown?
[15]
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Problem 6.
Salem drew a right triangle 𝐴𝐵𝐶 with a right angle at vertex 𝐵. The size
of the angle 𝐵𝐴𝐶 was 30 (in degree). Then he marked a midpoint of 𝐴𝐶
and named it M. Finally, he added a point 𝐷 on side 𝐴𝐵 such that
𝐵𝐷 = 𝐵𝐶. Find the size of the angle 𝐵𝑀𝐷 in degree.
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