 # SMO - Shine Mathematics Olympiad Exam - 2023-2024

## SMO - Shine Mathematics Olympiad

Shine Mathematics Olympiad is designed for grades 6th to 12th by Graposs Connect for Shine Olympiad. Mathematics as a discipline builds mental rigor in students and is also the foundation of academia. Mathematical literacy promotes understanding of other school subjects and also encourages quantitative reasoning and spatial ability.

Shine Mathematics Olympiad helps strengthen mental mathematical calculations in students which helps them be quicker and smarter at not only math but also holistically.

##### Available for classes 6th to 12th.
SYLLABUS AND OTHER DETAILS WATCH VIDEOS

## Syllabus & Marking scheme

#### Mathematics

###### Syllabus

Mathematical Thinking: Integers, Fractions and Decimals, Factors and Multiples LCM and HCF, Algebraic Expressions, Simplification; Application Mathematics: Fun with Numbers, Ratio, Proportion and Unitary Method, Geometrical Concept, Data Handling; Logical Thinking: Verbal Thinking, Non Verbal Thinking

###### Marking scheme
Section Number of Questions
Mathematical Thinking 20
Application Mathematics 10
Logical Thinking 15
Achiever’s Section 5
• The Olympiad exam will have a total of 50 questions as per the table above.
• 1 Mark shall be given for every correct answer.
• There shall be no Negative marking.
• Students shall be given 60 minutes to complete the test.
• Percentile Ranks shall be given to all students.
• Toppers shall be decided from the top percentile ranks on the basis of raw scores and time taken by the student to complete the exam.

#### Sample Questions

• a. 3, 5
• b. 11,13
• c. 5,7
• d. 17,23
###### Q.2 If the HCF of two numbers is 16 and their product is 3072 then their LCM is:
• a. 182
• b. 192
• c. 12
• d. None of these
###### Q.3 Choose the incorrect option:
• a. -8 < 8
• b. 0 < - 12
• c. -15 < - 5
• d. -386 < 308
• a. 1.2
• b. 0.12
• c. 0.012
• d. 1.02
• a. 99999
• b. 90009
• c. 98765
• d. 98009
###### Q.6 On a particular day the temperature of Delhi at 10.00 am was 13° C but by the midnight, it fell down to 6° C. The temperature of Mumbai at 10 am the same day was 18° C but fell down to 10° C by mid night. Which fall is greater?
• a. Delhi
• b. both are same
• c. Mumbai
• d. None of the above

#### Mathematics

###### Syllabus

Mathematical Thinking: Exponents and Powers, Algebraic Expression, Linear Equations, Perimeter and Area, Visualising solid shapes, Practical Geometry; Application Mathematics: Integers, Fractions and Decimals, Lines and Angles, The triangle and its Properties, Data Handling; Logical Thinking: Verbal Thinking, Non Verbal Thinking;

###### Marking scheme
Section Number of Questions
Mathematical Thinking 20
Application Mathematics 10
Logical Thinking 15
Achiever’s Section 5
• The Olympiad exam will have a total of 50 questions as per the table above.
• 1 Mark shall be given for every correct answer.
• There shall be no Negative marking.
• Students shall be given 60 minutes to complete the test.
• Percentile Ranks shall be given to all students.
• Toppers shall be decided from the top percentile ranks on the basis of raw scores and time taken by the student to complete the exam.

#### Sample Questions

• a. -9
• b. xyz
• c. xyz2
• d. -9xy
###### Q.2 a(b-c)+b(c-a)+c(a-b) is equal to
• a. ab+bc+ca
• b. 0
• c. 2(ab+bc+ca)
• d. none of these
• a. 5 cm
• b. 6 cm
• c. 7 cm
• d. 8 cm
###### Q.4 If P and Q are any two points on a circle, then the line segment PQ is called a
• a. radius of the circle
• b. diameter of the circle
• c. chord of the circle
• d. secant of the circle
• a. 40
• b. 60
• c. 80
• d. 96
• a. 30
• b. 33
• c. 36
• d. 45

#### Mathematics

###### Syllabus

Application Mathematics: Rational Number, Cube And Cube Roots, Linear Equation In One Variable, Understanding Quadrilaterals, Data Handling, Mensuration, Square And Square Roots, Exponents And Powers, Direct and Inverse, Proportions, Factorisation; Logical Thinking: Verbal Thinking, Non Verbal Thinking; Mathematical Thinking

###### Marking scheme
Section Number of Questions
Application Mathematics 10
Logical Thinking 15
Mathematical Thinking 20
Achiever’s Section 5
• The Olympiad exam will have a total of 50 questions as per the table above.
• 1 Mark shall be given for every correct answer.
• There shall be no Negative marking.
• Students shall be given 60 minutes to complete the test.
• Percentile Ranks shall be given to all students.
• Toppers shall be decided from the top percentile ranks on the basis of raw scores and time taken by the student to complete the exam.

#### Sample Questions

• a. 0
• b. 2
• c. 1
• d. 3
• a. 14
• b. 16
• c. 18
• d. 19
• a. 30
• b. 33
• c. 36
• d. 45
• a. 5
• b. 6
• c. 7
• d. 8
###### Q.5 If 5 is added to twice of a number it becomes 6, then the number is:
• a. 0.5
• b. 5
• c. 0.25
• d. None of these
• a. 25
• b. 10
• c. 15
• d. 20

#### Mathematics

###### Syllabus

Application Mathematics: Coordinate Geometry, Linear Equation in Two Variable, Lines And Angles, Triangles, Quadrilaterals, Areas of Parallelogram and Triangles, Circle, Surface Areas And Volume; Logical Thinking: Verbal Thinking, Non Verbal Thinking; Mathematical Thinking;

###### Marking scheme
Section Number of Questions
Application Mathematics 10
Logical Thinking 15
Mathematical Thinking 20
Achiever’s Section 5
• The Olympiad exam will have a total of 50 questions as per the table above.
• 1 Mark shall be given for every correct answer.
• There shall be no Negative marking.
• Students shall be given 60 minutes to complete the test.
• Percentile Ranks shall be given to all students.
• Toppers shall be decided from the top percentile ranks on the basis of raw scores and time taken by the student to complete the exam.

#### Sample Questions

• a. 30
• b. 33
• c. 36
• d. 45
• a. 9
• b. 8
• c. 6
• d. 7
• a. 6
• b. 3
• c. 2
• d. 12
###### Q.4- The sum of two numbers is 2490 and if 6.5% of one number is equal to 8.5% of the other, then numbers are-
• a. 1414, 1076
• b. 1411, 1079
• c. 1412, 1078
• d. None of these
###### Q.5- If 45% of a number is added to the another number, the first number becomes 135 times of the another number. What is the ratio of these two numbers?
• a. 8:7
• b. 3:2
• c. 7:8
• d. None of these
• a. 103
• b. 109
• c. 105
• d. 104

#### Mathematics

###### Syllabus

Application Mathematics: Similarity of Triangles, Coordinate Geometry, Circles, Area Related to Circles, Statistics; Logical Thinking: Verbal Thinking, Non Verbal Thinking; Mathematical Thinking: LCM and HCF, Polynomials, Pair of Linear Equations in two variables, Quadratic Equation, Arithmetic Progression, Trigonometry, Probability;

###### Marking scheme
Section Number of Questions
Application Mathematics 10
Logical Thinking 15
Mathematical Thinking 20
Achiever’s Section 5
• The Olympiad exam will have a total of 50 questions as per the table above.
• 1 Mark shall be given for every correct answer.
• There shall be no Negative marking.
• Students shall be given 60 minutes to complete the test.
• Percentile Ranks shall be given to all students.
• Toppers shall be decided from the top percentile ranks on the basis of raw scores and time taken by the student to complete the exam.

#### Sample Questions

###### Q.1- Pick the odd one out.
• a. 22, 16, 10, 4, ...
• b. -5, -3, -1, 1, ...
• c. -3, 3, -3, 3, 3, ...
• d. 3, 1, -1, -3, ...
• a. cos2A-1
• b. 2cos2A-1
• c. 2cos2A+1
• d. cos2A+1
• a. 0.13
• b. 0.38
• c. 0.63
• d. 0.37
• a. 25
• b. 32
• c. 26
• d. 13
• a. 124
• b. 129
• c. 127
• d. 305
• a. (2, 7)
• b. (-2, -7)
• c. (-7, 2)
• d. (7, -2)

#### Mathematics

###### Syllabus

Sets; Relations and Functions; Trigonometric Functions; Complex Numbers and Quadratic Equations; Linear Inequalities; Permutations and Combinations; Binomial Theorem; Sequence and Series; Straight Lines; Conic Sections; Introduction to Three Dimensional; Geometry; Limits and Derivatives; Mathematical Reasoning; Statistics; Probability;

###### Marking scheme
Section Number of Questions
Mathematics 50
• The Olympiad exam will have a total of 50 questions as per the table above.
• 1 Mark shall be given for every correct answer.
• There shall be no Negative marking.
• Students shall be given 60 minutes to complete the test.
• Percentile Ranks shall be given to all students.
• Toppers shall be decided from the top percentile ranks on the basis of raw scores and time taken by the student to complete the exam.

#### Sample Questions

• a. 4, 7
• b. 7, 4
• c. 4, 4
• d. 7, 7
###### Q.2- Let F1 be the set of parallelograms, F2 the set of rectangles, F3 the set of rhombuses, F4 the set of squares and F5 the set of trapeziums in a plane. Then F1 may be equal to:
• a. F2 ∩ F3
• b. F3 ∩ F4
• c. F2 ∪ F5
• d. F2 ∪ F3 ∪ F4 ∪ F1
###### Q.3- The domain and range of the function f given by f(x) = 2 - |x - 5| is:
• a. Domain = R+, Range = (-∞, 1]
• b. Domain = R, Range = (-∞, 2]
• c. Domain = R, Range = (-∞, 2)
• d. Domain = R+, Range = (-∞, 2]
• a. x = 0
• b. y = 0
• c. x ≠ 0
• d. x ≠ 0
• a. 3
• b. 2
• c. 6
• d. 4
###### Q.6- lf f(x) = ax + b, where a and b are integers, f(-1) = -5 and f(3) = 3, then a and b are equal to
• a. a = -3, b = -1
• b. a = 2, b = -3
• c. a = 0, b = 2
• d. a = 2, b = 3

#### Mathematics

###### Syllabus

Relations and Functions; Inverse Trigonometric; Function; Matrices; Determinants; Continuity and Differentiability; Application of Derivatives; Integrals; Application of Integrals; Differential Equations; Vector Algebra; Three Dimensional; Geometry; Linear Programming; Probability

###### Marking scheme
Section Number of Questions
Mathematics 50
• The Olympiad exam will have a total of 50 questions as per the table above.
• 1 Mark shall be given for every correct answer.
• There shall be no Negative marking.
• Students shall be given 60 minutes to complete the test.
• Percentile Ranks shall be given to all students.
• Toppers shall be decided from the top percentile ranks on the basis of raw scores and time taken by the student to complete the exam.

#### Sample Questions

###### Q.1- Consider the non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b. Then R is:
• a. symmetric but not transitive
• b. transitive but not symmetric
• c. neither symmetric nor transitive
• d. both symmetric and transitive
###### Q.2- The points at which the tangents to the curve y = x3 - I2x + 18 are parallel to X-axis are:
• a. (2, -2), (-2, -34)
• b. (2, 34), (-2, 0)
• c. (0, 34), (-2, 0)
• d. (2, 2), (-2, 34)
• a. 1
• b. 2
• c. 3
• d. 5
• a. 9
• b. 27
• c. 81
• d. 512
###### Q.5- If A and B are matrices of same order, then (AB'-BA') is a:
• a. skew symmetric matrix
• b. null matrix
• c. symmetric matrix
• d. unit matrix
###### Q.6- The function f(x) = tanx –x
• a. always increases
• b. always decreases
• c. never increases
• d. sometimes increases and sometimes decreases. #### Indian Language Chart

Language / Grade Class 6 Class 7 Class 8 Class 9 Class 10 Class 11 Class 12
English
Hindi
Bengali
Marathi
Gujarati
Tamil
Malayalam
Telugu
Odia

#### Register for Any Subject of Your Choice

Get ready for Shine National Olympiad with Practice tests and Progress reports.