Section 1: Real Numbers, Polynomials, Pair of Linear Equations in Two Variables, Quadratic Equations, Arithmetic Progressions, Triangles, Coordinate Geometry, Introduction to Trigonometry, Some Applications of Trigonometry, Circles, Constructions, Areas Related to Circles, Surface Areas and Volumes, Statistics, Probability.
Achievers Section: Higher Order Thinking Questions - Syllabus as per Section 1
If 1/(a + b), 1/(b + c), and 1/(c + a) are in AP, then which of the following is true?
Q.2
In ∆ABC, ∠B = 90⁰. P, Q and R are the midpoints of AB, BC and AC, respectively. Which of the following options can be the vertices of a cyclic quadrilateral?
Q.3
f(x) = x4 - 2x3 + 3x2 - ax + b is a polynomial such that when it is divided by (x - 1) and (x + 1), the remainders are 5 and 19, respectively. Determine the remainder when f(x) is divided by (x - 2).
Q.4
The areas of two similar triangles are 81 cm2 and 49 cm2, respectively, then what will be the ratio of their corresponding medians?
Q.5
If α, β are the roots of the equation x2 - 2x + 3 = 0, then find the equation whose roots are 1/α2 and 1/β2.
Q.6
In the given figure, AB || DE and the area of the parallelogram ABFD is 24 cm2. Find the areas of triangles AFB, AGB, and AEB.
Q.7
Find the quadratic equation whose roots are reciprocal of the roots of the equation 3x2 - 20x + 17 = 0.
Q.8
The volume of a pyramid whose base is an equilateral triangle is 12 cm3. If the height of the pyramid is 3√3 cm, then find the length of each side of the base:
Q.9
If [(x - a)/(b + c)] + [(x - b)/(c + a)] + [(x - c)/(a + b)] = 3, then find the value of x:
Q.10
The angles of elevation of the top of a tower from two points at distances m and n metres are complementary. If the two points and the base of the tower are on the same straight line, then what will be the height of the tower?
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Answers to Sample Questions from CREST Olympiads:
Q.1
a
Q.2
b
Q.3
b
Q.4
c
Q.5
b
Q.6
b
Q.7
a
Q.8
c
Q.9
b
Q.10
a
Practicing sample papers for CREST Mathematics Olympiad for class 10 is the best means to top the scoreboard in the examination. Sample papers are curated in such a way that it enables kids to have a closer look into the pattern & type of questions they will be encountered during the paper. All the questions asked in class 10 CMO are multiple-choice questions. Candidates should answer all questions in the exam as CREST Olympiads do not follow negative markings. Students by practicing Maths Olympiad previous years’ question papers for class 10 learn to manage time and able to analyze their preparation. The CREST Mathematics Olympiad sample papers are available on the website for easy access and free download.
Answers to Sample Questions from CREST Olympiads:
Q.1 : a | Q.2 : b | Q.3 : b | Q.4 : c | Q.5 : b | Q.6 : b | Q.7 : a | Q.8 : c | Q.9 : b | Q.10 : a
