**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

Q.1 | Q.2 | Q.3 | Q.4 | Q.5 | Q.6 | Q.7 | Q.8 | Q.9 | Q.10 |

Q.1 |
Two verticles of a triangle are (5, -1) and (-2, 3). If the orthocentre of the triangle is the origin, find the third vertex: |
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Q.2 |
How many 5-digit odd numbers can be formed using the digits 2, 3, 5, 7, 8, and 9 if every digit can occur at most once in any number? |
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Q.3 |
Find the values of a and b for which 3x |
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Q.4 |
To divide a line segment AB in the ratio 2: 5, first a ray AX is drawn, so that ∠BAX is an acute angle and then at equal distance points are marked on the ray AX such that the minimum number of these point is: |
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Q.5 |
Find the quadratic equation whose roots are reciprocal of the roots of the equation 3x |
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Q.6 |
A tower stands vertically on the ground. From a point on the ground which is 30 m away from the foot of a tower, the angle of elevation of the top of the tower is found to be 45⁰. Find the height of the tower: |
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Q.7 |
If sin A = √3/2 and A is an acute angle, then find the value of (tanA - cot A)/(√3 + cosec A): |
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Q.8 |
If [(x - a)/(b + c)] + [(x - b)/(c + a)] + [(x - c)/(a + b)] = 3, then find the value of x: |
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Q.9 |
The areas of two similar triangles are 81 cm |
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Q.10 |
In the adjoining figure, the bottom of the glass has a hemispherical raised portion. If the glass is filled with orange juice, then find the quantity of juice which a person will get: |
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**Sample PDF of CREST Mathematics Olympiad for Class 10:**

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Answers to Sample Questions from CREST Olympiads:

Q.1 : d | Q.2 : d | Q.3 : a | Q.4 : d | Q.5 : a | Q.6 : b | Q.7 : b | Q.8 : b | Q.9 : c | Q.10 : b