Masterstroke UP Board Mathematics (English) Class 10 Exam 2027 | Chapterwise Question Bank | Model Papers, MCQs

U.P. Board Class-10

(Academic Curriculum 2025-26)

Subject: Mathematics

 

Time: 3 Hours

 

This includes a 70-mark written exam and a 30-mark internal assessment at the school level. There will be project work. Minimum passing marks are 23 and 10, for a total of 33 marks.

 

No.	Unit	Marks
I)	Number System	05
II)	Algebra	18
III)	Co-ordinate Geometry	05
IV)	Geometry	10
V)	Trigonometry	12
VI)	Mensuration	10
VII)	Statistics and Probability	10
	Total	70
	Internal Assessment Work	30
	(Written 70 Marks + Internal Assessment Work 30 Marks)	100

 

Unit I: Number System                                                                                              (05 Marks)

• Real Numbers: Fundamental Theorem of Arithmetic with examples rounding off irrational numbers, verification of irrational numbers.

 

Unit II: Algebra                                                                                                         (18 Marks)

• Polynomials: Zeros of a polynomial. Relationship between coefficients and zeros of quadratic polynomials.

 

• Pair of Linear Equations in Two Variables: Solution of pair of linear equations in two variables algebraically:

1. By substitution,
2. By elimination.

 

• Quadratic Equations: Standard form of a quadratic equation ax² + bx + c = 0, (a ≠ 0). Solution of the quadratic equations (only real roots) by quadratic formula and factorization. Relationship between discriminant and nature of roots of quadratic equation. Application of quadratic equation in daily life and problems based on it. Problems related to day-to-day activities to be incorporated.

 

• Arithmetic Progressions: Derivation of standard results of finding the nth term and sum of first n terms. Problems related to day-to-day activities to be incorporated terms.

 

Unit III: Coordinate Geometry                                                                                 (05 Marks)

• Lines (In two-dimensions): Concepts of coordinate geometry, graphs of linear equations, distance formula, section formula (internal division).

 

Unit IV: Geometry                                                                                                     (10 Marks)

• Triangles: Definitions, examples, counter examples of similar triangles.

1. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
2. If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.

• If in two triangles, the corresponding angles are equal, their corresponding sides are proportional and the triangles are similar.

1. If the corresponding sides of two triangles are proportional, their corresponding angles are equal and the two triangles are similar.
2. If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are proportional, the two triangles are similar.

 

• Circles: Tangent of Circle, Point of Contact

1. The tangent at any point of a circle is perpendicular to the radius through the point of contact.
2. The lengths of tangents drawn from an external point to circle are equal.

 

 

Unit V: Trigonometry                                                                                                (12 Marks)

• Introduction to Trigonometry: Trigonometric ratios of an acute angle of a right-angled triangle. Trigonometric ratios of 0^° and 90^°. Values of the trigonometric ratios of (0°, 30°, 45°, 60°, 90°). Relationships between the ratios.

 

• Trigonometric Identities: Proof and applications of the identities sin²q + cos²q = 1, 1 + tan²q = sec²q, 1 + cot²q = cosec²q.

 

• Heights and Distances: Angle of elevation, Angle of depression Simple and believable problems on heights and distances (Problems should not involve more than two right triangles). Angles of elevation/depression should be only 30^°, 45^° and 60^°.

 

Unit VI: Mensuration                                                                                                 (10 Marks)

• Areas Related to Circles: Area of sectors and segments of a circle.

 

• Surface Areas and Volumes: Problems on finding surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres and right circular cylinders/cones.

 

Miscellaneous problems (problems related to combination of two different types of solids, not more than that).

 

Unit VII: Statistics and Probability                                                                           (10 Marks)

Statistics: Mean, median and mode of grouped data.

 

Probability: Classical definition of probability, Simple problems on single events.

 

Internal Assessment for the academic session 2025-26

 

1)       First Internal Assessment Examination (Exam + Project)	August month	5+5 marks
Project
(Get it prepared from the booklet titled “Traditional Mathematics Knowledge of India”)
2)       Second Internal Assessment Examination (Exam + Project)	December month	5+5 marks
3)       Four monthly examinations		10 marks
i)         First monthly examination (based on multiple-choice questions)		May month
ii)       Second monthly examination (based on descriptive questions)		July month
iii)      Third Monthly Examination (based on multiple-choice questions)		November month
iv)      Fourth Monthly Examination (based on descriptive questions)		December month