Free Practice Questions for UPMSP High School Mathematics

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Key Facts: UPMSP High School Mathematics Exam

928

UPMSP High School subject code for Mathematics

UPMSP subject directory / Board_Syllabus.aspx

70 + 30

Common Theory + Internal full marks pattern (total 100)

UPMSP Class 10 subject syllabi (e.g., Science, English PDFs)

3 h 15 m

Typical theory paper duration (confirm subject scheme)

UPMSP High School examination practice

33%

Common minimum pass threshold under UPMSP rules

Widely published UPMSP High School pass criteria (confirm circular)

6 subjects

High School candidates offer five compulsory + one optional subject

UPMSP High School subject combination rules PDF

MCQ study aid

Local bank adapts knowledge to four-option MCQs; official paper is mixed format

OpenExamPrep assessment-format policy

UPMSP High School (Class 10) Mathematics (code 928): mixed board paper, commonly Theory 70 + Internal 30 = 100, ~3h15m. Pass about 33% per UPMSP rules. Fee as per board notification. Free English MCQ study aid — not a full mixed-paper simulation.

Sample UPMSP High School Mathematics Practice Questions

Try these sample questions to review concepts for the UPMSP High School Mathematics exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Using Euclid's division algorithm, the HCF of 135 and 225 is:

A.15

B.45

C.75

D.90

Explanation: 225 = 135 × 1 + 90; 135 = 90 × 1 + 45; 90 = 45 × 2 + 0. The last non-zero remainder is 45, so HCF(135, 225) = 45.

2If HCF(a, b) = 12 and a × b = 1800, then LCM(a, b) equals:

A.120

B.150

C.180

D.1500

Explanation: For positive integers, HCF(a, b) × LCM(a, b) = a × b. Therefore LCM(a, b) = 1800 ÷ 12 = 150.

3The LCM of 12, 18 and 24 is:

A.36

B.48

C.72

D.96

Explanation: Prime factors: 12 = 2² × 3, 18 = 2 × 3², 24 = 2³ × 3. LCM takes highest powers: 2³ × 3² = 8 × 9 = 72.

4Which of the following is an irrational number?

A.√(16/25)

B.√49 − √9

C.√2 + √8

D.√(9/4)

Explanation: √2 + √8 = √2 + 2√2 = 3√2, which is irrational. √(16/25) = 4/5, √49 − √9 = 4, and √(9/4) = 3/2 are all rational.

5If p and q are distinct primes, then HCF(p³q, pq²) is:

A.pq

B.p³q²

C.p³q

D.pq²

Explanation: p³q = p³ × q¹ and pq² = p¹ × q². HCF takes the lowest powers of each prime: p¹q¹ = pq.

6If one zero of the polynomial 2x² − 5x + k is 2, then k equals:

A.2

B.4

C.6

D.8

Explanation: If x = 2 is a zero, 2(2)² − 5(2) + k = 0 → 8 − 10 + k = 0 → k = 2.

7For the quadratic polynomial x² − 5x + 6, the sum of zeros is:

A.−5

B.5

C.6

D.−6

Explanation: For ax² + bx + c, sum of zeros = −b/a. Here a = 1, b = −5, so sum = −(−5)/1 = 5. (Zeros are 2 and 3.)

8The product of the zeros of 3x² − 5x − 2 is:

A.−2/3

B.2/3

C.5/3

D.−5/3

Explanation: Product of zeros = c/a = −2/3.

9If the zeros of the polynomial x² − kx + 6 are in the ratio 1 : 2, then k equals:

A.√6

B.3√2

C.3√3

D.√18

Explanation: Let zeros be α and 2α. Product α·2α = 6 ⇒ 2α² = 6 ⇒ α² = 3 ⇒ α = √3 (positive). Sum k = α + 2α = 3α = 3√3.

10A cubic polynomial with zeros −1, 1 and 2 is:

A.x³ − 2x² − x + 2

B.x³ + 2x² − x − 2

C.x³ − 2x² + x + 2

D.x³ − x² − 2x + 2

Explanation: Polynomial = (x + 1)(x − 1)(x − 2) = (x² − 1)(x − 2) = x³ − 2x² − x + 2.

About the UPMSP High School Mathematics Exam

The Uttar Pradesh UPMSP High School (Class 10) Mathematics examination (subject code 928) is conducted by Uttar Pradesh Madhyamik Shiksha Parishad (UPMSP), Prayagraj. Official Board Syllabus pages on upmsp.edu.in list Class 9/10 PDFs for code 928. High School candidates offer six subjects under the published subject-combination rules (five compulsory + one optional). Common full-marks pattern is Theory 70 + Internal/Practical/Project 30 = 100 with approximately 3 hours 15 minutes for the theory paper (confirm the subject PDF). Official delivery commonly Hindi/English. Bank must include genuine calculation items. Aligned to UPMSP Class 10 Mathematics units (number systems through statistics/probability). Focus: Class 10 mathematics with genuine numeric MCQs across algebra, geometry, trigonometry, mensuration, and statistics. The 100 questions on this page are an English-language MCQ study adaptation for concept drills and self-assessment.

Exam sponsor: Uttar Pradesh Madhyamik Shiksha Parishad (UPMSP). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Official UPMSP High School mixed written theory paper (objective and constructed-response items as per subject design) with common Theory 70 + Internal 30 = 100 full marks pattern for many Class 10 subjects, duration typically 3 hours 15 minutes. Local bank: English-language four-option MCQ study adaptation with explanations — not a full mixed-paper simulation or official-format substitute. Subject code 928. Official delivery commonly Hindi/English. Bank must include genuine calculation items. Aligned to UPMSP Class 10 Mathematics units (number systems through statistics/probability). Subject code 928.

Time Limit

3 hours 15 minutes (typical UPMSP High School theory paper; confirm current scheme for the subject)

Passing Score

Minimum 33% marks in the subject (commonly 33/100 combined theory + internal/practical as applicable); for theory+internal schemes, school sources often cite minimum 23/70 theory and 10/30 internal — confirm current UPMSP regulations/circulars.

Exam / Certification Fees

As per UPMSP High School examination fee notification for school (institutional) and private candidates for the current examination year on upmsp.edu.in / prereg.upmsp.edu.in — confirm the latest circular; subject papers are not separately priced on this page. Class 9/11 advance registration fee of INR 50 per student is a separate pre-registration charge, not the High School exam form fee.

Exam sponsor website

Reported exam pass rate: See UPMSP High School results for the current cycle on results.upmsp.edu.in.. Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Official sources

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

28%

Number systems & algebra

Real numbers, polynomials, linear equations, quadratic equations, AP.

18%

Geometry & constructions concepts

Triangles, circles, constructions concepts.

16%

Trigonometry

Ratios, identities, heights and distances.

16%

Mensuration

Areas related to circles; surface areas and volumes.

22%

Statistics, probability & coordinate geometry

Mean/median/mode, probability, coordinate geometry.

Preparing for the UPMSP High School Mathematics Exam

What You Need to Know

Passing score: Minimum 33% marks in the subject (commonly 33/100 combined theory + internal/practical as applicable); for theory+internal schemes, school sources often cite minimum 23/70 theory and 10/30 internal — confirm current UPMSP regulations/circulars.
Assessment: Official UPMSP High School mixed written theory paper (objective and constructed-response items as per subject design) with common Theory 70 + Internal 30 = 100 full marks pattern for many Class 10 subjects, duration typically 3 hours 15 minutes. Local bank: English-language four-option MCQ study adaptation with explanations — not a full mixed-paper simulation or official-format substitute. Subject code 928. Official delivery commonly Hindi/English. Bank must include genuine calculation items. Aligned to UPMSP Class 10 Mathematics units (number systems through statistics/probability). Subject code 928.
Time limit: 3 hours 15 minutes (typical UPMSP High School theory paper; confirm current scheme for the subject)
Exam / certification fees: As per UPMSP High School examination fee notification for school (institutional) and private candidates for the current examination year on upmsp.edu.in / prereg.upmsp.edu.in — confirm the latest circular; subject papers are not separately priced on this page. Class 9/11 advance registration fee of INR 50 per student is a separate pre-registration charge, not the High School exam form fee. Official sources

Using Our Practice Resources

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UPMSP High School Mathematics: Suggested Study Strategy

1Map every practice session to the official UPMSP Class 10 Mathematics (code 928) syllabus PDF.

2After MCQ drills, write full answers from UPMSP-style model papers under timed conditions.

3Verify facts against UPMSP-prescribed textbooks and official PDFs before trusting third-party summaries.

4Track weak categories and re-attempt missed items after 48 hours.

5Complete internal assessment and any practical/performance components required by the school/board.

Frequently Asked Questions

Is the official UPMSP High School Mathematics exam multiple-choice only?

No. Official UPMSP papers mix objective and constructed-response tasks, with internal/practical components as applicable. The 100 questions here are an English-language MCQ study adaptation for concept practice only.

What are full marks and duration for UPMSP Mathematics?

Many UPMSP Class 10 subjects use Theory 70 + Internal/Practical/Project 30 = 100 with a theory paper of about 3 hours 15 minutes. Confirm the exact scheme for code 928 in the Class 10 PDF on https://www.upmsp.edu.in/Board_Syllabus.aspx.

What is the passing score?

How much does the exam cost?

Where is the official syllabus?

Class 9 and Class 10 subject PDFs including code 928 are linked from https://www.upmsp.edu.in/Board_Syllabus.aspx on the UPMSP website.

Is this bank an official UPMSP translation?

No. OpenExamPrep publishes one English-language practice bank per exam ID. Target-language terms and texts may appear when integral to the skill, but stems, explanations, and SEO copy are English study adaptations — not official translations or language-environment simulations.

How should I use MCQs for a mixed written/practical paper?

Use MCQs for daily concept drills and self-check. Also practise full written answers from UPMSP model papers and complete required practical/project work under school guidance.