BPSC TRE Maths Questions: Class 9-10 Solved Practice Set

If little time is left before BPSC TRE 4.0 and you are managing your study with a job or family duties, these BPSC TRE maths questions for Class 9-10 are made for you. This set gives you important, exam-level problems with full step-by-step solutions across Coordinate Geometry, Geometry, Trigonometry, Mensuration, Polynomials, Linear Equations, Quadratic Equations, Probability and Higher Mathematics — try each one yourself first, then check the solution.

This practice set is for every BPSC TRE 4.0 (Class 9-10) Mathematics aspirant — whether this is your first attempt or you are trying again after a near miss. Use it the honest way: attempt a question on paper before you look down, note where you got stuck, and only then read the worked solution to see the exact step you missed.

How should you use these BPSC TRE maths questions?

• Attempt first, then check. Solve on paper before reading the solution — this shows your real gaps, not just what you can follow.
• Time yourself. Give each question about a minute; if you cross two minutes, mark it and move on, just like in the real paper.
• Mark your weak topics. If Trigonometry or Mensuration keeps tripping you, write it down and revise that chapter the same day.
• Finish with a full test. After this set, try a full-length paper to build exam stamina.

Here is your step for today: attempt all the questions below, mark the two topics that felt hardest, and then take the free BPSC TRE Class 9-10 Maths full mock test to see how you do under time. When you are ready for more, the full BPSC TRE 4.0 Class 9-10 Maths mock test series has 80 tests and 2,772 questions for just ₹99.

<h2>BPSC TRE Maths Questions with Step-by-step Solutions (Class 9-10)</h2>

Quadratic Equations

1. What is the discriminant of 5x² − 3x + 6 = 0?

   • (A) −111
   • (B) 129
   • (C) −123
   • (D) 111

   Answer: (A) −111

   Explanation: D = b² − 4ac = 9 − (120) = −111.

2. What are the roots of the equation x² − 9x + 14 = 0?

   • (A) 2 and 7
   • (B) −2 and 7
   • (C) −7 and 2
   • (D) −7 and −2

   Answer: (A) 2 and 7

   Explanation: Factorising: (x − 7)(x − 2) = 0.

Probability

1. 2 coins are tossed together. What is the probability of getting at least one head?

   • (A) 7/4
   • (B) 1/2
   • (C) 3/4
   • (D) 1/4

   Answer: (C) 3/4

   Explanation: P = 1 − P(no head) = 1 − 1/4 = 3/4.

Geometry

1. The diagonals of a rhombus are:

   • (A) Always equal
   • (B) Parallel
   • (C) Not intersecting
   • (D) Perpendicular bisectors of each other

   Answer: (D) Perpendicular bisectors of each other

   Explanation: They bisect each other at right angles.

Trigonometry

1. What is the value of 3 sec² 45° − 4 cos 0°?

   • (A) 3
   • (B) 1
   • (C) 10
   • (D) 2

   Answer: (D) 2

   Explanation: sec² 45° = 2, cos 0° = 1; value = 2.

Linear Equations

1. Solve: 5x + 4y = −21 and 6x + 2y = −14.

   • (A) x = −1, y = 4
   • (B) x = −1, y = −4
   • (C) x = 1, y = −4
   • (D) x = −4, y = −1

   Answer: (B) x = −1, y = −4

   Explanation: Solving by elimination gives x = −1, y = −4; check: 5(−1) + 4(−4) = −21.

Polynomials

1. Which quadratic polynomial has zeros 3 and 6?

   • (A) x² + 9x − 18
   • (B) x² − 9x + 18
   • (C) x² − 9x − 18
   • (D) x² + 9x + 18

   Answer: (B) x² − 9x + 18

   Explanation: x² − (sum)x + product = x² − (9)x + (18).

Mensuration

1. What is the total surface area of a closed cylinder of radius 14 cm and height 7 cm? (π = 22/7)

   • (A) 616 cm²
   • (B) 4312 cm²
   • (C) 1848 cm²
   • (D) 1232 cm²

   Answer: (C) 1848 cm²

   Explanation: TSA = 2πr(r + h) = 2 × 22/7 × 14 × 21 = 1848 cm².

Coordinate Geometry

1. What is the centroid of the triangle with vertices (4, 4), (−7, 8) and (−6, 6)?

   • (A) (−3, 6)
   • (B) (6, −3)
   • (C) (−2, 6)
   • (D) (−9, 18)

   Answer: (A) (−3, 6)

   Explanation: Centroid = ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3) = (−3, 6).

Higher Mathematics

1. The distance of the point (x, y) from the origin is:

   • (A) √(x² + y²)
   • (B) x² + y²
   • (C) x + y
   • (D) √(x + y)

   Answer: (A) √(x² + y²)

   Explanation: Distance formula with (0, 0).

Take a full mock test

Start with the free mock test: Full Mock Test 1 — timed, with your score and analysis right away.

These questions come from SeatBeat's reviewed question bank. For full preparation, see the test series: BPSC TRE 4.0 (Class 9-10) Mathematics Mock Test Series

Frequently asked questions

Is Class 9-10 maths important for BPSC TRE 4.0?

Yes. In the BPSC TRE 4.0 (Class 9-10) Mathematics paper, the maths section carries real weight, so strong Class 9-10 concepts directly improve your score. Practising topic-wise questions like these is the fastest way to build that base.

Which maths topics are most important for BPSC TRE?

Focus on Coordinate Geometry, Geometry, Trigonometry, Mensuration, Polynomials, Linear Equations, Quadratic Equations, Probability and Higher Mathematics. These are the core Class 9-10 areas this set covers, so spread your revision across all of them instead of one or two.

Is there a free BPSC TRE maths mock test?

Yes. You can take the free <a href="/test-series/bpsc-tre-4-class-9-10-maths-mock-test/full-mock-test-1">Full Mock Test 1</a> before buying anything, so you can judge the level and your own speed first.

How many questions should I practise for BPSC TRE maths?

Practise as many fresh questions as you can under time. The full BPSC TRE 4.0 Class 9-10 Maths series gives you 2,772 questions across 80 tests, which is enough to cover every topic several times.

Can I prepare for BPSC TRE maths with a full-time job?

Yes, if you study in small daily blocks. Solve a few timed questions each day, check the solutions the same evening, and take one full mock on your weekly off — steady practice beats long gaps.