10th Maths Quarterly Question Paper 2023 Questions

The 10th Maths Quarterly Question Paper 2023 is designed to cover various topics students have studied during their academic year. This guide includes all types of questions and answers like multiple-choice, short answers, long answers, and word problems to help students understand and prepare better.

Algebra Questions and Answers

Question: Solve the equation: $3x+5=20$.

Answer: $x=5$.

Question: Find the value of $x$ if $2x-7=15$.

Answer: $x=11$.

Question: Factorize x2−9x^2 – 9x2−9.

Answer: $(x+3)(x-3)$.

Question: Expand $(x+2)(x-4)$.

Answer: x2−2x−8x^2 – 2x – 8x2−2x−8.

Question: If $y=3x+2$, find $y$ when $x=4$.

Answer: $y=14$.

Question: Simplify $2(x+3)+4(x-1)$.

Answer: $6x+2$.

Question: Solve: $5x-3=2x+12$.

Answer: $x=5$.

Question: If x2+7x+10=0x^2 + 7x + 10 = 0x2+7x+10=0, find the roots.

Answer: $x=-2,x=-5$.

Question: Simplify: $(2x+3)(x-1)$.

Answer: 2×2+x−32x^2 + x – 32x2+x−3.

Question: Solve: $4x+5=2x+15$.

Answer: $x=5$.

Question: Find the product of $(x+1)(x+6)$.

Answer: x2+7x+6x^2 + 7x + 6x2+7x+6.

Question: Simplify $3x+4x-2$.

Answer: $7x-2$.

Question: Solve: $6x-5=19$.

Answer: $x=4$.

Question: Factorize x2+5x+6x^2 + 5x + 6x2+5x+6.

Answer: $(x+2)(x+3)$.

Question: Expand (x+4)2(x + 4)^2(x+4)2.

Answer: x2+8x+16x^2 + 8x + 16x2+8x+16.

Question: If $x-2=5$, find $x$.

Answer: $x=7$.

Question: Simplify $(3x+4)-(2x-5)$.

Answer: $x+9$.

Question: Solve for $x$: $2x+3=x+7$.

Answer: $x=4$.

Question: If x2=49x^2 = 49x2=49, find $x$.

Answer: $x=7$ or $x=-7$.

Geometry Questions and Answers

Question: Find the area of a triangle with base $10$ cm and height $8$ cm.

Answer: Area = $40$ cm².

Question: Calculate the circumference of a circle with radius $7$ cm.

Answer: Circumference = $44$ cm.

Question: Find the length of the hypotenuse of a right triangle with legs $3$ cm and $4$ cm.

Answer: Hypotenuse = $5$ cm.

Question: If the perimeter of a rectangle is $20$ cm and its length is $6$ cm, find its width.

Answer: Width = $4$ cm.

Question: Calculate the volume of a cube with side $5$ cm.

Answer: Volume = $125$ cm³.

Question: Find the area of a circle with radius $3$ cm.

Answer: Area = $28.26$ cm².

Question: If a triangle has sides of $6$, $8$, and $10$ cm, find its perimeter.

Answer: Perimeter = $24$ cm.

Question: Find the surface area of a sphere with radius $7$ cm.

Answer: Surface area = $616$ cm².

Question: If the diagonal of a square is 10210\sqrt{2}102​ cm, find its side.

Answer: Side = $10$ cm.

Question: Calculate the area of a trapezium with bases $6$ cm and $8$ cm, and height $5$ cm.

Answer: Area = $35$ cm².

Question: Find the area of a parallelogram with base $12$ cm and height $7$ cm.

Answer: Area = $84$ cm².

Question: If the side of an equilateral triangle is $6$ cm, find its area.

Answer: Area = $15.59$ cm².

Question: Calculate the total surface area of a cylinder with radius $4$ cm and height $7$ cm.

Answer: Total surface area = $277.44$ cm².

Question: Find the volume of a cone with base radius $3$ cm and height $5$ cm.

Answer: Volume = $47.1$ cm³.

Question: If the radius of a hemisphere is $6$ cm, find its volume.

Answer: Volume = $452.16$ cm³.

Question: Calculate the area of a sector of a circle with radius $5$ cm and angle 60∘60^\circ60∘.

Answer: Area = $13.09$ cm².

Question: If the perimeter of a square is $16$ cm, find its area.

Answer: Area = $16$ cm².

Question: Find the slant height of a cone with radius $4$ cm and height $3$ cm.

Answer: Slant height = $5$ cm.

Question: Calculate the area of a rhombus with diagonals $6$ cm and $8$ cm.

Answer: Area = $24$ cm².

Trigonometry Questions and Answers

Question: Find sin⁡30∘\sin 30^\circsin30∘.

Answer: sin⁡30∘=0.5\sin 30^\circ = 0.5sin30∘=0.5.

Question: Calculate cos⁡60∘\cos 60^\circcos60∘.

Answer: cos⁡60∘=0.5\cos 60^\circ = 0.5cos60∘=0.5.

Question: Find tan⁡45∘\tan 45^\circtan45∘.

Answer: tan⁡45∘=1\tan 45^\circ = 1tan45∘=1.

Question: If $\sin A=0.6$, find $\cos A$.

Answer: $\cos A=0.8$.

Question: Simplify sin⁡2A+cos⁡2A\sin^2 A + \cos^2 Asin2A+cos2A.

Answer: $1$.

Question: Find the value of tan⁡30∘\tan 30^\circtan30∘.

Answer: tan⁡30∘=0.577\tan 30^\circ = 0.577tan30∘=0.577.

Question: Calculate sec⁡0∘\sec 0^\circsec0∘.

Answer: sec⁡0∘=1\sec 0^\circ = 1sec0∘=1.

Question: If $\cot A=1$, find $\tan A$.

Answer: $\tan A=1$.

Question: Simplify sec⁡2A−tan⁡2A\sec^2 A – \tan^2 Asec2A−tan2A.

Answer: $1$.

Question: Find cosec⁡90∘\cosec 90^\circcosec90∘.

Answer: cosec⁡90∘=1\cosec 90^\circ = 1cosec90∘=1.

Question: Calculate sin⁡90∘−cos⁡90∘\sin 90^\circ – \cos 90^\circsin90∘−cos90∘.

Answer: $1$.

Question: If $\tan A=3/4$, find $\sin A$.

Answer: $\sin A=3/5$.

Question: Simplify 1+tan⁡2A1 + \tan^2 A1+tan2A.

Answer: sec⁡2A\sec^2 Asec2A.

Question: Find the value of cos⁡245∘\cos^2 45^\circcos245∘.

Answer: $0.5$.

Question: If $\sin A=0.8$, find $\tan A$.

Answer: $\tan A=4/3$.

Question: Simplify 1−sin⁡2A1 – \sin^2 A1−sin2A.

Answer: cos⁡2A\cos^2 Acos2A.

Question: Find cot⁡45∘\cot 45^\circcot45∘.

Answer: $1$.

Question: Calculate tan⁡230∘+sec⁡60∘\tan^2 30^\circ + \sec 60^\circtan230∘+sec60∘.

Answer: $1.577$.

Question: Simplify cot⁡2A−cosec⁡2A\cot^2 A – \cosec^2 Acot2A−cosec2A.

Answer: $-1$.

The paper also includes short answer questions, graphs, and reasoning problems. Each topic is essential for scoring well.

The preparation for the 10th Maths Quarterly Question Paper 2023 requires understanding concepts and solving various types of questions to build confidence. Practice ensures success!