KTU S1 Maths Question Paper with Questions and Answers

Kerala Technological University (KTU) S1 Mathematics is an essential subject for engineering students. It focuses on calculus, algebra, geometry, and differential equations. To help students excel, this guide provides various questions and detailed answers to enhance understanding and improve problem-solving skills for academic success.

Algebra Questions and Answers

Question
Solve the equation $3x+5=14$.

Answer
Subtract 5 from both sides: $3x=9$.
Divide by 3: $x=3$.

Question
If $a=2$ and $b=3$, evaluate a2+b2a^2 + b^2a2+b2.

Answer
a2+b2=22+32=4+9=13a^2 + b^2 = 2^2 + 3^2 = 4 + 9 = 13a2+b2=22+32=4+9=13.

Question
Find the roots of the quadratic equation x2−4x−5=0x^2 – 4x – 5 = 0x2−4x−5=0.

Answer
Factorize: $(x-5)(x+1)=0$.
Roots are $x=5$ and $x=-1$.

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

Answer
Expand: 2×2−8x+3x−12=2×2−5x−122x^2 – 8x + 3x – 12 = 2x^2 – 5x – 122x2−8x+3x−12=2x2−5x−12.

Question
If $x=3$, find the value of 2×3−x2+42x^3 – x^2 + 42x3−x2+4.

Answer
2(33)−(32)+4=54−9+4=492(3^3) – (3^2) + 4 = 54 – 9 + 4 = 492(33)−(32)+4=54−9+4=49.

Question
Solve for $x$: $2x+1=7$.

Answer
Subtract 1: $2x=6$.
Divide by 2: $x=3$.

Question
If $a=1$ and $b=-2$, compute (a+b)2(a + b)^2(a+b)2.

Answer
(1−2)2=(−1)2=1(1 – 2)^2 = (-1)^2 = 1(1−2)2=(−1)2=1.

Question
Find the determinant of [1234]\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}[13​24​].

Answer
Determinant = $1(4)-2(3)=4-6=-2$.

Question
Solve $4x-5=3x+7$.

Answer
Subtract $3x$ and add 5: $x=12$.

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

Answer
x2+4x+4x^2 + 4x + 4x2+4x+4.

Question
Find the value of $3x-2y$ when $x=4$ and $y=3$.

Answer
$3(4)-2(3)=12-6=6$.

Question
Simplify 5×2+3x−2×2+7x−15x^2 + 3x – 2x^2 + 7x – 15x2+3x−2x2+7x−1.

Answer
Combine like terms: 3×2+10x−13x^2 + 10x – 13x2+10x−1.

Question
Find $x$ if $7x-4=3x+8$.

Answer
$4x=12$, $x=3$.

Question
Evaluate $2(a+b)$ if $a=1$ and $b=2$.

Answer
$2(1+2)=2(3)=6$.

Question
Simplify $(x+y)(x-y)$.

Answer
x2−y2x^2 – y^2x2−y2.

Question
Find the inverse of [1234]\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}[13​24​].

Answer
Inverse = 1−2[4−2−31]=[−211.5−0.5]\frac{1}{-2} \begin{bmatrix} 4 & -2 \\ -3 & 1 \end{bmatrix} = \begin{bmatrix} -2 & 1 \\ 1.5 & -0.5 \end{bmatrix}−21​[4−3​−21​]=[−21.5​1−0.5​].

Question
Solve 5×2−20=05x^2 – 20 = 05x2−20=0.

Answer
x2=4x^2 = 4x2=4, $x=\pm 2$.

Question
If $x=1$, find x3−x+2x^3 – x + 2x3−x+2.

Answer
$1-1+2=2$.

Question
Simplify (2x+3)2−(x+1)2(2x + 3)^2 – (x + 1)^2(2x+3)2−(x+1)2.

Answer
Expand and simplify: 4×2+12x+9−x2−2x−1=3×2+10x+84x^2 + 12x + 9 – x^2 – 2x – 1 = 3x^2 + 10x + 84x2+12x+9−x2−2x−1=3x2+10x+8.

Calculus Questions and Answers

Question
Find the derivative of f(x)=x3+2×2−x+5f(x) = x^3 + 2x^2 – x + 5f(x)=x3+2x2−x+5.

Answer
f′(x)=3×2+4x−1f'(x) = 3x^2 + 4x – 1f′(x)=3x2+4x−1.

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Conclusion
KTU S1 Maths question papers are vital for strengthening core concepts in mathematics. This guide covers algebra, calculus, and geometry to prepare students effectively for exams, ensuring a solid grasp of fundamental mathematical principles.