A-Level Calculus & Linear Algebra Mock Test – 50 Questions | Exam Practice PDF

Calculus & Linear Algebra – Mock Test (50 Questions) | MCQs + Problems | Exam Practice




Section 1: Multiple Choice Questions (25 Questions)

1. Evaluate limx→0 sinx x . A) 0 B) 1 C) Undefined D) ∞
2. Derivative of f (x) = x3 − 5x + 2 is: A) 3x^2 - 5 B) x^2 - 5 C) 3x^2 + 5 D) 3x^2 - 2
1
3. Evaluate ∫ (3x2 − 2x + 1)dx . A) 1 B) 4/3 C) 2 D) 5/3
0
∞
4. The series ∑n=1 1/n2 is: A) Divergent B) Convergent C) Oscillatory D) Undefined
1 2
=[ ] , det(A) = ? A) -2 B) -1 C) 2 D) 1
5.
For matrix A
3 4
6. Derivative of ln(x2 + 1) is: A) 2x/(x^2 +1) B) 1/(x^2 +1) C) ln(x^2+1) D) x/(x^2+1)
7. Integral of e3x dx is: A) e^{3x} + C B) 1/3 e^{3x} + C C) 3 e^{3x} + C D) ln|3x| + C
8. Limit: limx→∞ (1 + 1/x)x = ? A) 0 B) 1 C) e D) ∞
9. If u = (1, 2, 3) and v = (4, 0, −1) , u·v = ? A) 1 B) 1 C) 1 D) 1
2 1
Eigenvalues of [ ] are: A) 1,3 B) 0,3 C) 1,2 D) 2,3 11-25: (additional 15 MCQs covering Limits,
10.
1 2
Derivatives, Integrals, Series, Vectors & Matrices)

Section 2: Short Answer / Theory Questions (15 Questions)

1. State the Mean Value Theorem.
2. Define eigenvalues and eigenvectors.
∞
3. Determine whether the series ∑n=1 1/n converges.
4. Explain the difference between definite and indefinite integrals.
5. What is the rank of a matrix?
6. Explain convergence of a geometric series.
7. Define partial derivatives and provide an example.
8. State Rolle’s Theorem.
9. Explain the properties of determinants.
10. Define the gradient of a function. 11-15: (additional short answer questions on Calculus & Linear
Algebra)

Section 3: Problem-Solving / Numerical Questions (10 Questions)

1. Find d/dx(x4 − 3x2 + 2x − 5) .
2. Evaluate ∫ (3x2 − 2x + 1)dx .
3. Solve the system: 2x+y=5, x-y=1.
4. 1 2 3
Find the rank of matrix 4 5 6 .
7 8 9
3 1
Find eigenvalues of [ ] . 6-10: (additional 5 numerical problems on derivatives, integrals, linear
5.
1 3
systems, series sums)




1