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All Maths 11 papers

Class 11 · Past paper

Maths 11 past paper 2025

50 published questions in this index. The full practice view lets you work through them and track your own attempts.

18 MCQs32 written questionsPractise this paper

Question index

1
What are the multiplicative factors of $z^{2}+4z+5$?
MCQ1 marksannual
1
Solve the quadratic equation $3z^{2}+2z+2=0, z \in \mathbb{C}$ by completing the square method.
Part B4 marksannual
1
If $P(x)=2x^{3}+x^{2}-13x+6$, then: a) Verify that $(x+3)$ is a factor of $P(x)$. b) Factorize $P(x)$ using synthetic division. c) Find all the roots of $P(x)$. d) Write complete f…
Part C8 marksannual
2
The principal argument $(\theta)$ of the complex number $z=-1+i\sqrt{3}$ is:

This is a skimmable index, not a replacement for the study surface. Open the practice view to answer questions and use the linked study material.

Maths 11 Past Paper 2025 | Notely

MCQ1 marksannual

2

A triangular park has its three corners located at points $A(2,3,1)$, $B(5,7,2)$, and $C(1,4,3)$. Find the area of the park using the cross product of vectors.

Part B4 marksannual

2

If $\vec{a}=3\hat{i}-2\hat{j}+4\hat{k}$ and $\vec{b}=\hat{i}+2\hat{j}-\hat{k}$, then: (a) Find $\vec{a} \times \vec{b}$. (b) Find $(\vec{a} \times \vec{b}) \cdot \vec{a}$ and verif…

Part C8 marksannual

3

A system of linear equations is said to be **inconsistent** if it has:

MCQ1 marksannual

3

Verify that: $\sin \theta \cdot \sin \left(\frac{\pi}{3}-\theta\right) \cdot \sin \left(\frac{\pi}{3}+\theta\right) = \frac{1}{4} \sin 3\theta$

Part B4 marksannual

3

If $x$ is very small such that its square and higher powers can be neglected, then show that: $\frac{(16+4x)^{\frac{3}{4}}}{(4+x) \sqrt{9-6x}} \approx \frac{2}{3}+\frac{13x}{72}$

Part C8 marksannual

4

If $|A|$ is the determinant of a $3 \times 3$ matrix, then $|3A| = $

MCQ1 marksannual

4

Verify that: $\binom{n}{r} + \binom{n}{r-1} = \binom{n+1}{r}$

Part B4 marksannual

4

Verify the fundamental law of trigonometry: $\cos(\alpha - \beta) = \cos\alpha\cos\beta + \sin\alpha\sin\beta$ where $\alpha, \beta$ are real angles in standard position and $\alph…

Part C8 marksannual

5

In an arithmetic sequence, $a_{1}=5$ and $a_{15}=75$. What is the common difference?

MCQ1 marksannual

5

Find the value of $p$ such that vectors $\hat{i}+2\hat{j}+p\hat{k}$, $3\hat{i}+p\hat{j}+4\hat{k}$ and $2\hat{i}+3\hat{j}+4\hat{k}$ are coplanar.

Part B4 marksannual

5

Solve $x+2y-3z=4, 2x-3y+4z=5, 3x+4y-5z=6$ using the Gaussian elimination method.

Part C8 marksannual

6

If $\frac{1}{2}, \frac{1}{x}, \frac{1}{5}$ are in harmonic sequence then what is the value of $x$?

MCQ1 marksannual

6

Find the maximum and minimum values of the function $f(\theta) = \frac{1}{3+5 \cos (2\theta+\pi)}$

Part B4 marksannual

6

$y=3 \cos 2x; -\frac{\pi}{2} \leq x \leq \frac{\pi}{2}$ a) Make table of values for given interval. b) Draw the graph of the function for given interval.

Part C8 marksannual

7

What is the first term of an infinite geometric series whose sum is $10$, and common ratio $0.6$?

MCQ1 marksannual

7

If $P(x)=x^{4}-6x^{3}+11x^{2}-6x$, then: (a) Divide $P(x)$ by $(x-1)$ using synthetic division. (b) Solve the resulting depressed equation.

Part B4 marksannual

7

For an arithmetic-geometric series: $1+5\left(\frac{1}{2}\right)^{1}+9\left(\frac{1}{2}\right)^{2}+13\left(\frac{1}{2}\right)^{3}+\dots$ (a) Find general term of the series. (b) Su…

Part C8 marksannual

8

How many ways can a committee of $4$ people be chosen from a group of $6$?

MCQ1 marksannual

8

A harmonic sequence has $2^{\text{nd}}$ term $\frac{1}{6}$ and $4^{\text{th}}$ term $\frac{1}{12}$. Find general term of the sequence.

Part B4 marksannual

8

A company has $7$ engineers and $5$ managers. In how many ways can a project team of $5$ be selected if it includes: (a) $3$ engineers and $2$ managers? (b) $4$ engineers and $1$ m…

Part C8 marksannual

9

What is the middle term in the expansion of $(x+y)^{6}$?

MCQ1 marksannual

9

Without drawing graph find range, amplitude, period and frequency of the function $y=-4 \cos (7x-\pi)$

Part B4 marksannual

10

Find the term containing $x^{3}$ in the expansion of $(x+2)^{6}$.

Part B4 marksannual

11

If dot product of two vectors is zero then angle between them is:

MCQ1 marksannual

11

In an arithmetic sequence, the $5^{\text{th}}$ term is $15$, and the $12^{\text{th}}$ term is $50$. Find: a) Common difference and b) First term of the sequence.

Part B4 marksannual

12

If $\vec{a} \cdot (\vec{b} \times \vec{c})=12$ then volume of parallelepiped with $\vec{a}, \vec{b}$ and $\vec{c}$ as co-terminal edges is:

MCQ1 marksannual

12

Verify that: $\frac{1+\sin 2\theta+\cos 2\theta}{1+\sin 2\theta-\cos 2\theta} = \cot \theta$

Part B4 marksannual

13

A force $\vec{F}=2\hat{i}+\hat{j}+3\hat{k}$ moves an object from origin to $(2, -1, 1)$. The work done is:

MCQ1 marksannual

13

Verify that $\begin{vmatrix} 1 & a & a^{2} \\ 1 & b & b^{2} \\ 1 & c & c^{2} \end{vmatrix} = (b-a)(c-a)(c-b)$

Part B4 marksannual

14

If $\tan \theta = \frac{3}{4}$ with $\pi < \theta < \frac{3\pi}{2}$, find the exact values of (a) $\sin(\frac{\theta}{2})$ and (b) $\cos(\frac{\theta}{2})$ without using calculator…

Part B4 marksannual

15

If $\sin \theta = \frac{3}{5}$, then $\sin 2\theta = $

MCQ1 marksannual

15

A bouncing ball rebounds 80% of its previous height. If the ball is dropped from a height of 50 meters, find the total distance traveled by the ball before coming to rest.

Part B4 marksannual

16

If the graph of a function is symmetric about the origin (e.g. $\sin x$), what type of function is it?

MCQ1 marksannual

16

How many words can be formed by using the letters from the word "EDUCATION" such that all the vowels are never together?

Part B4 marksannual

17

The range of a trigonometric function $4 \sin 4x$ is:

MCQ1 marksannual

17

Use the principle of mathematical induction to prove that $1^{3}+2^{3}+3^{3}+\dots+n^{3} = \left(\frac{n(n+1)}{2}\right)^{2}$ for all $n \in \mathbb{N}$, $n \geq 1$.

Part B4 marksannual

18

The expression $\sin 75^{\circ} \cos 15^{\circ}$ is equivalent to:

MCQ1 marksannual

18

Find rank of the matrix $\begin{bmatrix} 1 & 1 & 0 & -2 \\ 2 & 0 & 2 & 2 \\ 4 & 1 & 3 & 1 \end{bmatrix}$

Part B4 marksannual

19

How many 5-letter words can be formed from the word 'MATHS' without repeating any letter?

MCQ1 marksannual

19

If $z_{1}=10(\cos 100^{\circ}+i \sin 100^{\circ})$ and $z_{2}=5(\cos 40^{\circ}+i \sin 40^{\circ})$, then find the following in polar form: (a) $z_{1} \cdot z_{2}$, (b) $\frac{z_{1…

Part B4 marksannual

20

In how many different ways can a player select $6$ numbers from a set of $49$ numbers in a lottery?

MCQ1 marksannual

20

A solar panel's sunlight reception is modeled as $P(\theta) = 100 \cos(3\theta - 90°)$, with $0° \leq \theta \leq 180°$. (a) Find angle for the maximum sunlight and the max sunligh…

Part B4 marksannual

21

A force $\vec{F}=6\hat{i}+8\hat{j}+4\hat{k}$ acts on an object. The object moves from $A(1,2,3)$ to point $B(4,6,5)$. (a) Find the displacement vector $\vec{d}$. (b) Calculate work…

Part B4 marksannual

22

If $P(x)=ax^{3}+bx^{2}+2x-1$, leaves remainder $5$ when divided by $(x-1)$ and leaves remainder $3$ when divided by $(x+1)$. Find values of $a$ and $b$ using remainder theorem.

Part B4 marksannual

23

Solve $x+y+z=3; y+z=2; z=2$ using Cramer's rule.

Part B4 marksannual

24

Use binomial theorem to approximate the value of $\sqrt{101} \times \sqrt{99}$ up to three places of decimal.

Part B4 marksannual