Mathematics 11 past paper 2024

What is the period of $3 \sin\left(\frac{x}{5}\right)$?

MCQ1 marksannual

Simplify $z = \frac{(3+i)^3}{3-i}$ in the form $a+ib$ where $i=\sqrt{-1}$ and find the value of $|z|$.

Part B4 marksannual

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

Part C8 marksannual

What is the value of $\sin^{-1}\left(-\frac{1}{2}\right)$?

MCQ1 marksannual

Find row rank of $\begin{bmatrix} 1 & 2 & 3 & 2 \\ 4 & 2 & 1 & 3 \\ 5 & 2 & -1 & 2 \end{bmatrix}$.

Part B4 marksannual

If $\underline{a} = -10\underline{i} + 2\underline{j} + 4\underline{k}$ and $\underline{b} = \underline{i} - \underline{j} + 2\underline{k}$ then find a unit vector orthogonal to $…

Part C8 marksannual

What is the multiplicative inverse of $-i$?

MCQ1 marksannual

Solve the system of linear equations: \begin{aligned} (3-2i)x + (1+2i)y - 1 &= 0 \\ (3+2i)x - (1-2i)y - 1 &= 0 \end{aligned}

Part B4 marksannual

Use Gauss Jordan method to solve the system of linear equations: $x - 2y + z = 3; \quad 3x + 5y = 11; \quad 4y + 3z = 13$.

Part C8 marksannual

The real part of $\frac{1+7i}{3-4i}$ is:

MCQ1 marksannual

If $4^{\text{th}}$ and $10^{\text{th}}$ terms of a HP are $\frac{2}{15}$ and $\frac{2}{33}$ respectively, then find its $23^{\text{rd}}$ term.

Part B4 marksannual

If $y = \frac{1}{2(1!)}\left(\frac{1}{6}\right) + \frac{1.3}{4(2!)}\left(\frac{1}{6}\right)^2 + \frac{1.3.5}{8(3!)}\left(\frac{1}{6}\right)^3 + \dots$ then verify that $5y^2 + 10y…

Part C8 marksannual

If $A$ is a $2 \times 3$ matrix and $B$ is a $3 \times 2$ matrix, then the order of $AB$ is:

MCQ1 marksannual

If $A = \begin{bmatrix} 5 & 9 & 2 \\ 4 & 8 & 1 \\ 3 & 7 & 0 \end{bmatrix}$, then show that $(A+A')$ is symmetric.

Part B4 marksannual

Find point of intersection of the functions $f(x) = -x + 6$ and $g(x) = x^2 - 4x + 6$ graphically.

Part C8 marksannual

If $A = \begin{bmatrix} i & 0 & 0 \\ 0 & i & 0 \\ 0 & 0 & i \end{bmatrix}$, then which one in the options is $A^3$?

MCQ1 marksannual

For what value of $p$, vectors $3p\underline{i} + 11\underline{j} - 5\underline{k}$ and $2p\underline{i} + p\underline{j} + 2\underline{k}$ are mutually perpendicular?

Part B4 marksannual

Find general solution of a trigonometric equation $3 \cos x + 3 = 2 \sin^2 x$.

Part C8 marksannual

Find the volume of a tetrahedron with vertices $A(1,2,2), B(2,1,1), C(3,3,4)$ and $D(0,1,5)$.

Part B4 marksannual

Find maximum and minimum values of a function $f(x, y) = 2x + 3y$ subject to the constraints $x + 2y \leq 10, \quad 3x + y \leq 9, \quad 9x + 8y \leq 72, \quad x \geq 0, y \geq 0$.

Part C8 marksannual

What is the value of the determinant $\begin{vmatrix} 2 & 3 \\ 4 & 5 \end{vmatrix}$?

MCQ1 marksannual

Insert four A.Ms between 5 and 25.

Part B4 marksannual

Sketch the graph of $y = 2 \cos \frac{\theta}{2}$; $-\pi \leq \theta \leq \pi$.

Part C8 marksannual

What is the sum of the first 3 terms of the sequence $a_n = 2n$?

MCQ1 marksannual

If $2^{\text{nd}}$ and $6^{\text{th}}$ terms of a GP are 3 and $\frac{3}{4}$ respectively, find its $16^{\text{th}}$ term.

Part B4 marksannual

The sum of the series $\sum_{r=1}^n (2r-1)^2$ is:

MCQ1 marksannual

Sum to $n$-terms the series $1.5 + 2.6 + 3.7 + 4.8 + \dots$.

Part B4 marksannual

In how many ways 5 persons can be seated at a round table?

MCQ1 marksannual

How many 7-digit different numbers can be formed from the digits 5, 5, 6, 6, 9, 9, 9 using all of them, and how many of them are greater than 9,950,000?

Part B4 marksannual

What is the probability of drawing a King from a well shuffled pack of 52 playing cards?

MCQ1 marksannual

Prove that $1+4+7+\dots+(3n-2) = \frac{n(3n-1)}{2}$ by using mathematical induction.

Part B4 marksannual

What is the coefficient of $3^{rd}$ term in the expansion of $\left(x-\frac{1}{x}\right)^8$?

MCQ1 marksannual

For a real valued function $f(x) = \frac{5x-2}{x+2}, x \neq -2$ find $f^{-1}(x)$ and determine its domain and range.

Part B4 marksannual

Which one in the given options is true if $2^n > 2(n+1)$ for all $n \in \mathbb{Z}^+$?

MCQ1 marksannual

If $\cos \alpha = \frac{3}{5}, \sin \beta = \frac{5}{13}$ with $\frac{\pi}{2} < \beta < \pi$ and $\frac{3\pi}{2} < \alpha < 2\pi$, then find the value of $\sin(\alpha+\beta)$.

Part B4 marksannual

The graph of $y=x^4$ is symmetrical about:

MCQ1 marksannual

State number of diagonals of an $n$-sided polygon and find number of diagonals of a nine sided polygon.

Part B4 marksannual

($-1, -1$) is a solution of the inequality:

MCQ1 marksannual

Prove that $\sin 2\theta + \sin 4\theta + \sin 6\theta + \sin 8\theta = 4 \sin 5\theta \cos 2\theta \cos \theta$.

Part B4 marksannual

Which of the following options equates $\cos 196^\circ$?

MCQ1 marksannual

Find the equation of a parabola $y = ax^2 + bx + c$ that cuts $x$-axis at points $(-4,0), (4,0)$ and passes through a point $(0,8)$.

Part B4 marksannual

If $\cos \beta = \frac{3}{4}$, then value of $\cos 2\beta$ is:

MCQ1 marksannual

A pair of fair dice is thrown. The number of dots on the top are added. What is the probability of getting a sum greater than 9 or a sum divisible by 5?

Part B4 marksannual

Area of a triangle $\triangle ABC$ (with usual notations) where $a=2, b=3, \gamma=30^\circ$ is:

MCQ1 marksannual

Verify that $\cos^4 \theta = \frac{1}{8}(3 + 2 \cos 2\theta + \cos 4\theta)$.

Part B4 marksannual

What is the shadow length of a $\sqrt{3} \text{ m}$ high tree if the sun's elevation angle is $45^\circ$?

MCQ1 marksannual

Solve triangle $ABC$ with $\alpha = 31^\circ 5'$, $\beta = 50^\circ 55'$ and $c = 13 \text{ cm}$ using usual notations.

Part B4 marksannual

Find radii of the escribed circles of triangle $ABC$ opposite to the largest and smallest sides given that $a=13, b=10$ and $c=7$ (using usual notations).

Part B4 marksannual

Without drawing, guess the graph of $y = \sin \frac{\theta}{6}$ and find its period, frequency and amplitude.

Part B4 marksannual

Verify that $2S = 8R \cos \frac{\alpha}{2} \sin \frac{\beta}{2} \cos \frac{\gamma}{2}$, where $S$ is the area of a triangle, $R$ is the circumradius, and $\alpha$, $\beta$, $\gamma…

Part B4 marksannual

Verify that $\tan^{-1} \frac{3}{4} - \tan^{-1} \frac{4}{3} + 2 \tan^{-1} \frac{1}{7} = 0$.

Part B4 marksannual