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Maths 11 Past Paper 2023 | Notely

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All Maths 11 papers

Class 11 · Past paper

Maths 11 past paper 2023

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

14 MCQs22 written questionsPractise this paper

Question index

1
The multiplicative inverse of $-i$ is:
MCQ1 marksannual
1
If $Z_1 = 2 + 3i$ and $Z_2 = 4 + 2i$, then show that $(Z_1 \overline{Z_2} + \overline{Z_1} Z_2)$ is a real number.
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1
Use Cramer's rule to solve the system of linear equations: $x+y-z=3$; $2x-y-z=1$; $3x+y+2z=0$.
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2
What is the modulus of a complex number $(8-15i)$?

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.

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2

Construct a truth table of a logical statement $(p \leftrightarrow q) \wedge (p \rightarrow q)$.

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2

If three consecutive numbers in an arithmetic progression are increased by 1, 2 and 3 respectively, the resulting numbers are in geometric progression. Find the original numbers if…

Part C8 marksannual

3

The contrapositive of a conditional $p \rightarrow q$ is:

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3

Solve for $x$: $\begin{vmatrix} x & -1 \\ 5 & 1-x \end{vmatrix} = \begin{vmatrix} 1 & 0 & -3 \\ 2 & x & -6 \\ 1 & 3 & x-5 \end{vmatrix}$.

Part B4 marksannual

3

If $y = \frac{1}{4} + \frac{1 \cdot 3}{4 \cdot 8} + \frac{1 \cdot 3 \cdot 5}{4 \cdot 8 \cdot 12} + \dots$ then prove that $y^2 + 2y - 1 = 0$.

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4

Which structure in the following is true for the set of natural numbers under multiplication?

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4

If $\alpha, \beta$ are the roots of $x^2 + px + q = 0$, find the quadratic equation whose roots are $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$.

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4

Without using calculator, prove that $\cos 10^\circ \cdot \cos 30^\circ \cos 50^\circ \cdot \cos 70^\circ = \frac{3}{16}$.

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5

Identify the correct matrix representation from the options provided.

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5

Using properties of the cube roots of unity, verify that $(1+\omega) + (1+\omega)^2 + (1+\omega)^3 = 2\omega$.

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5

Solve the following system of equations: $5x^2 - 14xy + 9y^2 = 0$; $4x^2 - 3xy - 16 = 0$.

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6

Rank of matrix $\begin{bmatrix} -2 \\ 0 \\ -1 \end{bmatrix}$ is:

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6

Express $\frac{125 + 4x - 9x^2}{(x-1)(x+3)(x+4)}$ in partial fractions.

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6

Solve triangles $\triangle ABC$ (with usual notations) if: (a) $\alpha = 60^\circ, \beta = 15^\circ$ and $b = 33$ (b) $b = 23, c = 24$ and $\alpha = 75^\circ$

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7

Second term of a geometric sequence is 9 and its fourth term is 1. Find sum to infinity.

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8

One of the multiplicative factors of $(x^4 - 5x^2 + 4)$ is:

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8

Insert six arithmetic means between 15 and -13.

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9

Which one of the following represents $\frac{x^3 + 2x^2 + 3}{(x^2 + 1)(x + 4)}$?

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9

Prove that Sine is a periodic function and its period is $2\pi$.

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10

For what value of $x$, the numbers $\frac{1}{2}, \frac{1}{5}, \frac{1}{x}$ are in harmonic progression?

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10

A die is thrown twice. Find the probability that the sum of the upper face numbers is a prime number or an odd number.

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11

If $\binom{n}{8} = \binom{n}{12}$, then value of $n$ is:

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11

Find the value of $k$, if the constant term in the expansion of $(2x^2 + \frac{k}{x})^6$ is 960.

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12

If $\cos \theta = \frac{\sqrt{10}}{10}$ with $2\pi < \theta < \frac{5\pi}{2}$, then find values of the remaining five trigonometric ratios.

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13

The coefficient of the third term in the expansion of $(x - \frac{1}{x})^8$ is:

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13

Verify that: $\cos 4x \cos x - \sin 6x \sin 3x = \cos 7x \cos 2x$.

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14

In which quadrant does the terminal side of the angle $-510°$ lie?

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14

In an oblique triangle $\triangle ABC$ (with usual notations) $a=6$, $c=12$ and $\beta=124^\circ$. Apply law of cosines and law of sines to find the values of $b$, $\alpha$ and $\g…

Part B4 marksannual

15

Verify that: $2 \tan^{-1} \frac{1}{2} + \tan^{-1} \frac{1}{7} = \tan^{-1} \frac{31}{17}$.

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16

The value of $\cos(x + 60^\circ) + \cos(x - 60^\circ)$ is:

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16

Solve the trigonometric equation $\cos 5\theta + \cos \theta = \cos 3\theta$ where $\theta \in [0, \pi]$.

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17

The period of $\frac{8}{7} \sec(x - \pi)$ is:

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