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Maths 11 Past Paper 2022 | Notely

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All Maths 11 papers

Class 11 · Past paper

Maths 11 past paper 2022

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

39 MCQs44 written questionsPractise this paper

Question index

1
For a complex number $z$, all the following formulas are true **EXCEPT**:
MCQ1 marksannual
1
Solve the following system by reducing their augmented matrix to the echelon form: $$\begin{aligned} x_1 + 4x_2 + 2x_3 &= 2 \\ 2x_1 + x_2 - 2x_3 &= 9 \\ 2x_1 + 2x_2 - 2x_3 &= 12 \e…
Part C8 marksannual
1
If $a, b, c$ are real numbers such that $a < b$, $c < 0$, $a \neq 0$, $b \neq 0$, then which of the following inequalities holds:
MCQ1 marksannual
1
Separate $\frac{(2-3i)^2}{1-i}$ into real and imaginary parts.

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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1

Find the real and imaginary parts of the complex number $\frac{(\sqrt{3} - i)^5}{(\sqrt{3} + i)^5}$.

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2

Which of the following sets forms an **abelian group** under the operation of multiplication?

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2

If $U = \text{the set of the English alphabets}$, $A$ and $B$ are subsets of $U$, where $A = \{x \mid x \text{ is a vowel}\}$ and $B = \{y \mid y \text{ is a consonant}\}$, then ve…

Part B4 marksannual

2

Solve the system of simultaneous equations: $$3x + 2y = 7$$ $$3x^2 = 25 + 2y^2$$

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2

What is the converse of $p \rightarrow q$?

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2

Determine whether $p \rightarrow (q \rightarrow p)$ is a tautology, a contingency or an absurdity.

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2

Find the value of $\lambda$ for which the system $$\begin{cases} x + y + z = 0 \\ 2x + y - \lambda z = 0 \\ x + 2y - 2z = 0 \end{cases}$$ has a non-trivial solution. Also solve the…

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3

Suppose the number of players that play cricket and hockey are $15$ and $13$ respectively. If the total number of players is $21$, what is the number of players that play **both**…

MCQ1 marksannual

3

Construct the truth table for the biconditional $p \leftrightarrow q$.

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3

Resolve $\frac{2x^4}{(x+3)(x-2)^2}$ into partial fractions.

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3

The set of non-zero rational numbers is a group under the operation of:

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3

If $A = \{1, 2, 3, 4\}$, state the domain and range of the relation $R = \{(x, y) \mid x + y = 5\}$.

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3

Resolve $\frac{x^2}{(x^2 + 4)(x + 2)}$ into partial fractions.

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4

If $A$ is a matrix of order $3 \times 4$, then which of the following equalities is **TRUE**?

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4

If $A = [1 \quad 1+i \quad i]$, then find $(\overline{A})' A$.

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4

Find the sum $S_n$ of the Arithmetic Series $a + (a+d) + (a+2d) + \dots + (a+(n-1)d)$.

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4

Under the operation "*", complete the following table to obtain a semigroup: | * | a | b | c | |---|---|---|---| | a | c | a | b | | b | ... | ... | c | | c | b | c | a |

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4

Prove that ${}^nC_k + {}^nC_{k-1} = {}^{n+1}C_k$.

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5

$\left|\begin{array}{ccc} 1 & 0 & 0 \\ 2 & -i & 0 \\ 3 & -2 & i \end{array}\right| =$

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5

Without expansion, show that $\left|\begin{array}{ccc} 2 & 3 & -1 \\ 1 & 1 & 0 \\ 2 & -3 & 5 \end{array}\right| = 0$.

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5

Find the sum of the following series to $n$-terms: $1 + (1+2) + (1+2+3) + \dots

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5

If $A$ is a skew-symmetric matrix then:

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5

Find the matrix $A$ if $\begin{bmatrix} 2 & -1 \\ -1 & 2 \end{bmatrix} A = \begin{bmatrix} 0 & -3 & 8 \\ 3 & 3 & -7 \end{bmatrix}$.

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5

Expand $(1 - 2x)^{\frac{1}{3}}$ to four terms and apply it to evaluate $(0.8)^{\frac{1}{3}}$ correct to three places of decimal.

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6

If $f(x)$ is a polynomial with only two roots $1$ and $2$, then $f(x) =$

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6

Find the numerical value of $k$ if the polynomial $x^3 + kx^2 - 7x + 6$ has remainder $4$ when divided by $x - 2$.

Part B4 marksannual

6

If $2y = \frac{1}{2^2} + \frac{1 \cdot 3}{2!} \cdot \frac{1}{2^4} + \frac{1 \cdot 3 \cdot 5}{3!} \cdot \frac{1}{2^6} + \dots$ then prove that $4y^2 + 4y - 1 = 0$.

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6

If the polynomial $f(x)$ is divided by $x+2$, the quotient is $x-2$ and the remainder is 2, then $f(x)$ will be:

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6

Find the inverse of matrix $A = \begin{bmatrix} 2i & i \ i & -i \end{bmatrix}$, hence show that $AA^{-1} = I_2$.

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6

If $\sin \alpha = \frac{4}{5}$ and $\sin \beta = \frac{12}{13}$, where $\frac{\pi}{2} < \alpha < \pi$ and $\frac{\pi}{2} < \beta < \pi$. Find (i) $\cos(\alpha + \beta)$ (ii) $\sin(…

Part C8 marksannual

7

If one root of the equation $f(x) = 0$ is $-1$, then $5 - f(-1) =$

MCQ1 marksannual

7

Find the two consecutive numbers whose product is 72.

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7

Without using calculator/table prove that $\sin 10^\circ \sin 30^\circ \sin 50^\circ \sin 70^\circ = \frac{1}{16}$.

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7

If $w$ is a cube root of unity, then which of the following equations is true?

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7

Show that $R = \frac{abc}{4\Delta}$.

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8

The partial fraction of $\frac{1}{1-x^3}$ will be in the form of:

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8

If $5, 8$ are two arithmetic means between $a$ and $b$, then find $a$ and $b$.

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8

What is the partial fraction decomposition of $\frac{x^2 + 2x - 1}{x^2 - 1}$?

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8

Resolve $\frac{3x - 11}{(x + 3)(x^2 + 1)}$ into partial fractions.

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8

Solve the equation $\sqrt{3} \tan x - \sec x - 1 = 0$ for its general solution.

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9

If $a_1 = -1$ in a sequence with general term $a_n = n + a_{n-1}$, then the sum of the first two terms $S_2$ is:

MCQ1 marksannual

9

Find the $9^{\text{th}}$ term of the harmonic sequence $-\frac{1}{5}, -\frac{1}{3}, -1, \dots$.

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9

Find the second term of the sequence whose general term is $a_n = 2n^2 - 3$.

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9

If $y = 1 - \frac{x}{2} + \frac{x^2}{4} - \dots$, then show that $x = 2\left(\frac{1-y}{y}\right)$.

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10

If $b$ is a harmonic mean between $-2$ and $4$, then $b = \dots$

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10

Find values of $n$ and $r$, when ${}^nC_r = 56$ and ${}^nP_r = 336$.

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10

If $s_{\infty} = \frac{2}{3}$ and $a = \frac{2}{7}$ in an infinite geometric progression, then the common ratio is:

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10

Find values of $n$ and $r$, when ${}^nC_r = 10$ and ${}^nP_r = 60$.

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11

$\binom{8}{7} + \binom{8}{6} =$

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11

If $x$ is so small that its square and higher powers can be neglected, then show that $\frac{\sqrt{4+x}}{(1+x)^3} \cong 2 - \frac{23}{4}x$.

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11

For what values of $x$, the binomial expansion of $(1 - \frac{x}{2})^{-1}$ is convergent (valid)?

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11

There are 9 green and 6 red balls in a box. A ball is drawn (taken out). What is the probability that (i) the ball is green (ii) the ball is red.

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12

If a fair die is rolled, then what is the probability that the top is an even number?

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12

Show that the area of a sector of a circular region of radius $r$ is $\frac{1}{2}r^2\theta$, where $\theta$ is the circular measure of the central angle of the sector.

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12

What is the radius of the circle whose arc-length of measure 4 has a central angle of $\frac{\pi}{2}$?

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12

Expand and simplify $(2 + i)^4 - (2 - i)^4$.

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13

Which of the following expressions is the sum of the series $1 - x + x^2 - x^3 + \dots$?

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13

If $\cot \theta = \frac{4}{3}$ and the terminal arm of the angle is not in the quadrant-I, find the values of $\cos \theta$ and $\csc \theta$.

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13

If $D(-5, 5\sqrt{2})$ lies on the terminal side of $\theta$, then find the value of $\tan \theta$.

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13

Find the remaining trigonometric functions if $\cos \theta = -\frac{1}{2}$ and the terminal arm of angle $\theta$ is in quad-III.

Part B4 marksannual

14

What is the length of the arc that subtends an angle of measure $60^\circ$ at the centre of a circle with radius $6$?

MCQ1 marksannual

14

Show that $\frac{\cos(\pi+\theta) \sec(\pi-\theta)}{\sin^2(\pi+\theta) \cdot \tan(\pi-\theta)} = -\cot \theta \cdot \csc^2 \theta$.

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14

If ${}^nC_4 = {}^nC_{10}$, then $n = \dots$

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14

Show that $\frac{\sin(\alpha - \beta)}{\sin(\alpha + \beta)} = \frac{\tan \alpha - \tan \beta}{\tan \alpha + \tan \beta}$.

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15

$\sin\left(\frac{7\pi}{6}\right) =$

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15

Prove that $\cot 2x = \frac{\sin x - \sin 3x}{\cos 3x - \cos x}$.

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15

How many distinct three-digit numbers can be formed from the integers $1, 2, 3, 4, 5, 6$ if each digit is used at most once?

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16

Which of the following trigonometric expressions is identically equal to $1 - \cos 2\theta$?

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16

Show that $\tan^{-1}\left(\frac{27}{11}\right) - \tan^{-1}\left(\frac{8}{19}\right) = \frac{\pi}{4}$.

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16

What is the middle term in the expansion of $(x + x^{-1})^{14}$?

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16

Show that $2 \cos^{-1} \frac{4}{5} = \sin^{-1} \frac{24}{25}$.

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17

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

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17

$\sin(\frac{3\pi}{2} - \alpha) =$

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18

The circumradius $R$ of a triangle with sides $a, b, c$ is equal to:

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18

What is the primary period of $\frac{\sin 2x}{1 + \cos 2x}$?

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19

For what value of $x$, $\tan(x - 30^\circ) = \cot x$?

MCQ1 marksannual

19

A ladder makes an angle of $30^\circ$ with the wall of height $8\text{ m}$. What is the length of the ladder?

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20

What is the solution of $\sec x = 2$ in the interval $[0, \pi]$?

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20

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

MCQ1 marksannual