ICSE Class 10 · Mathematics · Algebra (Unit 2)

Class 10 Mathematics – Algebra (Unit 2) Quiz

Test your understanding of linear inequations, quadratic equations, ratio and proportion, factorisation of polynomials, matrices, arithmetic progression and geometric progression with this 30-question interactive quiz.

This quiz is timed. You have 30 minutes to answer all 30 questions. When the time is up, the quiz submits automatically.

Question sourcing: 12 of the 30 questions are verified ICSE board questions from the 2023 and 2024 papers, tagged ICSE Board. The remaining 18 are original exam-style questions created by Vyasa Academy. In the quiz, options appear in a shuffled order, so the letter labels are not the same as any printed source.

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Question 1 of 30 Time Remaining: 30:00

Question 1EasyICSE Board 2023

Solve the inequation \(2x + 4 \le 14\), where \(x \in \mathbb{W}\) (whole numbers). The solution set is:

A\(\{0, 1, 2, 3, 4, 5\}\) B\(\{0, 1, 2, 3, 4\}\) C\(\{1, 2, 3, 4, 5\}\) D\(\{0, 1, 2, 3, 4, 5, 6\}\)

Question 2EasyOriginal

Solve the inequation \(3x + 2 \ge 2x + 9\), where \(x \in \mathbb{I}\) (integers). The solution set is:

A\(\{7, 8, 9, \ldots\}\) B\(\{x : x \ge 7,\ x \in \mathbb{R}\}\) C\(\{6, 7, 8, \ldots\}\) D\(\{x : x \le 7,\ x \in \mathbb{I}\}\)

Question 3ModerateOriginal

Solve the inequation \(-2 \le 3x - 1 < 8\), where \(x \in \mathbb{R}\). The solution set is:

A\(\{x : x \in \mathbb{R},\; -\dfrac{1}{3} < x \le 3\}\) B\(\{x : x \in \mathbb{R},\; -\dfrac{1}{3} \le x < 3\}\) C\(\{x : x \in \mathbb{R},\; -1 \le x < 3\}\) D\(\{x : x \in \mathbb{R},\; -\dfrac{2}{3} \le x < 8\}\)

Question 4EasyICSE Board 2023

If 3 is a root of the quadratic equation \(x^2 - px + 3 = 0\), the value of \(p\) is:

A\(4\) B\(-4\) C\(6\) D\(2\)

Question 5ModerateICSE Board 2024

The roots of the quadratic equation \(px^2 - qx + r = 0\) are real and equal. Which statement is true?

A\(q^2 > 4pr\) B\(q^2 < 4pr\) C\(q^2 = -4pr\) D\(q^2 = 4pr\)

Question 6EasyOriginal

Solve the quadratic equation \(x^2 - 8x + 15 = 0\) by factorisation.

A\(x = -3\) or \(x = 5\) B\(x = 3\) or \(x = -5\) C\(x = 3\) or \(x = 5\) D\(x = 15\) or \(x = 1\)

Question 7EasyICSE Board 2023

The mean proportional between 4 and 9 is:

A\(36\) B\(6\) C\(6.5\) D\(13\)

Question 8ModerateOriginal

If \(a : b = 3 : 4\) and \(b : c = 8 : 9\), find the ratio \(a : c\).

A\(2 : 3\) B\(3 : 4\) C\(3 : 2\) D\(4 : 3\)

Question 9EasyICSE Board 2023

If \(x - 2\) is a factor of \(x^3 - kx - 12\), the value of \(k\) is:

A\(2\) B\(1\) C\(-4\) D\(-2\)

Question 10EasyOriginal

Factorise \(x^2 + 5x + 6\).

A\((x - 2)(x + 3)\) B\((x + 2)(x + 3)\) C\((x + 2)(x - 3)\) D\((x + 1)(x + 6)\)

Question 11ModerateOriginal

The remainder when \(x^3 - 2x^2 + x + 5\) is divided by \(x - 1\) is:

A\(5\) B\(3\) C\(7\) D\(0\)

Question 12ModerateICSE Board 2024

If \(A = \begin{bmatrix}2 & 2 \\ 0 & 2\end{bmatrix}\) and \(A^2 = \begin{bmatrix}4 & x \\ 0 & 4\end{bmatrix}\), the value of \(x\) is:

A\(4\) B\(6\) C\(8\) D\(2\)

Question 13EasyOriginal

The order of the matrix \(\begin{bmatrix}1 & 2 & 3 \\ 4 & 5 & 6\end{bmatrix}\) is:

A\(2 \times 3\) B\(3 \times 2\) C\(2 \times 2\) D\(1 \times 6\)

Question 14ModerateOriginal

If \(\begin{bmatrix}x + 2 & 3 \\ 4 & 2y\end{bmatrix} = \begin{bmatrix}5 & 3 \\ 4 & 10\end{bmatrix}\), then \(x\) and \(y\) are:

A\(x = 3,\ y = 10\) B\(x = 5,\ y = 5\) C\(x = 2,\ y = 8\) D\(x = 3,\ y = 5\)

Question 15EasyICSE Board 2023

The \(n\)th term of an AP is \(2n + 5\). Its 10th term is:

A\(24\) B\(25\) C\(26\) D\(15\)

Question 16ModerateICSE Board 2024

The first three terms of an AP are \(\dfrac{1}{a},\; \dfrac{1}{a} + 1,\; \dfrac{1}{a} + 2, \ldots\) Its 7th term is:

A\(\dfrac{1}{a} + 6\) B\(\dfrac{1}{a} + 7\) C\(\dfrac{1}{a} + 5\) D\(\dfrac{7}{a}\)

Question 17EasyOriginal

The 20th term of the AP \(5, 9, 13, \ldots\) is:

A\(80\) B\(85\) C\(81\) D\(77\)

Question 18EasyOriginal

The sum \(1 + 2 + 3 + \cdots + 50\) equals:

A\(1275\) B\(1270\) C\(2550\) D\(1250\)

Question 19ModerateOriginal

The common ratio of the GP \(\dfrac{1}{3},\; -\dfrac{1}{9},\; \dfrac{1}{27}, \ldots\) is:

A\(\dfrac{1}{3}\) B\(-\dfrac{1}{3}\) C\(\dfrac{1}{9}\) D\(-3\)

Question 20EasyOriginal

The 4th term of a GP whose first term is 2 and common ratio is 3 is:

A\(48\) B\(162\) C\(24\) D\(54\)

Question 21ModerateOriginal

Solve the inequation \(-3 < 2x + 1 \le 11\), where \(x \in \mathbb{R}\). The solution set is:

A\(\{x : -2 < x \le 5,\; x \in \mathbb{R}\}\) B\(\{x : -2 \le x < 5,\; x \in \mathbb{R}\}\) C\(\{x : -1 < x \le 5,\; x \in \mathbb{R}\}\) D\(\{x : -2 < x < 5,\; x \in \mathbb{R}\}\)

Question 22ModerateOriginal

The roots of the quadratic equation \(2x^2 - 7x + 3 = 0\) are:

A\(\dfrac{1}{2}\) and \(3\) B\(-\dfrac{1}{2}\) and \(-3\) C\(\dfrac{1}{2}\) and \(-3\) D\(3\) and \(2\)

Question 23ChallengingICSE Board 2024

If \(\dfrac{(a + b)^3}{(a - b)^3} = \dfrac{64}{27}\), find the ratio \(a : b\).

A\(7 : 1\) B\(1 : 7\) C\(4 : 3\) D\(3 : 4\)

Question 24ModerateOriginal

If \(x : y = 5 : 3\) and \(y : z = 2 : 7\), then \(x : z\) is:

A\(10 : 21\) B\(21 : 10\) C\(5 : 7\) D\(15 : 14\)

Question 25ModerateICSE Board 2023

If \(x - a\) is a factor of \(3x^3 + x^2 - ax - 81\), then the value of \(a\) is:

A\(3\) B\(-3\) C\(9\) D\(27\)

Question 26ModerateICSE Board 2024

Find the value of \(k\) for which \(3x^3 + 8x^2 - 15x + k\) has a factor \((x - 1)\).

A\(4\) B\(-4\) C\(8\) D\(-8\)

Question 27ChallengingICSE Board 2023

Given \(A = \begin{bmatrix}1 & 3 \\ 2 & 4\end{bmatrix}\), \(B = \begin{bmatrix}1 & 2 \\ 2 & 4\end{bmatrix}\), \(C = \begin{bmatrix}4 & 1 \\ 1 & 5\end{bmatrix}\) and \(I = \begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}\), the matrix \(A(B + C) - 14I\) is:

A\(\begin{bmatrix}0 & 30 \\ 22 & 28\end{bmatrix}\) B\(\begin{bmatrix}14 & 30 \\ 22 & 42\end{bmatrix}\) C\(\begin{bmatrix}0 & 30 \\ 22 & 14\end{bmatrix}\) D\(\begin{bmatrix}14 & 0 \\ 0 & 14\end{bmatrix}\)

Question 28ModerateOriginal

The 10th term of the AP \(7, 11, 15, \ldots\) is:

A\(43\) B\(39\) C\(47\) D\(40\)

Question 29ModerateOriginal

The sum of the first 4 terms of the GP \(2, 6, 18, \ldots\) is:

A\(80\) B\(54\) C\(40\) D\(162\)

Question 30ModerateOriginal

Which term of the GP \(3, 6, 12, \ldots\) is \(96\)?

A5th term B6th term C7th term D8th term

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For each question, your answer and the correct answer are shown, with a short explanation. Questions tagged ICSE Board are verified CISCE board questions.

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