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Algebra

Each subtopic includes About section, revision page link, 10 preview questions, and practice CTAs.

Linear Inequations

Subtopic

Linear Inequations under Algebra for Grade 10 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the solution set of x2+2>2\frac{x}{2} + 2 > 2 for x∈Z−x \in \mathbb{Z}^- (Negative Integers).

    A.

    {−1,−2,...}\{-1, -2, ...\}

    B.

    {−1}\{-1\}

    C.

    ∅\emptyset

    D.

    {0}\{0\}

  2. 2.

    Solve x−1≥−1x - 1 \geq -1 for x∈Nx \in \mathbb{N}.

    A.

    {1,2,3,...}\{1, 2, 3, ...\}

    B.

    {0,1,2,...}\{0, 1, 2, ...\}

    C.

    {2,3,4,...}\{2, 3, 4, ...\}

    D.

    {1}\{1\}

  3. 3.

    Given x∈{2,4,6}x \in \{2, 4, 6\}, solve the inequation 3x+1≤103x + 1 \leq 10.

    A.

    {2,4}\{2, 4\}

    B.

    {2}\{2\}

    C.

    {4}\{4\}

    D.

    {2,4,6}\{2, 4, 6\}

Download the worksheet for Algebra - Linear Inequations to practice offline. It includes additional chapter-level practice questions.

Quadratic Equations in one variable

Subtopic

Quadratic Equations in one variable under Algebra for Grade 10 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    The roots of the equation 3x2−27=03x^2 - 27 = 0 are:

    A.

    x=3x = 3

    B.

    x=9x = 9

    C.

    x=±3x = \pm 3

    D.

    x=±9x = \pm 9

  2. 2.

    Find the value of cc for the equation x2−5x=−6x^2 - 5x = -6 when written in standard form.

    A.

    −6-6

    B.

    5

    C.

    6

    D.

    0

  3. 3.

    Convert (x−2)(x−5)=0(x-2)(x-5) = 0 into the form ax2+bx+c=0ax^2 + bx + c = 0.

    A.

    x2−7x+10=0x^2 - 7x + 10 = 0

    B.

    x2+7x+10=0x^2 + 7x + 10 = 0

    C.

    x2−7x−10=0x^2 - 7x - 10 = 0

    D.

    x2+10=0x^2 + 10 = 0

Download the worksheet for Algebra - Quadratic Equations in one variable to practice offline. It includes additional chapter-level practice questions.

Ratio and Proportion

Subtopic

Ratio and Proportion under Algebra for Grade 10 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If ab=cd=ef=23\frac{a}{b} = \frac{c}{d} = \frac{e}{f} = \frac{2}{3}, find the value of a+c+eb+d+f\frac{a+c+e}{b+d+f}.

    A.

    11

    B.

    23\frac{2}{3}

    C.

    32\frac{3}{2}

    D.

    49\frac{4}{9}

  2. 2.

    The sub-duplicate ratio of x2:y2x^2:y^2 is:

    A.

    x4:y4x^4:y^4

    B.

    x:y2x:y^2

    C.

    x:yx:y

    D.

    y:xy:x

  3. 3.

    What is the inverse ratio of 3:2:13:2:1?

    A.

    1:2:31:2:3

    B.

    3:2:13:2:1

    C.

    6:3:26:3:2

    D.

    2:3:62:3:6

Download the worksheet for Algebra - Ratio and Proportion to practice offline. It includes additional chapter-level practice questions.

Factorization of polynomials (Remainder and Factor Theorems)

Subtopic

Factorization of polynomials (Remainder and Factor Theorems) under Algebra for Grade 10 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If (x−k)(x - k) is a factor of x2−5x+6x^2 - 5x + 6 and k>2k > 2, find the value of kk.

    A.

    2

    B.

    3

    C.

    4

    D.

    5

  2. 2.

    Find the remainder when x2+8x+15x^2 + 8x + 15 is divided by (x+5)(x + 5).

    A.

    0

    B.

    5

    C.

    10

    D.

    15

  3. 3.

    Find the remainder when x3−27x^3 - 27 is divided by (x−3)(x - 3).

    A.

    0

    B.

    27

    C.

    54

    D.

    -27

Download the worksheet for Algebra - Factorization of polynomials (Remainder and Factor Theorems) to practice offline. It includes additional chapter-level practice questions.

Matrices

Subtopic

Matrices under Algebra for Grade 10 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the transpose of a null matrix?

    A.

    Identity matrix

    B.

    Row matrix

    C.

    Null matrix

    D.

    Column matrix

  2. 2.

    If A=[68]A = \begin{bmatrix} 6 & 8 \end{bmatrix}, then 12A\frac{1}{2}A is:

    A.

    [1216]\begin{bmatrix} 12 & 16 \end{bmatrix}

    B.

    [34]\begin{bmatrix} 3 & 4 \end{bmatrix}

    C.

    [64]\begin{bmatrix} 6 & 4 \end{bmatrix}

    D.

    [38]\begin{bmatrix} 3 & 8 \end{bmatrix}

  3. 3.

    In a 2×22 \times 2 matrix, the elements a11a_{11} and a22a_{22} form the:

    A.

    Leading diagonal

    B.

    Second row

    C.

    First column

    D.

    Null diagonal

Download the worksheet for Algebra - Matrices to practice offline. It includes additional chapter-level practice questions.

Arithmetic Progression (AP)

Subtopic

Arithmetic Progression (AP) under Algebra for Grade 10 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If a=10a = 10 and d=10d = 10, what is the 4th4^{th} term?

    A.

    3030

    B.

    4040

    C.

    5050

    D.

    6060

  2. 2.

    Which term of the AP 2,4,6,8,…2, 4, 6, 8, \dots is 5050?

    A.

    20th20^{th}

    B.

    24th24^{th}

    C.

    25th25^{th}

    D.

    50th50^{th}

  3. 3.

    Find the common difference of the AP: 10,6,2,−2,…10, 6, 2, -2, \dots

    A.

    44

    B.

    −4-4

    C.

    22

    D.

    −2-2

Download the worksheet for Algebra - Arithmetic Progression (AP) to practice offline. It includes additional chapter-level practice questions.

Geometric Progression (GP)

Subtopic

Geometric Progression (GP) under Algebra for Grade 10 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    In a Geometric Progression, if the first term is 2020 and the common ratio is 0.10.1, find the 2nd2^{nd} term.

    A.

    200

    B.

    0.2

    C.

    10

    D.

    2

  2. 2.

    Find the 3rd3^{rd} term of a Geometric Progression if the first term is 22 and the common ratio is 55.

    A.

    10

    B.

    25

    C.

    50

    D.

    100

  3. 3.

    If x,15,75x, 15, 75 are three consecutive terms of a Geometric Progression, find the value of xx.

    A.

    5

    B.

    3

    C.

    1

    D.

    15

Download the worksheet for Algebra - Geometric Progression (GP) to practice offline. It includes additional chapter-level practice questions.

Coordinate Geometry (Reflection, Section Formula, Equation of a Line)

Subtopic

Coordinate Geometry (Reflection, Section Formula, Equation of a Line) under Algebra for Grade 10 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the slope of the line 2x+3y=52x + 3y = 5.

    A.

    2/32/3

    B.

    −2/3-2/3

    C.

    3/23/2

    D.

    −3/2-3/2

  2. 2.

    Reflect the point (2,−3)(2, -3) in the line x=0x = 0.

    A.

    (−2,−3)(-2, -3)

    B.

    (2,3)(2, 3)

    C.

    (−2,3)(-2, 3)

    D.

    (3,−2)(3, -2)

  3. 3.

    If the point (1,2)(1, 2) is reflected to become (−1,−2)(-1, -2), what is the mirror or center of reflection?

    A.

    xx-axis

    B.

    yy-axis

    C.

    Origin

    D.

    Line y=xy=x

Download the worksheet for Algebra - Coordinate Geometry (Reflection, Section Formula, Equation of a Line) to practice offline. It includes additional chapter-level practice questions.