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Algebra

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

Expansion and Factorization

Subtopic

Expansion and Factorization under Algebra for Grade 12 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Expand: 7(2x−3)7(2x - 3)

    A.

    14x−314x - 3

    B.

    9x−109x - 10

    C.

    14x−2114x - 21

    D.

    14x+2114x + 21

  2. 2.

    Factorize the following trinomial: x2−2x−8x^2 - 2x - 8

    A.

    (x−4)(x+2)(x - 4)(x + 2)

    B.

    (x+4)(x−2)(x + 4)(x - 2)

    C.

    (x−8)(x+1)(x - 8)(x + 1)

    D.

    (x−2)(x+4)(x - 2)(x + 4)

  3. 3.

    Factorize: 100−x2100 - x^2

    A.

    (x−10)(x+10)(x - 10)(x + 10)

    B.

    (10−x)(10+x)(10 - x)(10 + x)

    C.

    (10−x)2(10 - x)^2

    D.

    (50−x)(2+x)(50 - x)(2 + x)

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

Quadratic Equations and Inequalities

Subtopic

Quadratic Equations and Inequalities under Algebra for Grade 12 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the discriminant of the quadratic equation x2+2x+5=0x^2 + 2x + 5 = 0?

    A.

    −16-16

    B.

    2424

    C.

    44

    D.

    −20-20

  2. 2.

    Solve x2+x−6=0x^2 + x - 6 = 0.

    A.

    x=2,x=−3x = 2, x = -3

    B.

    x=−2,x=3x = -2, x = 3

    C.

    x=2,x=3x = 2, x = 3

    D.

    x=−2,x=−3x = -2, x = -3

  3. 3.

    If x2=kx^2 = k and k<0k < 0, how many real solutions are there for xx?

    A.

    00

    B.

    11

    C.

    22

    D.

    Infinitely many

Download the worksheet for Algebra - Quadratic Equations and Inequalities to practice offline. It includes additional chapter-level practice questions.

Linear and Simultaneous Equations

Subtopic

Linear and Simultaneous Equations under Algebra for Grade 12 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Solve for xx: 11x+2=2411x + 2 = 24.

    A.

    x=2x = 2

    B.

    x=22x = 22

    C.

    x=1.5x = 1.5

    D.

    x=3x = 3

  2. 2.

    Solve for xx: 7−2x=137 - 2x = 13.

    A.

    x=3x = 3

    B.

    x=−3x = -3

    C.

    x=−10x = -10

    D.

    x=10x = 10

  3. 3.

    Solve for xx: x5−1=2\frac{x}{5} - 1 = 2.

    A.

    x=5x = 5

    B.

    x=15x = 15

    C.

    x=3x = 3

    D.

    x=11x = 11

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

Indices and Surds

Subtopic

Indices and Surds under Algebra for Grade 12 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Simplify 20\sqrt{20}.

    A.

    454\sqrt{5}

    B.

    10210\sqrt{2}

    C.

    2102\sqrt{10}

    D.

    252\sqrt{5}

  2. 2.

    Evaluate 491/249^{1/2}.

    A.

    24.5

    B.

    7

    C.

    9.8

    D.

    49

  3. 3.

    Solve for nn: 3n=1/93^n = 1/9.

    A.

    n=2n=2

    B.

    n=−2n=-2

    C.

    n=3n=3

    D.

    n=−3n=-3

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

Functions (Composite and Inverse)

Subtopic

Functions (Composite and Inverse) under Algebra for Grade 12 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the inverse function h−1(x)h^{-1}(x) for h(x)=6−xh(x) = 6 - x.

    A.

    h−1(x)=6−xh^{-1}(x) = 6 - x

    B.

    h−1(x)=x−6h^{-1}(x) = x - 6

    C.

    h−1(x)=6+xh^{-1}(x) = 6 + x

    D.

    h−1(x)=16−xh^{-1}(x) = \frac{1}{6-x}

  2. 2.

    Given f(x)=3x+1f(x) = 3x + 1, find the value of ff(1)ff(1).

    A.

    13

    B.

    4

    C.

    10

    D.

    16

  3. 3.

    If g(x)=x+34g(x) = \frac{x+3}{4}, find g−1(x)g^{-1}(x).

    A.

    g−1(x)=4x−3g^{-1}(x) = 4x - 3

    B.

    g−1(x)=4x+3g^{-1}(x) = 4x + 3

    C.

    g−1(x)=4x+3g^{-1}(x) = \frac{4}{x+3}

    D.

    g−1(x)=x−4g^{-1}(x) = x - 4

Download the worksheet for Algebra - Functions (Composite and Inverse) to practice offline. It includes additional chapter-level practice questions.

Logarithmic and Exponential Functions

Subtopic

Logarithmic and Exponential Functions under Algebra for Grade 12 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Evaluate the value of log⁡10(0.01)\log_{10}(0.01).

    A.

    -2

    B.

    2

    C.

    0.1

    D.

    -1

  2. 2.

    Simplify the expression ln⁡(e5)\ln(e^{5}).

    A.

    ee

    B.

    5

    C.

    ln⁡(5)\ln(5)

    D.

    1

  3. 3.

    Which of the following is the logarithmic form of the exponential equation 53=1255^{3} = 125?

    A.

    log⁡3(125)=5\log_{3}(125) = 5

    B.

    log⁡5(3)=125\log_{5}(3) = 125

    C.

    log⁡5(125)=3\log_{5}(125) = 3

    D.

    log⁡125(5)=3\log_{125}(5) = 3

Download the worksheet for Algebra - Logarithmic and Exponential Functions to practice offline. It includes additional chapter-level practice questions.

Sequences and Series

Subtopic

Sequences and Series under Algebra for Grade 12 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the common difference in the sequence 10,6,2,−2,…10, 6, 2, -2, \dots.

    A.

    4

    B.

    -4

    C.

    -2

    D.

    6

  2. 2.

    Calculate the sum to infinity for a=6a = 6 and r=−1/2r = -1/2.

    A.

    12

    B.

    4

    C.

    9

    D.

    3

  3. 3.

    What is the sum of the first 4 terms of the sequence un=2n+1u_n = 2n + 1?

    A.

    20

    B.

    24

    C.

    12

    D.

    16

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