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Algebra and Graphs

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

Algebraic manipulation and factorisation

Subtopic

Algebraic manipulation and factorisation under Algebra and Graphs for Grade 11 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Factorise 36x2−49y236x^2 - 49y^2.

    A.

    (6x−7y)2(6x - 7y)^2

    B.

    (6x−7y)(6x+7y)(6x - 7y)(6x + 7y)

    C.

    (18x−24.5y)(18x+24.5y)(18x - 24.5y)(18x + 24.5y)

    D.

    (6x+7y)2(6x + 7y)^2

  2. 2.

    Simplify 14m57m5\frac{14m^5}{7m^5}.

    A.

    2m2m

    B.

    22

    C.

    7m7m

    D.

    2m102m^{10}

  3. 3.

    Expand and simplify (x+7)(x−2)(x + 7)(x - 2).

    A.

    x2+9x−14x^2 + 9x - 14

    B.

    x2−5x−14x^2 - 5x - 14

    C.

    x2+5x−14x^2 + 5x - 14

    D.

    x2−14x^2 - 14

Download the worksheet for Algebra and Graphs - Algebraic manipulation and factorisation to practice offline. It includes additional chapter-level practice questions.

Linear and quadratic equations

Subtopic

Linear and quadratic equations under Algebra and Graphs for Grade 11 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the y-intercept of the graph of the function f(x)=3x2−2x−7f(x) = 3x^2 - 2x - 7.

    A.

    (0,3)(0, 3)

    B.

    (0,−2)(0, -2)

    C.

    (0,0)(0, 0)

    D.

    (0,−7)(0, -7)

  2. 2.

    Find the solutions to the quadratic equation x2−5x+6=0x^2 - 5x + 6 = 0.

    A.

    x=−2,x=−3x = -2, x = -3

    B.

    x=1,x=6x = 1, x = 6

    C.

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

    D.

    x=−1,x=−6x = -1, x = -6

  3. 3.

    What is the gradient (slope) of the line with the equation 2y+6x=102y + 6x = 10?

    A.

    −3-3

    B.

    33

    C.

    66

    D.

    −6-6

Download the worksheet for Algebra and Graphs - Linear and quadratic equations to practice offline. It includes additional chapter-level practice questions.

Simultaneous equations

Subtopic

Simultaneous equations under Algebra and Graphs for Grade 11 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Given y=6xy = 6x and x+y=7x + y = 7, solve for xx and yy.

    A.

    x=2,y=12x = 2, y = 12

    B.

    x=1,y=6x = 1, y = 6

    C.

    x=0.5,y=3x = 0.5, y = 3

    D.

    x=7,y=0x = 7, y = 0

  2. 2.

    Find the solution to x+y=3x + y = 3 and 3x−y=13x - y = 1.

    A.

    x=1,y=2x = 1, y = 2

    B.

    x=2,y=1x = 2, y = 1

    C.

    x=0,y=3x = 0, y = 3

    D.

    x=1,y=1x = 1, y = 1

  3. 3.

    Solve for xx and yy: 2x−y=12x - y = 1 and x+y=5x + y = 5.

    A.

    x=1,y=4x = 1, y = 4

    B.

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

    C.

    x=4,y=1x = 4, y = 1

    D.

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

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

Linear inequalities

Subtopic

Linear inequalities under Algebra and Graphs for Grade 11 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Solve for xx: x−1>5\frac{x}{-1} > 5.

    A.

    x>−5x > -5

    B.

    x<−5x < -5

    C.

    x<5x < 5

    D.

    x>5x > 5

  2. 2.

    Find the solution to 9≤x+49 \le x + 4.

    A.

    x≥13x \ge 13

    B.

    x≤5x \le 5

    C.

    x≥5x \ge 5

    D.

    x>5x > 5

  3. 3.

    Solve the inequality: x−10>−15x - 10 > -15.

    A.

    x>−5x > -5

    B.

    x<−5x < -5

    C.

    x>−25x > -25

    D.

    x<5x < 5

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

Function notation and inverse functions

Subtopic

Function notation and inverse functions under Algebra and Graphs for Grade 11 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Given h(x)=x2h(x) = x^2, evaluate h(−1)h(-1).

    A.

    -1

    B.

    1

    C.

    -2

    D.

    2

  2. 2.

    If g(x)=3xg(x) = 3x, find xx when g(x)=27g(x) = 27.

    A.

    9

    B.

    81

    C.

    3

    D.

    24

  3. 3.

    For the function f(x)=15−xf(x) = 15 - x, find f(20)f(20).

    A.

    5

    B.

    35

    C.

    -5

    D.

    -35

Download the worksheet for Algebra and Graphs - Function notation and inverse functions to practice offline. It includes additional chapter-level practice questions.

Linear, quadratic, and exponential graphs

Subtopic

Linear, quadratic, and exponential graphs under Algebra and Graphs for Grade 11 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Which line is perpendicular to the y-axis?

    A.

    x=2x = 2

    B.

    y=xy = x

    C.

    y=−5y = -5

    D.

    x=0x = 0

  2. 2.

    What is the y-intercept of y=2x2−5x+8y = 2x^2 - 5x + 8?

    A.

    -5

    B.

    2

    C.

    8

    D.

    0

  3. 3.

    The point (3,9)(3, 9) lies on which quadratic graph?

    A.

    y=x2y = x^2

    B.

    y=x2+1y = x^2 + 1

    C.

    y=2x2y = 2x^2

    D.

    y=x2−3y = x^2 - 3

Download the worksheet for Algebra and Graphs - Linear, quadratic, and exponential graphs to practice offline. It includes additional chapter-level practice questions.

Solving equations by graphical methods

Subtopic

Solving equations by graphical methods under Algebra and Graphs for Grade 11 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If you are given the graph of y=f(x)y = f(x), the solutions to f(x)=xf(x) = x are found where the curve meets:

    A.

    The xx-axis

    B.

    The yy-axis

    C.

    The line y=xy = x

    D.

    The line y=0y = 0

  2. 2.

    To find the solutions to x2−4x+3=0x^2 - 4x + 3 = 0, you look for the xx-intercepts of which function?

    A.

    y=x2y = x^2

    B.

    y=−4x+3y = -4x + 3

    C.

    y=x2−4x+3y = x^2 - 4x + 3

    D.

    y=3y = 3

  3. 3.

    If the graph of y=3xy = 3^x intersects the line y=1y = 1 at (0,1)(0, 1), what is the solution to 3x=13^x = 1?

    A.

    x=1x = 1

    B.

    x=3x = 3

    C.

    x=0x = 0

    D.

    x=−1x = -1

Download the worksheet for Algebra and Graphs - Solving equations by graphical methods to practice offline. It includes additional chapter-level practice questions.

Basic differentiation and gradients

Subtopic

Basic differentiation and gradients under Algebra and Graphs for Grade 11 IGCSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the gradient of y=12x2+4y = \frac{1}{2}x^2 + 4 at x=2x = 2.

    A.

    22

    B.

    44

    C.

    11

    D.

    66

  2. 2.

    Find the gradient of the curve y=5x−x2y = 5x - x^2 at x=3x = 3.

    A.

    −1-1

    B.

    55

    C.

    22

    D.

    11

  3. 3.

    What is the gradient of y=2x2+xy = 2x^2 + x at x=1x = 1?

    A.

    44

    B.

    55

    C.

    33

    D.

    22

Download the worksheet for Algebra and Graphs - Basic differentiation and gradients to practice offline. It includes additional chapter-level practice questions.

Algebra and Graphs - IGCSE Grade 11 Maths Notes & Revision | Krit.club