📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 061

Grades 6/7Non-calculator

  1. Question 1. Here is a right-angled triangle ABC.
    Sam says that x = 12 sin 40^°.
    Priya says that x = 12 cos 40^°.
    Who is correct? Give a reason for your answer.

    Show worked answerHide worked answer
    1. M1: sin 40° = x/12 (x is opposite, 12 cm is the hypotenuse)
    2. A1: Sam
    Answer: Sam; x is opposite the 40° angle and 12 is the hypotenuse, so sin is used (7.7 cm)
    Finding Side Lengths Using SOH, CAH, TOA
    x12 cm40°ABC
    [2 marks]

  2. Question 2. Simplify fully dfrac5x² - 10xx - 2

    Show worked answerHide worked answer
    1. M1: numerator 5x(x - 2)
    2. A1: 5x
    Answer: 5x
    Simplifying Algebraic Fractions
    [2 marks]

  3. Question 3. Work out an estimate for √7.9² + 14.8²
    Round each number to the nearest integer before you work out the root.
    Give your answer as an integer.

    Show worked answerHide worked answer
    1. M1: 8² + 15²
    2. M1: 64 + 225 = 289
    3. A1: 17
    Answer: 17
    Estimating Roots
    [3 marks]

  4. Question 4. The region R satisfies y ≥ 1, y ≤ x + 3 and x + y ≤ 8
    For each of the points (2, 4) and (5, 4), decide whether it is in R.
    Show your working.

    Show worked answerHide worked answer
    1. M1: (2, 4): 4 ≥ 1, 4 ≤ 5, 6 ≤ 8
    2. A1: (2, 4) is in R
    3. M1: (5, 4): 5 + 4 = 9
    4. A1: (5, 4) is not in R because 9 > 8
    Answer: (2, 4) is in R; (5, 4) is not, because 9 > 8
    Shading Regions with Graphical Inequalities
    [4 marks]

  5. Question 5. A frustum is made by cutting a cone of radius 4 cm and height 6 cm from the top of a cone of radius 8 cm and height 12 cm.
    Work out the volume of the frustum in terms of π
    (Volume of a cone = dfrac13π r²h)

    Show worked answerHide worked answer
    1. M1: large cone 1/3 × π × 8² × 12 = 256π
    2. M1: small cone 1/3 × π × 4² × 6 = 32π
    3. M1: 256π - 32π
    4. A1: 224π
    Answer: 224π cm³
    Volume of Frustums
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 061

Grades 6/7Non-calculator

  1. Question 1. Here is a right-angled triangle ABC.
    Sam says that x = 12 sin 40^°.
    Priya says that x = 12 cos 40^°.
    Who is correct? Give a reason for your answer.

    [2 marks]
    x12 cm40°ABC
    Show worked answerHide worked answer
    1. M1: sin 40° = x/12 (x is opposite, 12 cm is the hypotenuse)
    2. A1: Sam
    Answer: Sam; x is opposite the 40° angle and 12 is the hypotenuse, so sin is used (7.7 cm)
    Finding Side Lengths Using SOH, CAH, TOA

  2. Question 2. Simplify fully dfrac5x² - 10xx - 2

    [2 marks]
    Show worked answerHide worked answer
    1. M1: numerator 5x(x - 2)
    2. A1: 5x
    Answer: 5x
    Simplifying Algebraic Fractions

  3. Question 3. Work out an estimate for √7.9² + 14.8²
    Round each number to the nearest integer before you work out the root.
    Give your answer as an integer.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 8² + 15²
    2. M1: 64 + 225 = 289
    3. A1: 17
    Answer: 17
    Estimating Roots

  4. Question 4. The region R satisfies y ≥ 1, y ≤ x + 3 and x + y ≤ 8
    For each of the points (2, 4) and (5, 4), decide whether it is in R.
    Show your working.

    [4 marks]
    Show worked answerHide worked answer
    1. M1: (2, 4): 4 ≥ 1, 4 ≤ 5, 6 ≤ 8
    2. A1: (2, 4) is in R
    3. M1: (5, 4): 5 + 4 = 9
    4. A1: (5, 4) is not in R because 9 > 8
    Answer: (2, 4) is in R; (5, 4) is not, because 9 > 8
    Shading Regions with Graphical Inequalities

  5. Question 5. A frustum is made by cutting a cone of radius 4 cm and height 6 cm from the top of a cone of radius 8 cm and height 12 cm.
    Work out the volume of the frustum in terms of π
    (Volume of a cone = dfrac13π r²h)

    [4 marks]
    Show worked answerHide worked answer
    1. M1: large cone 1/3 × π × 8² × 12 = 256π
    2. M1: small cone 1/3 × π × 4² × 6 = 32π
    3. M1: 256π - 32π
    4. A1: 224π
    Answer: 224π cm³
    Volume of Frustums
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 061

Grades 6/7Non-calculator

  1. Question 1. Here is a right-angled triangle ABC.
    Sam says that x = 12 sin 40^°.
    Priya says that x = 12 cos 40^°.
    Who is correct? Give a reason for your answer.

    Show worked answerHide worked answer
    1. M1: sin 40° = x/12 (x is opposite, 12 cm is the hypotenuse)
    2. A1: Sam
    Answer: Sam; x is opposite the 40° angle and 12 is the hypotenuse, so sin is used (7.7 cm)
    Finding Side Lengths Using SOH, CAH, TOA
    x12 cm40°ABC
    [2 marks]

  2. Question 2. Simplify fully dfrac5x² - 10xx - 2

    Show worked answerHide worked answer
    1. M1: numerator 5x(x - 2)
    2. A1: 5x
    Answer: 5x
    Simplifying Algebraic Fractions
    [2 marks]

  3. Question 3. Work out an estimate for √7.9² + 14.8²
    Round each number to the nearest integer before you work out the root.
    Give your answer as an integer.

    Show worked answerHide worked answer
    1. M1: 8² + 15²
    2. M1: 64 + 225 = 289
    3. A1: 17
    Answer: 17
    Estimating Roots
    [3 marks]

  4. Question 4. The region R satisfies y ≥ 1, y ≤ x + 3 and x + y ≤ 8
    For each of the points (2, 4) and (5, 4), decide whether it is in R.
    Show your working.

    Show worked answerHide worked answer
    1. M1: (2, 4): 4 ≥ 1, 4 ≤ 5, 6 ≤ 8
    2. A1: (2, 4) is in R
    3. M1: (5, 4): 5 + 4 = 9
    4. A1: (5, 4) is not in R because 9 > 8
    Answer: (2, 4) is in R; (5, 4) is not, because 9 > 8
    Shading Regions with Graphical Inequalities
    [4 marks]

  5. Question 5. A frustum is made by cutting a cone of radius 4 cm and height 6 cm from the top of a cone of radius 8 cm and height 12 cm.
    Work out the volume of the frustum in terms of π
    (Volume of a cone = dfrac13π r²h)

    Show worked answerHide worked answer
    1. M1: large cone 1/3 × π × 8² × 12 = 256π
    2. M1: small cone 1/3 × π × 4² × 6 = 32π
    3. M1: 256π - 32π
    4. A1: 224π
    Answer: 224π cm³
    Volume of Frustums
    [4 marks]