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

Mixed Topic Worksheet Grades 6/7: Day 097

Grades 6/7Non-calculator

  1. Question 1. Here is a pyramid with a square base of side 8 cm.
    The slant height of each triangular face is 7 cm.
    Work out the total surface area of the pyramid.

    Show worked answerHide worked answer
    1. M1: 8 × 8 and 4 × 1/2 × 8 × 7
    2. A1: 176
    Answer: 176 cm²
    Surface Area of Pyramids
    8 cm7 cm
    [2 marks]

  2. Question 2. Simplify fully dfrac15a³b20ab²

    Show worked answerHide worked answer
    1. M1: divides 15 and 20 by 5, or gives a², or gives dfrac1b
    2. A1: dfrac3a²4b
    Answer: dfrac3a²4b
    Simplifying Algebraic Fractions
    [2 marks]

  3. Question 3. Hana works out an estimate for √250 Her working is 250 ÷ 2 = 125 Hana says that an estimate for √250 is 125 Is Hana correct? You must give a reason.

    Show worked answerHide worked answer
    1. B1: No
    2. B1: 15² = 225 and 16² = 256, so the root is between 15 and 16
    Answer: No. 15² = 225 and 16² = 256, so √250 is between 15 and 16
    Estimating Roots
    [2 marks]

  4. Question 4. The intensity I of light from a lamp is inversely proportional to the square of the distance d metres from the lamp.
    I = 40 when d = 3.
    Work out the value of I when d = 6.

    Show worked answerHide worked answer
    1. M1: 40 = k ÷ 3²
    2. M1: I = 360 ÷ 6²
    3. A1: 10
    Answer: 10
    Algebraic Inverse Proportion
    [3 marks]

  5. Question 5. Here is the graph of y = k × ax where a is positive.
    A(1, 12) and B(4, 96) lie on the graph.
    (a) Work out a [3]
    (b) Work out k [1]

    Show worked answerHide worked answer
    1. (a) M1: ka⁴ ÷ ka = 96 ÷ 12
    2. (a) M1: a³ = 8
    3. (a) A1: a = 2
    4. (b) B1: k × 2 = 12, so k = 6
    Answer: (a) 2; (b) 6
    Sketching Exponential Graphs
    xy24487296AB−112340
    [4 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 097

Grades 6/7Non-calculator

  1. Question 1. Here is a pyramid with a square base of side 8 cm.
    The slant height of each triangular face is 7 cm.
    Work out the total surface area of the pyramid.

    [2 marks]
    8 cm7 cm
    Show worked answerHide worked answer
    1. M1: 8 × 8 and 4 × 1/2 × 8 × 7
    2. A1: 176
    Answer: 176 cm²
    Surface Area of Pyramids

  2. Question 2. Simplify fully dfrac15a³b20ab²

    [2 marks]
    Show worked answerHide worked answer
    1. M1: divides 15 and 20 by 5, or gives a², or gives dfrac1b
    2. A1: dfrac3a²4b
    Answer: dfrac3a²4b
    Simplifying Algebraic Fractions

  3. Question 3. Hana works out an estimate for √250 Her working is 250 ÷ 2 = 125 Hana says that an estimate for √250 is 125 Is Hana correct? You must give a reason.

    [2 marks]
    Show worked answerHide worked answer
    1. B1: No
    2. B1: 15² = 225 and 16² = 256, so the root is between 15 and 16
    Answer: No. 15² = 225 and 16² = 256, so √250 is between 15 and 16
    Estimating Roots

  4. Question 4. The intensity I of light from a lamp is inversely proportional to the square of the distance d metres from the lamp.
    I = 40 when d = 3.
    Work out the value of I when d = 6.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 40 = k ÷ 3²
    2. M1: I = 360 ÷ 6²
    3. A1: 10
    Answer: 10
    Algebraic Inverse Proportion

  5. Question 5. Here is the graph of y = k × ax where a is positive.
    A(1, 12) and B(4, 96) lie on the graph.
    (a) Work out a [3]
    (b) Work out k [1]

    [4 marks]
    xy24487296AB−112340
    Show worked answerHide worked answer
    1. (a) M1: ka⁴ ÷ ka = 96 ÷ 12
    2. (a) M1: a³ = 8
    3. (a) A1: a = 2
    4. (b) B1: k × 2 = 12, so k = 6
    Answer: (a) 2; (b) 6
    Sketching Exponential Graphs
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 097

Grades 6/7Non-calculator

  1. Question 1. Here is a pyramid with a square base of side 8 cm.
    The slant height of each triangular face is 7 cm.
    Work out the total surface area of the pyramid.

    Show worked answerHide worked answer
    1. M1: 8 × 8 and 4 × 1/2 × 8 × 7
    2. A1: 176
    Answer: 176 cm²
    Surface Area of Pyramids
    8 cm7 cm
    [2 marks]

  2. Question 2. Simplify fully dfrac15a³b20ab²

    Show worked answerHide worked answer
    1. M1: divides 15 and 20 by 5, or gives a², or gives dfrac1b
    2. A1: dfrac3a²4b
    Answer: dfrac3a²4b
    Simplifying Algebraic Fractions
    [2 marks]

  3. Question 3. Hana works out an estimate for √250 Her working is 250 ÷ 2 = 125 Hana says that an estimate for √250 is 125 Is Hana correct? You must give a reason.

    Show worked answerHide worked answer
    1. B1: No
    2. B1: 15² = 225 and 16² = 256, so the root is between 15 and 16
    Answer: No. 15² = 225 and 16² = 256, so √250 is between 15 and 16
    Estimating Roots
    [2 marks]

  4. Question 4. The intensity I of light from a lamp is inversely proportional to the square of the distance d metres from the lamp.
    I = 40 when d = 3.
    Work out the value of I when d = 6.

    Show worked answerHide worked answer
    1. M1: 40 = k ÷ 3²
    2. M1: I = 360 ÷ 6²
    3. A1: 10
    Answer: 10
    Algebraic Inverse Proportion
    [3 marks]

  5. Question 5. Here is the graph of y = k × ax where a is positive.
    A(1, 12) and B(4, 96) lie on the graph.
    (a) Work out a [3]
    (b) Work out k [1]

    Show worked answerHide worked answer
    1. (a) M1: ka⁴ ÷ ka = 96 ÷ 12
    2. (a) M1: a³ = 8
    3. (a) A1: a = 2
    4. (b) B1: k × 2 = 12, so k = 6
    Answer: (a) 2; (b) 6
    Sketching Exponential Graphs
    xy24487296AB−112340
    [4 marks]