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Mixed Topic Worksheet Grades 6/7: Day 009

Grades 6/7Non-calculator

  1. Question 1. A pen costs £3.85
    Work out an estimate for the cost of 52 pens.

    Show worked answerHide worked answer
    1. M1: 3.85 rounded to 4 or 52 rounded to 50
    2. M1: 4 × 50
    3. A1: £200
    Answer: £200
    Applied Estimating
    [3 marks]

  2. Question 2. Make x the subject of y = dfracx + 53

    Show worked answerHide worked answer
    1. M1: multiplies both sides by 3, giving 3y = x + 5
    2. A1: subtracts 5, giving x = 3y - 5
    Answer: x = 3y - 5
    Rearranging Harder Equations
    [2 marks]

  3. Question 3. Write down the whole number that is closest to √45

    Show worked answerHide worked answer
    1. M1: 6² = 36 and 7² = 49 with 45 nearer to 49
    2. A1: 7
    Answer: 7
    Estimating Roots
    [2 marks]

  4. Question 4. The graph of y = x² + bx + c has a turning point at (3, -4).
    Work out the value of b and the value of c.

    Show worked answerHide worked answer
    1. M1: y = (x - 3)² - 4
    2. A1: b = -6
    3. A1: c = 5
    Answer: b = -6 and c = 5
    Turning Points of Quadratics
    [3 marks]

  5. Question 5. A plane parallel to its base cuts a small cone from the top of a cone. The small cone has base radius 4 cm and slant height 7 cm. The large cone has base radius 12 cm. Work out the curved surface area of the frustum that remains. Give your answer in terms of π.

    Show worked answerHide worked answer
    1. M1: scale factor 12 ÷ 4 = 3, so large slant height = 21
    2. M1: π × 12 × 21 - π × 4 × 7
    3. A1: 224π
    Answer: 224π cm²
    Surface Area of Frustums
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 009

Grades 6/7Non-calculator

  1. Question 1. A pen costs £3.85
    Work out an estimate for the cost of 52 pens.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 3.85 rounded to 4 or 52 rounded to 50
    2. M1: 4 × 50
    3. A1: £200
    Answer: £200
    Applied Estimating

  2. Question 2. Make x the subject of y = dfracx + 53

    [2 marks]
    Show worked answerHide worked answer
    1. M1: multiplies both sides by 3, giving 3y = x + 5
    2. A1: subtracts 5, giving x = 3y - 5
    Answer: x = 3y - 5
    Rearranging Harder Equations

  3. Question 3. Write down the whole number that is closest to √45

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 6² = 36 and 7² = 49 with 45 nearer to 49
    2. A1: 7
    Answer: 7
    Estimating Roots

  4. Question 4. The graph of y = x² + bx + c has a turning point at (3, -4).
    Work out the value of b and the value of c.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: y = (x - 3)² - 4
    2. A1: b = -6
    3. A1: c = 5
    Answer: b = -6 and c = 5
    Turning Points of Quadratics

  5. Question 5. A plane parallel to its base cuts a small cone from the top of a cone. The small cone has base radius 4 cm and slant height 7 cm. The large cone has base radius 12 cm. Work out the curved surface area of the frustum that remains. Give your answer in terms of π.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: scale factor 12 ÷ 4 = 3, so large slant height = 21
    2. M1: π × 12 × 21 - π × 4 × 7
    3. A1: 224π
    Answer: 224π cm²
    Surface Area of Frustums
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 009

Grades 6/7Non-calculator

  1. Question 1. A pen costs £3.85
    Work out an estimate for the cost of 52 pens.

    Show worked answerHide worked answer
    1. M1: 3.85 rounded to 4 or 52 rounded to 50
    2. M1: 4 × 50
    3. A1: £200
    Answer: £200
    Applied Estimating
    [3 marks]

  2. Question 2. Make x the subject of y = dfracx + 53

    Show worked answerHide worked answer
    1. M1: multiplies both sides by 3, giving 3y = x + 5
    2. A1: subtracts 5, giving x = 3y - 5
    Answer: x = 3y - 5
    Rearranging Harder Equations
    [2 marks]

  3. Question 3. Write down the whole number that is closest to √45

    Show worked answerHide worked answer
    1. M1: 6² = 36 and 7² = 49 with 45 nearer to 49
    2. A1: 7
    Answer: 7
    Estimating Roots
    [2 marks]

  4. Question 4. The graph of y = x² + bx + c has a turning point at (3, -4).
    Work out the value of b and the value of c.

    Show worked answerHide worked answer
    1. M1: y = (x - 3)² - 4
    2. A1: b = -6
    3. A1: c = 5
    Answer: b = -6 and c = 5
    Turning Points of Quadratics
    [3 marks]

  5. Question 5. A plane parallel to its base cuts a small cone from the top of a cone. The small cone has base radius 4 cm and slant height 7 cm. The large cone has base radius 12 cm. Work out the curved surface area of the frustum that remains. Give your answer in terms of π.

    Show worked answerHide worked answer
    1. M1: scale factor 12 ÷ 4 = 3, so large slant height = 21
    2. M1: π × 12 × 21 - π × 4 × 7
    3. A1: 224π
    Answer: 224π cm²
    Surface Area of Frustums
    [3 marks]