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

Mixed Topic Worksheet Grades 6/7: Day 028

Grades 6/7Calculator

  1. Question 1. P is the point (2, 3), A is the point (-1, -1) and B is the point (7, 7).
    Which of A and B is nearer to P?
    You must show your working.

    Show worked answerHide worked answer
    1. M1: PA = √3² + 4²
    2. M1: PB = √5² + 4²
    3. A1: PA = 5 and PB = 6.4 to 1 decimal place, so A is nearer
    Answer: A is nearer: PA = 5 and PB = 6.4
    Finding the Distance Between Two Points
    [3 marks]

  2. Question 2. Simplify dfrac6x² + 3x3x

    Show worked answerHide worked answer
    1. M1: factorises numerator 3x(2x+1)
    2. A1: 2x + 1
    Answer: 2x + 1
    Simplifying Algebraic Fractions
    [2 marks]

  3. Question 3. Shop A: minimum 4, lower quartile 9, median 12, upper quartile 15, maximum 30. Shop B: minimum 6, lower quartile 8, median 12, upper quartile 14, maximum 18. Compare the ranges and the interquartile ranges.

    Show worked answerHide worked answer
    1. B1: ranges: A 26, B 12
    2. B1: IQRs: A 6, B 6
    3. B1: A has the greater range but the IQRs are equal
    Answer: Range: A 26, B 12. IQR: both 6. A has the greater range; the middle halves are equally spread.
    Comparing Data Using Box Plots
    [3 marks]

  4. Question 4. Triangle ABC has AB = 8 cm, BC = 11 cm and angle ABC = 40^°
    Work out its area.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 1/2 × 8 × 11 × sin 40^°
    2. A1: 28.3
    Answer: 28.3 cm²
    Calculating Area Using ½ab sin C
    [2 marks]

  5. Question 5. The sides of a rectangle are 8.5 cm and 4.2 cm.
    Each length is correct to 1 decimal place.
    Work out the lower bound of the area of the rectangle.

    Show worked answerHide worked answer
    1. M1: 8.5 - 0.05 and 4.2 - 0.05
    2. M1: 8.45 × 4.15
    3. A1: 35.0675
    Answer: 35.0675 cm²
    Bounds & Error Intervals Involving Calculations
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 028

Grades 6/7Calculator

  1. Question 1. P is the point (2, 3), A is the point (-1, -1) and B is the point (7, 7).
    Which of A and B is nearer to P?
    You must show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: PA = √3² + 4²
    2. M1: PB = √5² + 4²
    3. A1: PA = 5 and PB = 6.4 to 1 decimal place, so A is nearer
    Answer: A is nearer: PA = 5 and PB = 6.4
    Finding the Distance Between Two Points

  2. Question 2. Simplify dfrac6x² + 3x3x

    [2 marks]
    Show worked answerHide worked answer
    1. M1: factorises numerator 3x(2x+1)
    2. A1: 2x + 1
    Answer: 2x + 1
    Simplifying Algebraic Fractions

  3. Question 3. Shop A: minimum 4, lower quartile 9, median 12, upper quartile 15, maximum 30. Shop B: minimum 6, lower quartile 8, median 12, upper quartile 14, maximum 18. Compare the ranges and the interquartile ranges.

    [3 marks]
    Show worked answerHide worked answer
    1. B1: ranges: A 26, B 12
    2. B1: IQRs: A 6, B 6
    3. B1: A has the greater range but the IQRs are equal
    Answer: Range: A 26, B 12. IQR: both 6. A has the greater range; the middle halves are equally spread.
    Comparing Data Using Box Plots

  4. Question 4. Triangle ABC has AB = 8 cm, BC = 11 cm and angle ABC = 40^°
    Work out its area.
    Give your answer to 1 decimal place.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 1/2 × 8 × 11 × sin 40^°
    2. A1: 28.3
    Answer: 28.3 cm²
    Calculating Area Using ½ab sin C

  5. Question 5. The sides of a rectangle are 8.5 cm and 4.2 cm.
    Each length is correct to 1 decimal place.
    Work out the lower bound of the area of the rectangle.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 8.5 - 0.05 and 4.2 - 0.05
    2. M1: 8.45 × 4.15
    3. A1: 35.0675
    Answer: 35.0675 cm²
    Bounds & Error Intervals Involving Calculations
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 028

Grades 6/7Calculator

  1. Question 1. P is the point (2, 3), A is the point (-1, -1) and B is the point (7, 7).
    Which of A and B is nearer to P?
    You must show your working.

    Show worked answerHide worked answer
    1. M1: PA = √3² + 4²
    2. M1: PB = √5² + 4²
    3. A1: PA = 5 and PB = 6.4 to 1 decimal place, so A is nearer
    Answer: A is nearer: PA = 5 and PB = 6.4
    Finding the Distance Between Two Points
    [3 marks]

  2. Question 2. Simplify dfrac6x² + 3x3x

    Show worked answerHide worked answer
    1. M1: factorises numerator 3x(2x+1)
    2. A1: 2x + 1
    Answer: 2x + 1
    Simplifying Algebraic Fractions
    [2 marks]

  3. Question 3. Shop A: minimum 4, lower quartile 9, median 12, upper quartile 15, maximum 30. Shop B: minimum 6, lower quartile 8, median 12, upper quartile 14, maximum 18. Compare the ranges and the interquartile ranges.

    Show worked answerHide worked answer
    1. B1: ranges: A 26, B 12
    2. B1: IQRs: A 6, B 6
    3. B1: A has the greater range but the IQRs are equal
    Answer: Range: A 26, B 12. IQR: both 6. A has the greater range; the middle halves are equally spread.
    Comparing Data Using Box Plots
    [3 marks]

  4. Question 4. Triangle ABC has AB = 8 cm, BC = 11 cm and angle ABC = 40^°
    Work out its area.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 1/2 × 8 × 11 × sin 40^°
    2. A1: 28.3
    Answer: 28.3 cm²
    Calculating Area Using ½ab sin C
    [2 marks]

  5. Question 5. The sides of a rectangle are 8.5 cm and 4.2 cm.
    Each length is correct to 1 decimal place.
    Work out the lower bound of the area of the rectangle.

    Show worked answerHide worked answer
    1. M1: 8.5 - 0.05 and 4.2 - 0.05
    2. M1: 8.45 × 4.15
    3. A1: 35.0675
    Answer: 35.0675 cm²
    Bounds & Error Intervals Involving Calculations
    [3 marks]