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

Mixed Topic Worksheet Grades 6/7: Day 015

Grades 6/7Non-calculator

  1. Question 1. The graph of y = x² + 16x + 64 touches the x-axis at one point.
    Work out the x-coordinate of this point.

    Show worked answerHide worked answer
    1. M1: (x + 8)² = 0
    2. A1: x = -8
    Answer: -8
    x-Intercepts of Quadratics
    [2 marks]

  2. Question 2. The point A(4, 5) is enlarged by scale factor -2, centre (1, 3).
    Work out the coordinates of the image of A.

    Show worked answerHide worked answer
    1. M1: from the centre to A is 3 right and 2 up
    2. M1: times -2: 6 left and 4 down from the centre
    3. A1: (-5, -1)
    Answer: (-5, -1)
    Enlargements with Negative Integer Scale Factors
    [3 marks]

  3. Question 3. Rectangle A and rectangle B are similar.
    The area of rectangle A is 12 cm².
    Work out the area of rectangle B.

    Show worked answerHide worked answer
    1. M1: 15 ÷ 6 = 2.5
    2. M1: 2.5² × 12
    3. A1: 75
    Answer: 75 cm²
    Similar Areas & Volumes
    6 cm15 cmABNot drawn accurately
    [3 marks]

  4. Question 4. Prove algebraically that the difference between any two odd numbers is even.
    The smaller number is subtracted from the larger.

    Show worked answerHide worked answer
    1. M1: (2m + 1) - (2n + 1) for two odd numbers
    2. C1: 2(m - n), which is even
    Answer: 2(m - n)
    Proof with Odd Numbers
    [2 marks]

  5. Question 5. A right-angled triangle has two equal shorter sides. The hypotenuse of the triangle is 10 cm. Work out the length of one of the equal sides, giving your answer in the form a√2 where a is an integer.

    Show worked answerHide worked answer
    1. M1: 2x² = 10² so x = dfrac10√2
    2. M1: dfrac10√22
    3. A1: 5√2 cm
    Answer: 5√2 cm
    Rationalising Denominators of the Form √a
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 015

Grades 6/7Non-calculator

  1. Question 1. The graph of y = x² + 16x + 64 touches the x-axis at one point.
    Work out the x-coordinate of this point.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: (x + 8)² = 0
    2. A1: x = -8
    Answer: -8
    x-Intercepts of Quadratics

  2. Question 2. The point A(4, 5) is enlarged by scale factor -2, centre (1, 3).
    Work out the coordinates of the image of A.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: from the centre to A is 3 right and 2 up
    2. M1: times -2: 6 left and 4 down from the centre
    3. A1: (-5, -1)
    Answer: (-5, -1)
    Enlargements with Negative Integer Scale Factors

  3. Question 3. Rectangle A and rectangle B are similar.
    The area of rectangle A is 12 cm².
    Work out the area of rectangle B.

    [3 marks]
    6 cm15 cmABNot drawn accurately
    Show worked answerHide worked answer
    1. M1: 15 ÷ 6 = 2.5
    2. M1: 2.5² × 12
    3. A1: 75
    Answer: 75 cm²
    Similar Areas & Volumes

  4. Question 4. Prove algebraically that the difference between any two odd numbers is even.
    The smaller number is subtracted from the larger.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: (2m + 1) - (2n + 1) for two odd numbers
    2. C1: 2(m - n), which is even
    Answer: 2(m - n)
    Proof with Odd Numbers

  5. Question 5. A right-angled triangle has two equal shorter sides. The hypotenuse of the triangle is 10 cm. Work out the length of one of the equal sides, giving your answer in the form a√2 where a is an integer.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 2x² = 10² so x = dfrac10√2
    2. M1: dfrac10√22
    3. A1: 5√2 cm
    Answer: 5√2 cm
    Rationalising Denominators of the Form √a
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 015

Grades 6/7Non-calculator

  1. Question 1. The graph of y = x² + 16x + 64 touches the x-axis at one point.
    Work out the x-coordinate of this point.

    Show worked answerHide worked answer
    1. M1: (x + 8)² = 0
    2. A1: x = -8
    Answer: -8
    x-Intercepts of Quadratics
    [2 marks]

  2. Question 2. The point A(4, 5) is enlarged by scale factor -2, centre (1, 3).
    Work out the coordinates of the image of A.

    Show worked answerHide worked answer
    1. M1: from the centre to A is 3 right and 2 up
    2. M1: times -2: 6 left and 4 down from the centre
    3. A1: (-5, -1)
    Answer: (-5, -1)
    Enlargements with Negative Integer Scale Factors
    [3 marks]

  3. Question 3. Rectangle A and rectangle B are similar.
    The area of rectangle A is 12 cm².
    Work out the area of rectangle B.

    Show worked answerHide worked answer
    1. M1: 15 ÷ 6 = 2.5
    2. M1: 2.5² × 12
    3. A1: 75
    Answer: 75 cm²
    Similar Areas & Volumes
    6 cm15 cmABNot drawn accurately
    [3 marks]

  4. Question 4. Prove algebraically that the difference between any two odd numbers is even.
    The smaller number is subtracted from the larger.

    Show worked answerHide worked answer
    1. M1: (2m + 1) - (2n + 1) for two odd numbers
    2. C1: 2(m - n), which is even
    Answer: 2(m - n)
    Proof with Odd Numbers
    [2 marks]

  5. Question 5. A right-angled triangle has two equal shorter sides. The hypotenuse of the triangle is 10 cm. Work out the length of one of the equal sides, giving your answer in the form a√2 where a is an integer.

    Show worked answerHide worked answer
    1. M1: 2x² = 10² so x = dfrac10√2
    2. M1: dfrac10√22
    3. A1: 5√2 cm
    Answer: 5√2 cm
    Rationalising Denominators of the Form √a
    [3 marks]