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

Mixed Topic Worksheet Grades 6/7: Day 022

Grades 6/7Calculator

  1. Question 1. n(xi)=50, P(A)=0.4, P(B)=0.3 and P(A cap B)=0.1. Work out the number of members of xi in neither A nor B.

    Show worked answerHide worked answer
    1. M1: P(A cup B)=0.4+0.3-0.1=0.6
    2. M1: P(neither)=1-0.6=0.4
    3. A1: 0.4 × 50=20
    Answer: 20
    Finding Probabilities of Sets
    [3 marks]

  2. Question 2. Write down the least integer that is greater than the cube root of 200

    Show worked answerHide worked answer
    1. M1: 5³ = 125 and 6³ = 216, so 125 < 200 < 216
    2. A1: 6
    Answer: 6
    Estimating Roots
    [2 marks]

  3. Question 3. A reflection maps the point (1, 6) onto the point (7, 6).
    Work out the coordinates of the image of the point (2, 3) under the same reflection.

    Show worked answerHide worked answer
    1. M1: the mirror line is halfway between x = 1 and x = 7
    2. M1: (2, 3) is 4 - 2 = 2 left of the mirror line x = 4, so its image is 2 to the right of it
    3. A1: (6, 3)
    Answer: (6, 3)
    Invariant Points
    [3 marks]

  4. Question 4. Prove algebraically that the sum of any two even numbers is even.

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

  5. Question 5. Here is triangle ABC.
    Work out the size of angle CBA.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 17² = 22² + 24² - 2 × 22 × 24 × cos CBA
    2. M1: cos CBA = dfrac22² + 24² - 17²2 × 22 × 24 = 0.7301
    3. A1: CBA = 43.1^°
    Answer: 43.1^°
    Finding Angles Using the Cosine Rule
    24 cm22 cm17 cmABC
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 022

Grades 6/7Calculator

  1. Question 1. n(xi)=50, P(A)=0.4, P(B)=0.3 and P(A cap B)=0.1. Work out the number of members of xi in neither A nor B.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: P(A cup B)=0.4+0.3-0.1=0.6
    2. M1: P(neither)=1-0.6=0.4
    3. A1: 0.4 × 50=20
    Answer: 20
    Finding Probabilities of Sets

  2. Question 2. Write down the least integer that is greater than the cube root of 200

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 5³ = 125 and 6³ = 216, so 125 < 200 < 216
    2. A1: 6
    Answer: 6
    Estimating Roots

  3. Question 3. A reflection maps the point (1, 6) onto the point (7, 6).
    Work out the coordinates of the image of the point (2, 3) under the same reflection.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: the mirror line is halfway between x = 1 and x = 7
    2. M1: (2, 3) is 4 - 2 = 2 left of the mirror line x = 4, so its image is 2 to the right of it
    3. A1: (6, 3)
    Answer: (6, 3)
    Invariant Points

  4. Question 4. Prove algebraically that the sum of any two even numbers is even.

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

  5. Question 5. Here is triangle ABC.
    Work out the size of angle CBA.
    Give your answer to 1 decimal place.

    [3 marks]
    24 cm22 cm17 cmABC
    Show worked answerHide worked answer
    1. M1: 17² = 22² + 24² - 2 × 22 × 24 × cos CBA
    2. M1: cos CBA = dfrac22² + 24² - 17²2 × 22 × 24 = 0.7301
    3. A1: CBA = 43.1^°
    Answer: 43.1^°
    Finding Angles Using the Cosine Rule
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 022

Grades 6/7Calculator

  1. Question 1. n(xi)=50, P(A)=0.4, P(B)=0.3 and P(A cap B)=0.1. Work out the number of members of xi in neither A nor B.

    Show worked answerHide worked answer
    1. M1: P(A cup B)=0.4+0.3-0.1=0.6
    2. M1: P(neither)=1-0.6=0.4
    3. A1: 0.4 × 50=20
    Answer: 20
    Finding Probabilities of Sets
    [3 marks]

  2. Question 2. Write down the least integer that is greater than the cube root of 200

    Show worked answerHide worked answer
    1. M1: 5³ = 125 and 6³ = 216, so 125 < 200 < 216
    2. A1: 6
    Answer: 6
    Estimating Roots
    [2 marks]

  3. Question 3. A reflection maps the point (1, 6) onto the point (7, 6).
    Work out the coordinates of the image of the point (2, 3) under the same reflection.

    Show worked answerHide worked answer
    1. M1: the mirror line is halfway between x = 1 and x = 7
    2. M1: (2, 3) is 4 - 2 = 2 left of the mirror line x = 4, so its image is 2 to the right of it
    3. A1: (6, 3)
    Answer: (6, 3)
    Invariant Points
    [3 marks]

  4. Question 4. Prove algebraically that the sum of any two even numbers is even.

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

  5. Question 5. Here is triangle ABC.
    Work out the size of angle CBA.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: 17² = 22² + 24² - 2 × 22 × 24 × cos CBA
    2. M1: cos CBA = dfrac22² + 24² - 17²2 × 22 × 24 = 0.7301
    3. A1: CBA = 43.1^°
    Answer: 43.1^°
    Finding Angles Using the Cosine Rule
    24 cm22 cm17 cmABC
    [3 marks]