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

Mixed Topic Worksheet Grades 6/7: Day 074

Grades 6/7Calculator

  1. Question 1. xi=1, 2, 3, ldots, 60, A=multiples of 6 and B=multiples of 8. A number is chosen at random from xi. Work out P(A cup B).

    Show worked answerHide worked answer
    1. M1: n(A)=10, n(B)=7 and A cap B=24, 48
    2. M1: n(A cup B)=10+7-2=15
    3. A1: dfrac1560=dfrac14
    Answer: dfrac14
    Finding Probabilities of Sets
    [3 marks]

  2. Question 2. A shape is reflected in the line y = x.
    Which of these points are invariant?
    A(3, 3) B(3, -3) C(-2, -2) D(0, 4)

    Show worked answerHide worked answer
    1. B1: one of A or C, as it lies on y = x
    2. B1: A and C only
    Answer: A and C
    Invariant Points
    [2 marks]

  3. Question 3. n is a positive integer. √n is rounded to the nearest integer and the answer is 8 Work out the smallest possible value of n.

    Show worked answerHide worked answer
    1. M1: √n ≥ 7.5
    2. M1: 7.5² = 56.25 so n must be at least 57
    3. A1: 57
    Answer: 57
    Estimating Roots
    [3 marks]

  4. Question 4. In parallelogram PQRS, PQ = 7.2 cm, QR = 5.5 cm and angle PQR = 112°. Work out the area of PQRS. Give your answer correct to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: 7.2 × 5.5 × sin 112°
    2. A1: 36.7 cm²
    Answer: 36.7 cm²
    Finding the Area of a Parallelogram
    [2 marks]

  5. Question 5. Here is an identity
    a(x - b) equiv -2x + 6
    Work out the values of a and b.

    Show worked answerHide worked answer
    1. M1: a = −2 from the x terms
    2. M1: −ab = 6 (constants compared)
    3. A1: a = −2, b = 3
    Answer: a = -2, b = 3
    Equating Coefficients
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 074

Grades 6/7Calculator

  1. Question 1. xi=1, 2, 3, ldots, 60, A=multiples of 6 and B=multiples of 8. A number is chosen at random from xi. Work out P(A cup B).

    [3 marks]
    Show worked answerHide worked answer
    1. M1: n(A)=10, n(B)=7 and A cap B=24, 48
    2. M1: n(A cup B)=10+7-2=15
    3. A1: dfrac1560=dfrac14
    Answer: dfrac14
    Finding Probabilities of Sets

  2. Question 2. A shape is reflected in the line y = x.
    Which of these points are invariant?
    A(3, 3) B(3, -3) C(-2, -2) D(0, 4)

    [2 marks]
    Show worked answerHide worked answer
    1. B1: one of A or C, as it lies on y = x
    2. B1: A and C only
    Answer: A and C
    Invariant Points

  3. Question 3. n is a positive integer. √n is rounded to the nearest integer and the answer is 8 Work out the smallest possible value of n.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: √n ≥ 7.5
    2. M1: 7.5² = 56.25 so n must be at least 57
    3. A1: 57
    Answer: 57
    Estimating Roots

  4. Question 4. In parallelogram PQRS, PQ = 7.2 cm, QR = 5.5 cm and angle PQR = 112°. Work out the area of PQRS. Give your answer correct to 3 significant figures.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 7.2 × 5.5 × sin 112°
    2. A1: 36.7 cm²
    Answer: 36.7 cm²
    Finding the Area of a Parallelogram

  5. Question 5. Here is an identity
    a(x - b) equiv -2x + 6
    Work out the values of a and b.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: a = −2 from the x terms
    2. M1: −ab = 6 (constants compared)
    3. A1: a = −2, b = 3
    Answer: a = -2, b = 3
    Equating Coefficients
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 074

Grades 6/7Calculator

  1. Question 1. xi=1, 2, 3, ldots, 60, A=multiples of 6 and B=multiples of 8. A number is chosen at random from xi. Work out P(A cup B).

    Show worked answerHide worked answer
    1. M1: n(A)=10, n(B)=7 and A cap B=24, 48
    2. M1: n(A cup B)=10+7-2=15
    3. A1: dfrac1560=dfrac14
    Answer: dfrac14
    Finding Probabilities of Sets
    [3 marks]

  2. Question 2. A shape is reflected in the line y = x.
    Which of these points are invariant?
    A(3, 3) B(3, -3) C(-2, -2) D(0, 4)

    Show worked answerHide worked answer
    1. B1: one of A or C, as it lies on y = x
    2. B1: A and C only
    Answer: A and C
    Invariant Points
    [2 marks]

  3. Question 3. n is a positive integer. √n is rounded to the nearest integer and the answer is 8 Work out the smallest possible value of n.

    Show worked answerHide worked answer
    1. M1: √n ≥ 7.5
    2. M1: 7.5² = 56.25 so n must be at least 57
    3. A1: 57
    Answer: 57
    Estimating Roots
    [3 marks]

  4. Question 4. In parallelogram PQRS, PQ = 7.2 cm, QR = 5.5 cm and angle PQR = 112°. Work out the area of PQRS. Give your answer correct to 3 significant figures.

    Show worked answerHide worked answer
    1. M1: 7.2 × 5.5 × sin 112°
    2. A1: 36.7 cm²
    Answer: 36.7 cm²
    Finding the Area of a Parallelogram
    [2 marks]

  5. Question 5. Here is an identity
    a(x - b) equiv -2x + 6
    Work out the values of a and b.

    Show worked answerHide worked answer
    1. M1: a = −2 from the x terms
    2. M1: −ab = 6 (constants compared)
    3. A1: a = −2, b = 3
    Answer: a = -2, b = 3
    Equating Coefficients
    [3 marks]