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

Mixed Topic Worksheet Grades 6/7: Day 072

Grades 6/7Calculator

  1. Question 1. A boat leaves A and sails to B on a bearing of 038^°.
    B is 9.6 km east of A.
    Work out the distance AB.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: sin 38° = 9.6/AB
    2. M1: AB = 9.6 ÷ sin 38°
    3. A1: 15.6
    Answer: 15.6 km
    Bearings Problems Involving SOH, CAH, TOA
    N038°AB9.6 kmABNot drawn accurately
    [3 marks]

  2. Question 2. Jo says: “When I add two irrational numbers, the answer is always irrational.”
    Show that Jo is wrong.

    Show worked answerHide worked answer
    1. M1: two irrational numbers chosen, such as √2 and -√2
    2. A1: their sum 0 is rational
    Answer: For example √2 + (-√2) = 0, which is rational.
    Rational & Irrational Numbers
    [2 marks]

  3. Question 3. The area of triangle XYZ is 24 cm².
    Angle x is acute.
    Work out the size of angle x.
    Give your answer to 1 decimal place.
    Diagram not drawn accurately.

    Show worked answerHide worked answer
    1. M1: 1/2 × 9 × 6 × sin x = 24
    2. M1: sin x = 48/54
    3. A1: 62.7
    Answer: 62.7^°
    Area of Triangles Using ½ab sin C
    9 cm6 cmxXYZ
    [3 marks]

  4. Question 4. Prove algebraically that the sum of four consecutive even numbers is a multiple of 4.

    Show worked answerHide worked answer
    1. M1: 2n + (2n + 2) + (2n + 4) + (2n + 6)
    2. A1: 8n + 12
    3. C1: 4(2n + 3), which is a multiple of 4
    Answer: 4(2n + 3)
    Proof with Even Numbers
    [3 marks]

  5. Question 5. y is inversely proportional to the square of x.
    x is increased by 25%.
    Work out the percentage decrease in y.

    Show worked answerHide worked answer
    1. M1: y is multiplied by 1 ÷ (1 + 25 ÷ 100)²
    2. M1: 1 ÷ 1.5625 = 0.64
    3. A1: 36%
    Answer: 36%
    Algebraic Inverse Proportion
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 6/7: Day 072

Grades 6/7Calculator

  1. Question 1. A boat leaves A and sails to B on a bearing of 038^°.
    B is 9.6 km east of A.
    Work out the distance AB.
    Give your answer to 1 decimal place.

    [3 marks]
    N038°AB9.6 kmABNot drawn accurately
    Show worked answerHide worked answer
    1. M1: sin 38° = 9.6/AB
    2. M1: AB = 9.6 ÷ sin 38°
    3. A1: 15.6
    Answer: 15.6 km
    Bearings Problems Involving SOH, CAH, TOA

  2. Question 2. Jo says: “When I add two irrational numbers, the answer is always irrational.”
    Show that Jo is wrong.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: two irrational numbers chosen, such as √2 and -√2
    2. A1: their sum 0 is rational
    Answer: For example √2 + (-√2) = 0, which is rational.
    Rational & Irrational Numbers

  3. Question 3. The area of triangle XYZ is 24 cm².
    Angle x is acute.
    Work out the size of angle x.
    Give your answer to 1 decimal place.
    Diagram not drawn accurately.

    [3 marks]
    9 cm6 cmxXYZ
    Show worked answerHide worked answer
    1. M1: 1/2 × 9 × 6 × sin x = 24
    2. M1: sin x = 48/54
    3. A1: 62.7
    Answer: 62.7^°
    Area of Triangles Using ½ab sin C

  4. Question 4. Prove algebraically that the sum of four consecutive even numbers is a multiple of 4.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: 2n + (2n + 2) + (2n + 4) + (2n + 6)
    2. A1: 8n + 12
    3. C1: 4(2n + 3), which is a multiple of 4
    Answer: 4(2n + 3)
    Proof with Even Numbers

  5. Question 5. y is inversely proportional to the square of x.
    x is increased by 25%.
    Work out the percentage decrease in y.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: y is multiplied by 1 ÷ (1 + 25 ÷ 100)²
    2. M1: 1 ÷ 1.5625 = 0.64
    3. A1: 36%
    Answer: 36%
    Algebraic Inverse Proportion
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 6/7: Day 072

Grades 6/7Calculator

  1. Question 1. A boat leaves A and sails to B on a bearing of 038^°.
    B is 9.6 km east of A.
    Work out the distance AB.
    Give your answer to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: sin 38° = 9.6/AB
    2. M1: AB = 9.6 ÷ sin 38°
    3. A1: 15.6
    Answer: 15.6 km
    Bearings Problems Involving SOH, CAH, TOA
    N038°AB9.6 kmABNot drawn accurately
    [3 marks]

  2. Question 2. Jo says: “When I add two irrational numbers, the answer is always irrational.”
    Show that Jo is wrong.

    Show worked answerHide worked answer
    1. M1: two irrational numbers chosen, such as √2 and -√2
    2. A1: their sum 0 is rational
    Answer: For example √2 + (-√2) = 0, which is rational.
    Rational & Irrational Numbers
    [2 marks]

  3. Question 3. The area of triangle XYZ is 24 cm².
    Angle x is acute.
    Work out the size of angle x.
    Give your answer to 1 decimal place.
    Diagram not drawn accurately.

    Show worked answerHide worked answer
    1. M1: 1/2 × 9 × 6 × sin x = 24
    2. M1: sin x = 48/54
    3. A1: 62.7
    Answer: 62.7^°
    Area of Triangles Using ½ab sin C
    9 cm6 cmxXYZ
    [3 marks]

  4. Question 4. Prove algebraically that the sum of four consecutive even numbers is a multiple of 4.

    Show worked answerHide worked answer
    1. M1: 2n + (2n + 2) + (2n + 4) + (2n + 6)
    2. A1: 8n + 12
    3. C1: 4(2n + 3), which is a multiple of 4
    Answer: 4(2n + 3)
    Proof with Even Numbers
    [3 marks]

  5. Question 5. y is inversely proportional to the square of x.
    x is increased by 25%.
    Work out the percentage decrease in y.

    Show worked answerHide worked answer
    1. M1: y is multiplied by 1 ÷ (1 + 25 ÷ 100)²
    2. M1: 1 ÷ 1.5625 = 0.64
    3. A1: 36%
    Answer: 36%
    Algebraic Inverse Proportion
    [3 marks]