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

Mixed Topic Worksheet Grades 8/9: Day 026

Grades 8/9Calculator

  1. Question 1. cos 25^° = 0.906 correct to 3 decimal places. Write down the two values of x, between 0^° and 360^°, for which cos x = -0.906

    Show worked answerHide worked answer
    1. M1: 180^° - 25^° or 180^° + 25^°
    2. A1: 155^° and 205^°
    Answer: x = 155^° and x = 205^°
    Calculating Values of Trig Functions Using Graphs
    [2 marks]

  2. Question 2. A pyramid has a rectangular base 8 cm by 6 cm. Its apex is 10 cm vertically above the centre of the base. Work out the angle between a sloping edge and the base. Give your answer correct to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: half the base diagonal = 1/2√8² + 6² = 5
    2. M1: tanθ = 10/5 = 2
    3. A1: 63.4°
    Answer: 63.4°
    3D Trigonometry
    [3 marks]

  3. Question 3. y is inversely proportional to √x. When x=25, y=4. Work out the value of y when x=100.

    Show worked answerHide worked answer
    1. M1: y=dfrack√x, 4=dfrack5, k=20
    2. M1: y=dfrac20√100
    3. A1: y=2
    Answer: y=2
    Direct & Inverse Proportion with Functions
    [3 marks]

  4. Question 4. Work out the area of the rectangle.

    Show worked answerHide worked answer
    1. M1: dfracx+54×dfrac12x²-25
    2. M2: x²-25=(x-5)(x+5), cancels (x+5) and divides by 4
    3. A1: dfrac3x-5
    Answer: dfrac3x-5 cm²
    Multiplying & Dividing Algebraic Fractions
    (x + 5)/4 cm12/(x2 − 25) cmABCDNot drawn accurately
    [4 marks]

  5. Question 5. overrightarrowOP=2mathbfa+mathbfb and overrightarrowOR=7mathbfa-4mathbfb. Q lies on PR with PQ:QR=2:3. Find overrightarrowOQ in terms of mathbfa and mathbfb.

    Show worked answerHide worked answer
    1. M1: overrightarrowPR=(7mathbfa-4mathbfb)-(2mathbfa+mathbfb)=5mathbfa-5mathbfb
    2. M1: overrightarrowOQ=2mathbfa+mathbfb+2/5(5mathbfa-5mathbfb)
    3. A1: 4mathbfa-mathbfb
    Answer: overrightarrowOQ=4mathbfa-mathbfb
    Vector Ratio Problems
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 026

Grades 8/9Calculator

  1. Question 1. cos 25^° = 0.906 correct to 3 decimal places. Write down the two values of x, between 0^° and 360^°, for which cos x = -0.906

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 180^° - 25^° or 180^° + 25^°
    2. A1: 155^° and 205^°
    Answer: x = 155^° and x = 205^°
    Calculating Values of Trig Functions Using Graphs

  2. Question 2. A pyramid has a rectangular base 8 cm by 6 cm. Its apex is 10 cm vertically above the centre of the base. Work out the angle between a sloping edge and the base. Give your answer correct to 1 decimal place.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: half the base diagonal = 1/2√8² + 6² = 5
    2. M1: tanθ = 10/5 = 2
    3. A1: 63.4°
    Answer: 63.4°
    3D Trigonometry

  3. Question 3. y is inversely proportional to √x. When x=25, y=4. Work out the value of y when x=100.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: y=dfrack√x, 4=dfrack5, k=20
    2. M1: y=dfrac20√100
    3. A1: y=2
    Answer: y=2
    Direct & Inverse Proportion with Functions

  4. Question 4. Work out the area of the rectangle.

    [4 marks]
    (x + 5)/4 cm12/(x2 − 25) cmABCDNot drawn accurately
    Show worked answerHide worked answer
    1. M1: dfracx+54×dfrac12x²-25
    2. M2: x²-25=(x-5)(x+5), cancels (x+5) and divides by 4
    3. A1: dfrac3x-5
    Answer: dfrac3x-5 cm²
    Multiplying & Dividing Algebraic Fractions

  5. Question 5. overrightarrowOP=2mathbfa+mathbfb and overrightarrowOR=7mathbfa-4mathbfb. Q lies on PR with PQ:QR=2:3. Find overrightarrowOQ in terms of mathbfa and mathbfb.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: overrightarrowPR=(7mathbfa-4mathbfb)-(2mathbfa+mathbfb)=5mathbfa-5mathbfb
    2. M1: overrightarrowOQ=2mathbfa+mathbfb+2/5(5mathbfa-5mathbfb)
    3. A1: 4mathbfa-mathbfb
    Answer: overrightarrowOQ=4mathbfa-mathbfb
    Vector Ratio Problems
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 026

Grades 8/9Calculator

  1. Question 1. cos 25^° = 0.906 correct to 3 decimal places. Write down the two values of x, between 0^° and 360^°, for which cos x = -0.906

    Show worked answerHide worked answer
    1. M1: 180^° - 25^° or 180^° + 25^°
    2. A1: 155^° and 205^°
    Answer: x = 155^° and x = 205^°
    Calculating Values of Trig Functions Using Graphs
    [2 marks]

  2. Question 2. A pyramid has a rectangular base 8 cm by 6 cm. Its apex is 10 cm vertically above the centre of the base. Work out the angle between a sloping edge and the base. Give your answer correct to 1 decimal place.

    Show worked answerHide worked answer
    1. M1: half the base diagonal = 1/2√8² + 6² = 5
    2. M1: tanθ = 10/5 = 2
    3. A1: 63.4°
    Answer: 63.4°
    3D Trigonometry
    [3 marks]

  3. Question 3. y is inversely proportional to √x. When x=25, y=4. Work out the value of y when x=100.

    Show worked answerHide worked answer
    1. M1: y=dfrack√x, 4=dfrack5, k=20
    2. M1: y=dfrac20√100
    3. A1: y=2
    Answer: y=2
    Direct & Inverse Proportion with Functions
    [3 marks]

  4. Question 4. Work out the area of the rectangle.

    Show worked answerHide worked answer
    1. M1: dfracx+54×dfrac12x²-25
    2. M2: x²-25=(x-5)(x+5), cancels (x+5) and divides by 4
    3. A1: dfrac3x-5
    Answer: dfrac3x-5 cm²
    Multiplying & Dividing Algebraic Fractions
    (x + 5)/4 cm12/(x2 − 25) cmABCDNot drawn accurately
    [4 marks]

  5. Question 5. overrightarrowOP=2mathbfa+mathbfb and overrightarrowOR=7mathbfa-4mathbfb. Q lies on PR with PQ:QR=2:3. Find overrightarrowOQ in terms of mathbfa and mathbfb.

    Show worked answerHide worked answer
    1. M1: overrightarrowPR=(7mathbfa-4mathbfb)-(2mathbfa+mathbfb)=5mathbfa-5mathbfb
    2. M1: overrightarrowOQ=2mathbfa+mathbfb+2/5(5mathbfa-5mathbfb)
    3. A1: 4mathbfa-mathbfb
    Answer: overrightarrowOQ=4mathbfa-mathbfb
    Vector Ratio Problems
    [3 marks]