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

Mixed Topic Worksheet Grades 8/9: Day 012

Grades 8/9Calculator

  1. Question 1. The histogram is part drawn. It shows the weights, w kg, of 105 dogs. Work out the height of the undrawn bar for 40 < w ≤ 60.

    Show worked answerHide worked answer
    1. M1: 105 - (2 × 10 + 3.5 × 10 + 1.5 × 20)
    2. M1: 20 ÷ (60 - 40)
    3. A1: 1
    Answer: 1
    Interpreting Histograms
    Weight, w (kg)Frequency density012340204060
    [3 marks]

  2. Question 2. Use your calculator to find the two values of x, between 0^° and 360^°, for which cos x = -0.62. Give your answers correct to 1 decimal place

    Show worked answerHide worked answer
    1. M1: x = cos⁻¹(-0.62)
    2. M1: second solution is 360^° minus the first
    3. A1: 128.3^° and 231.7^°
    Answer: x = 128.3^° and x = 231.7^°
    Calculating Values of Trig Functions Using Graphs
    [3 marks]

  3. Question 3. A rectangle has area 48 cm² and diagonal 10 cm
    Work out the perimeter of the rectangle

    Show worked answerHide worked answer
    1. M1: x² + y² = 100 and xy = 48
    2. M1: (x + y)² = 100 + 2 × 48 = 196
    3. A1: x + y = 14 so perimeter = 28 cm
    Answer: 28 cm
    Solving Quadratic Simultaneous Equations
    [3 marks]

  4. Question 4. The equation x² + kx + 9 = 0 has no real solutions.
    Work out the possible values of k

    Show worked answerHide worked answer
    1. M1: uses b² - 4ac < 0 to get k² - 36 < 0
    2. M1: finds the critical values k = 6 and k = -6
    3. M1: the expression k² - 36 is negative between its roots
    4. A1: -6 < k < 6
    Answer: -6 < k < 6
    Sketching Quadratic Inequalities
    [4 marks]

  5. Question 5. overrightarrowOA=mathbfa, overrightarrowOB=mathbfb, M is the midpoint of AB and overrightarrowOC=3mathbfa+3mathbfb. Show that O, M and C lie on a straight line.

    Show worked answerHide worked answer
    1. M2: overrightarrowOM=1/2(mathbfa+mathbfb), so overrightarrowOC=6overrightarrowOM
    2. A1: parallel and both from O, so O, M, C are collinear
    Answer: overrightarrowOC=6overrightarrowOM, common point O
    Vectors Along a Straight Line
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 012

Grades 8/9Calculator

  1. Question 1. The histogram is part drawn. It shows the weights, w kg, of 105 dogs. Work out the height of the undrawn bar for 40 < w ≤ 60.

    [3 marks]
    Weight, w (kg)Frequency density012340204060
    Show worked answerHide worked answer
    1. M1: 105 - (2 × 10 + 3.5 × 10 + 1.5 × 20)
    2. M1: 20 ÷ (60 - 40)
    3. A1: 1
    Answer: 1
    Interpreting Histograms

  2. Question 2. Use your calculator to find the two values of x, between 0^° and 360^°, for which cos x = -0.62. Give your answers correct to 1 decimal place

    [3 marks]
    Show worked answerHide worked answer
    1. M1: x = cos⁻¹(-0.62)
    2. M1: second solution is 360^° minus the first
    3. A1: 128.3^° and 231.7^°
    Answer: x = 128.3^° and x = 231.7^°
    Calculating Values of Trig Functions Using Graphs

  3. Question 3. A rectangle has area 48 cm² and diagonal 10 cm
    Work out the perimeter of the rectangle

    [3 marks]
    Show worked answerHide worked answer
    1. M1: x² + y² = 100 and xy = 48
    2. M1: (x + y)² = 100 + 2 × 48 = 196
    3. A1: x + y = 14 so perimeter = 28 cm
    Answer: 28 cm
    Solving Quadratic Simultaneous Equations

  4. Question 4. The equation x² + kx + 9 = 0 has no real solutions.
    Work out the possible values of k

    [4 marks]
    Show worked answerHide worked answer
    1. M1: uses b² - 4ac < 0 to get k² - 36 < 0
    2. M1: finds the critical values k = 6 and k = -6
    3. M1: the expression k² - 36 is negative between its roots
    4. A1: -6 < k < 6
    Answer: -6 < k < 6
    Sketching Quadratic Inequalities

  5. Question 5. overrightarrowOA=mathbfa, overrightarrowOB=mathbfb, M is the midpoint of AB and overrightarrowOC=3mathbfa+3mathbfb. Show that O, M and C lie on a straight line.

    [3 marks]
    Show worked answerHide worked answer
    1. M2: overrightarrowOM=1/2(mathbfa+mathbfb), so overrightarrowOC=6overrightarrowOM
    2. A1: parallel and both from O, so O, M, C are collinear
    Answer: overrightarrowOC=6overrightarrowOM, common point O
    Vectors Along a Straight Line
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 012

Grades 8/9Calculator

  1. Question 1. The histogram is part drawn. It shows the weights, w kg, of 105 dogs. Work out the height of the undrawn bar for 40 < w ≤ 60.

    Show worked answerHide worked answer
    1. M1: 105 - (2 × 10 + 3.5 × 10 + 1.5 × 20)
    2. M1: 20 ÷ (60 - 40)
    3. A1: 1
    Answer: 1
    Interpreting Histograms
    Weight, w (kg)Frequency density012340204060
    [3 marks]

  2. Question 2. Use your calculator to find the two values of x, between 0^° and 360^°, for which cos x = -0.62. Give your answers correct to 1 decimal place

    Show worked answerHide worked answer
    1. M1: x = cos⁻¹(-0.62)
    2. M1: second solution is 360^° minus the first
    3. A1: 128.3^° and 231.7^°
    Answer: x = 128.3^° and x = 231.7^°
    Calculating Values of Trig Functions Using Graphs
    [3 marks]

  3. Question 3. A rectangle has area 48 cm² and diagonal 10 cm
    Work out the perimeter of the rectangle

    Show worked answerHide worked answer
    1. M1: x² + y² = 100 and xy = 48
    2. M1: (x + y)² = 100 + 2 × 48 = 196
    3. A1: x + y = 14 so perimeter = 28 cm
    Answer: 28 cm
    Solving Quadratic Simultaneous Equations
    [3 marks]

  4. Question 4. The equation x² + kx + 9 = 0 has no real solutions.
    Work out the possible values of k

    Show worked answerHide worked answer
    1. M1: uses b² - 4ac < 0 to get k² - 36 < 0
    2. M1: finds the critical values k = 6 and k = -6
    3. M1: the expression k² - 36 is negative between its roots
    4. A1: -6 < k < 6
    Answer: -6 < k < 6
    Sketching Quadratic Inequalities
    [4 marks]

  5. Question 5. overrightarrowOA=mathbfa, overrightarrowOB=mathbfb, M is the midpoint of AB and overrightarrowOC=3mathbfa+3mathbfb. Show that O, M and C lie on a straight line.

    Show worked answerHide worked answer
    1. M2: overrightarrowOM=1/2(mathbfa+mathbfb), so overrightarrowOC=6overrightarrowOM
    2. A1: parallel and both from O, so O, M, C are collinear
    Answer: overrightarrowOC=6overrightarrowOM, common point O
    Vectors Along a Straight Line
    [3 marks]