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

Mixed Topic Worksheet Grades 8/9: Day 057

Grades 8/9Non-calculator

  1. Question 1. The cosine graph repeats every 360°. Write down the value of cos 540°.

    Show worked answerHide worked answer
    1. M1: 540 - 360 = 180
    2. A1: -1
    Answer: -1
    Sketching sin, cos & tan
    [2 marks]

  2. Question 2. The histogram shows the lengths, x cm, of some ropes. Assume values are spread evenly in each class and the median is the n/2th value. Work out an estimate for the median length.

    Show worked answerHide worked answer
    1. M1: 1 × 10 + 3 × 10 + 2.5 × 20 + 1.5 × 20, then half
    2. M1: 20 + dfrac60 - 4050 × 20
    3. A1: 28
    Answer: 28 cm
    Median from a Histogram
    Length, x (cm)Frequency density012340204060
    [3 marks]

  3. Question 3. x = 4, y = 6; x = 9, y = 9; x = 36, y = 18
    Ben says y is directly proportional to the square root of x.
    Is Ben correct? You must show your working.

    Show worked answerHide worked answer
    1. M1: y ÷ √x for one pair, e.g. 6 ÷ 2 = 3
    2. M1: 9 ÷ 3 = 3 and 18 ÷ 6 = 3
    3. A1: Yes, y ÷ √x is always 3
    Answer: Yes, y ÷ √x = 3 for every pair
    Direct & Inverse Proportion with Functions
    [3 marks]

  4. Question 4. Simplify fully dfrac2x² + 5x - 3x² - 9

    Show worked answerHide worked answer
    1. M1: (2x - 1)(x + 3)
    2. M1: (x - 3)(x + 3)
    3. A1: dfrac2x - 1x - 3
    Answer: dfrac2x - 1x - 3
    Algebraic Fractions Involving Factorising
    [3 marks]

  5. Question 5. The table shows the speed, in metres per second, of a go-kart at different times. Use 5 trapezia of equal width to work out an estimate for the distance travelled in the first 10 seconds.

    Show worked answerHide worked answer
    1. M1: each strip is 2 seconds wide so each trapezium has area dfrac12 × 2 × (a + b)
    2. M1: (0 + 5) + (5 + 8) + (8 + 9) + (9 + 10) + (10 + 10)
    3. A1: 74 m
    Answer: 74 m
    Estimating Areas Under Curves
    Time (s)0246810Speed (m/s)05891010
    [3 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 057

Grades 8/9Non-calculator

  1. Question 1. The cosine graph repeats every 360°. Write down the value of cos 540°.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 540 - 360 = 180
    2. A1: -1
    Answer: -1
    Sketching sin, cos & tan

  2. Question 2. The histogram shows the lengths, x cm, of some ropes. Assume values are spread evenly in each class and the median is the n/2th value. Work out an estimate for the median length.

    [3 marks]
    Length, x (cm)Frequency density012340204060
    Show worked answerHide worked answer
    1. M1: 1 × 10 + 3 × 10 + 2.5 × 20 + 1.5 × 20, then half
    2. M1: 20 + dfrac60 - 4050 × 20
    3. A1: 28
    Answer: 28 cm
    Median from a Histogram

  3. Question 3. x = 4, y = 6; x = 9, y = 9; x = 36, y = 18
    Ben says y is directly proportional to the square root of x.
    Is Ben correct? You must show your working.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: y ÷ √x for one pair, e.g. 6 ÷ 2 = 3
    2. M1: 9 ÷ 3 = 3 and 18 ÷ 6 = 3
    3. A1: Yes, y ÷ √x is always 3
    Answer: Yes, y ÷ √x = 3 for every pair
    Direct & Inverse Proportion with Functions

  4. Question 4. Simplify fully dfrac2x² + 5x - 3x² - 9

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (2x - 1)(x + 3)
    2. M1: (x - 3)(x + 3)
    3. A1: dfrac2x - 1x - 3
    Answer: dfrac2x - 1x - 3
    Algebraic Fractions Involving Factorising

  5. Question 5. The table shows the speed, in metres per second, of a go-kart at different times. Use 5 trapezia of equal width to work out an estimate for the distance travelled in the first 10 seconds.

    [3 marks]
    Time (s)0246810Speed (m/s)05891010
    Show worked answerHide worked answer
    1. M1: each strip is 2 seconds wide so each trapezium has area dfrac12 × 2 × (a + b)
    2. M1: (0 + 5) + (5 + 8) + (8 + 9) + (9 + 10) + (10 + 10)
    3. A1: 74 m
    Answer: 74 m
    Estimating Areas Under Curves
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 057

Grades 8/9Non-calculator

  1. Question 1. The cosine graph repeats every 360°. Write down the value of cos 540°.

    Show worked answerHide worked answer
    1. M1: 540 - 360 = 180
    2. A1: -1
    Answer: -1
    Sketching sin, cos & tan
    [2 marks]

  2. Question 2. The histogram shows the lengths, x cm, of some ropes. Assume values are spread evenly in each class and the median is the n/2th value. Work out an estimate for the median length.

    Show worked answerHide worked answer
    1. M1: 1 × 10 + 3 × 10 + 2.5 × 20 + 1.5 × 20, then half
    2. M1: 20 + dfrac60 - 4050 × 20
    3. A1: 28
    Answer: 28 cm
    Median from a Histogram
    Length, x (cm)Frequency density012340204060
    [3 marks]

  3. Question 3. x = 4, y = 6; x = 9, y = 9; x = 36, y = 18
    Ben says y is directly proportional to the square root of x.
    Is Ben correct? You must show your working.

    Show worked answerHide worked answer
    1. M1: y ÷ √x for one pair, e.g. 6 ÷ 2 = 3
    2. M1: 9 ÷ 3 = 3 and 18 ÷ 6 = 3
    3. A1: Yes, y ÷ √x is always 3
    Answer: Yes, y ÷ √x = 3 for every pair
    Direct & Inverse Proportion with Functions
    [3 marks]

  4. Question 4. Simplify fully dfrac2x² + 5x - 3x² - 9

    Show worked answerHide worked answer
    1. M1: (2x - 1)(x + 3)
    2. M1: (x - 3)(x + 3)
    3. A1: dfrac2x - 1x - 3
    Answer: dfrac2x - 1x - 3
    Algebraic Fractions Involving Factorising
    [3 marks]

  5. Question 5. The table shows the speed, in metres per second, of a go-kart at different times. Use 5 trapezia of equal width to work out an estimate for the distance travelled in the first 10 seconds.

    Show worked answerHide worked answer
    1. M1: each strip is 2 seconds wide so each trapezium has area dfrac12 × 2 × (a + b)
    2. M1: (0 + 5) + (5 + 8) + (8 + 9) + (9 + 10) + (10 + 10)
    3. A1: 74 m
    Answer: 74 m
    Estimating Areas Under Curves
    Time (s)0246810Speed (m/s)05891010
    [3 marks]