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

Mixed Topic Worksheet Grades 8/9: Day 053

Grades 8/9Non-calculator

  1. Question 1. sin 30^° = 0.5
    Solve sin x = 0.5 for 0^° ≤ x ≤ 360^°

    Show worked answerHide worked answer
    1. B1: x = 30^°
    2. B1: x = 180 - 30 = 150^°, by the symmetry of the sine graph
    Answer: 30^° and 150^°
    Solving Trigonometric Equations Using a Graph
    [2 marks]

  2. Question 2. The table shows the heights, h cm, of some plants. Assume values are spread evenly in each class and the median is the n/2th value. Work out an estimate for the median height.

    Show worked answerHide worked answer
    1. M1: 2 × 5 + 1.5 × 10 + 3 × 10 + 2 × 20, then half
    2. M1: 20 + dfrac47.5 - 2530 × 10
    3. A1: 27.5
    Answer: 27.5 cm
    Median from a Histogram
    Height, h (cm)Frequency density5 < h ≤ 10210 < h ≤ 201.520 < h ≤ 30330 < h ≤ 502
    [3 marks]

  3. Question 3. y is inversely proportional to the square of x. y is increased by 300%. Work out the percentage decrease in x.

    Show worked answerHide worked answer
    1. M1: new y=4y, so x_2²=dfracx²4
    2. M1: x_2=dfracx2
    3. A1: 50% decrease
    Answer: 50%
    Direct & Inverse Proportion with Functions
    [3 marks]

  4. Question 4. Prove that the difference between the squares of two consecutive even numbers is always a multiple of 4.

    Show worked answerHide worked answer
    1. M1: (2n+2)² - (2n)²
    2. M1: = 4n²+8n+4-4n² = 8n+4
    3. C1: = 4(2n+1), a multiple of 4
    Answer: 4(2n+1), a multiple of 4
    Proof with Consecutive Numbers
    [3 marks]

  5. Question 5. overrightarrowPQ=4mathbfa+6mathbfb and overrightarrowPR=6mathbfa+9mathbfb. Show that P, Q and R lie on a straight line.

    Show worked answerHide worked answer
    1. M1: 6mathbfa+9mathbfb=3/2(4mathbfa+6mathbfb), so overrightarrowPR=3/2overrightarrowPQ
    2. A1: parallel vectors with common point P, so P, Q, R are collinear
    Answer: overrightarrowPR=3/2overrightarrowPQ, parallel with a common point P, so collinear
    Vectors Along a Straight Line
    [2 marks]
📅 Free lesson: Tue 17th NovSave your place →

Mixed Topic Worksheet Grades 8/9: Day 053

Grades 8/9Non-calculator

  1. Question 1. sin 30^° = 0.5
    Solve sin x = 0.5 for 0^° ≤ x ≤ 360^°

    [2 marks]
    Show worked answerHide worked answer
    1. B1: x = 30^°
    2. B1: x = 180 - 30 = 150^°, by the symmetry of the sine graph
    Answer: 30^° and 150^°
    Solving Trigonometric Equations Using a Graph

  2. Question 2. The table shows the heights, h cm, of some plants. Assume values are spread evenly in each class and the median is the n/2th value. Work out an estimate for the median height.

    [3 marks]
    Height, h (cm)Frequency density5 < h ≤ 10210 < h ≤ 201.520 < h ≤ 30330 < h ≤ 502
    Show worked answerHide worked answer
    1. M1: 2 × 5 + 1.5 × 10 + 3 × 10 + 2 × 20, then half
    2. M1: 20 + dfrac47.5 - 2530 × 10
    3. A1: 27.5
    Answer: 27.5 cm
    Median from a Histogram

  3. Question 3. y is inversely proportional to the square of x. y is increased by 300%. Work out the percentage decrease in x.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: new y=4y, so x_2²=dfracx²4
    2. M1: x_2=dfracx2
    3. A1: 50% decrease
    Answer: 50%
    Direct & Inverse Proportion with Functions

  4. Question 4. Prove that the difference between the squares of two consecutive even numbers is always a multiple of 4.

    [3 marks]
    Show worked answerHide worked answer
    1. M1: (2n+2)² - (2n)²
    2. M1: = 4n²+8n+4-4n² = 8n+4
    3. C1: = 4(2n+1), a multiple of 4
    Answer: 4(2n+1), a multiple of 4
    Proof with Consecutive Numbers

  5. Question 5. overrightarrowPQ=4mathbfa+6mathbfb and overrightarrowPR=6mathbfa+9mathbfb. Show that P, Q and R lie on a straight line.

    [2 marks]
    Show worked answerHide worked answer
    1. M1: 6mathbfa+9mathbfb=3/2(4mathbfa+6mathbfb), so overrightarrowPR=3/2overrightarrowPQ
    2. A1: parallel vectors with common point P, so P, Q, R are collinear
    Answer: overrightarrowPR=3/2overrightarrowPQ, parallel with a common point P, so collinear
    Vectors Along a Straight Line
📅 Free live lesson: Tuesday 17th NovemberSave your free place →

Mixed Topic Worksheet Grades 8/9: Day 053

Grades 8/9Non-calculator

  1. Question 1. sin 30^° = 0.5
    Solve sin x = 0.5 for 0^° ≤ x ≤ 360^°

    Show worked answerHide worked answer
    1. B1: x = 30^°
    2. B1: x = 180 - 30 = 150^°, by the symmetry of the sine graph
    Answer: 30^° and 150^°
    Solving Trigonometric Equations Using a Graph
    [2 marks]

  2. Question 2. The table shows the heights, h cm, of some plants. Assume values are spread evenly in each class and the median is the n/2th value. Work out an estimate for the median height.

    Show worked answerHide worked answer
    1. M1: 2 × 5 + 1.5 × 10 + 3 × 10 + 2 × 20, then half
    2. M1: 20 + dfrac47.5 - 2530 × 10
    3. A1: 27.5
    Answer: 27.5 cm
    Median from a Histogram
    Height, h (cm)Frequency density5 < h ≤ 10210 < h ≤ 201.520 < h ≤ 30330 < h ≤ 502
    [3 marks]

  3. Question 3. y is inversely proportional to the square of x. y is increased by 300%. Work out the percentage decrease in x.

    Show worked answerHide worked answer
    1. M1: new y=4y, so x_2²=dfracx²4
    2. M1: x_2=dfracx2
    3. A1: 50% decrease
    Answer: 50%
    Direct & Inverse Proportion with Functions
    [3 marks]

  4. Question 4. Prove that the difference between the squares of two consecutive even numbers is always a multiple of 4.

    Show worked answerHide worked answer
    1. M1: (2n+2)² - (2n)²
    2. M1: = 4n²+8n+4-4n² = 8n+4
    3. C1: = 4(2n+1), a multiple of 4
    Answer: 4(2n+1), a multiple of 4
    Proof with Consecutive Numbers
    [3 marks]

  5. Question 5. overrightarrowPQ=4mathbfa+6mathbfb and overrightarrowPR=6mathbfa+9mathbfb. Show that P, Q and R lie on a straight line.

    Show worked answerHide worked answer
    1. M1: 6mathbfa+9mathbfb=3/2(4mathbfa+6mathbfb), so overrightarrowPR=3/2overrightarrowPQ
    2. A1: parallel vectors with common point P, so P, Q, R are collinear
    Answer: overrightarrowPR=3/2overrightarrowPQ, parallel with a common point P, so collinear
    Vectors Along a Straight Line
    [2 marks]