Geometry and Statistics Quiz
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Questions and Answers

What is the total number of adults recorded who are under 50 years of age and have normal blood pressure?

  • 15
  • 11
  • 58
  • 32 (correct)

    • What is the total percentage of adults aged 50 years or over that have low blood pressure?

  • 19.2% (correct)
  • 38.5%
  • 5%
  • 9.6%

    • How many adults in total were studied?

  • 110 (correct)
  • 112
  • 120
  • 108

    • Which blood pressure category has the highest number of adults aged 50 years or over?

    <p>High</p> Signup and view all the answers

    What proportion of adults under 50 years have high blood pressure?

    <p>26%</p> Signup and view all the answers

    Which of the following statements about the variables is true?

    <p>One is nominal and the other is ordinal.</p> Signup and view all the answers

    If an adult is randomly selected from the study, what is the probability they will have normal blood pressure?

    <p>40%</p> Signup and view all the answers

    Which age group has a higher total count of adults with normal blood pressure?

    <p>Under 50 years</p> Signup and view all the answers

    Which child takes the least time to complete Job 5?

    <p>Ewen</p> Signup and view all the answers

    What is the total time taken if Deidre is assigned Job 4 and Ewen is assigned Job 2?

    <p>17 minutes</p> Signup and view all the answers

    If Chamath is assigned Job 3 and Brianna is assigned Job 1, who finishes first?

    <p>Brianna</p> Signup and view all the answers

    Which combination of assignments results in the minimum overall time taken if all jobs are completed simultaneously?

    <p>Alan: Job 1, Brianna: Job 2, Chamath: Job 3, Deidre: Job 4, Ewen: Job 5</p> Signup and view all the answers

    Which jobs take the same amount of time for both Alan and Chamath?

    <p>Job 2 and Job 5</p> Signup and view all the answers

    What is the straight-line distance, in metres, between Marcus and the horse?

    <p>95</p> Signup and view all the answers

    What is the height, OE, of the pyramid in centimetres?

    <p>10.4</p> Signup and view all the answers

    If the edge length of each black flag is twice that of each white flag, what is the ratio of the total area of black flags to that of white flags?

    <p>4 times the total area of the white flags.</p> Signup and view all the answers

    Given the base dimensions of the pyramid are AB = DC = 24 cm and AD = BC = 10 cm, what is the area of the base?

    <p>240 cm²</p> Signup and view all the answers

    What is the significance of the apex point E in the pyramid structure?

    <p>It is the point where all triangular faces meet.</p> Signup and view all the answers

    How would you calculate the volume of the pyramid with a rectangular base?

    <p>Base Area × Height × 1/3</p> Signup and view all the answers

    What happens to the area of black flags if the edge length is increased?

    <p>It increases by the square of the edge length.</p> Signup and view all the answers

    If the total number of flags is seven with a mixture of black and white flags, what constraints would apply to the numbers?

    <p>The total number of flags cannot exceed seven.</p> Signup and view all the answers

    What effect does decreasing a country's carbon dioxide emissions have on the Human Development Index?

    <p>It increases the Human Development Index.</p> Signup and view all the answers

    Which statement accurately reflects the relationship between carbon dioxide emissions and Human Development Index?

    <p>Higher Human Development Index tends to accompany higher carbon dioxide emissions.</p> Signup and view all the answers

    What is the primary characteristic observed in the time series plot provided?

    <p>Seasonality with an increasing trend and irregular fluctuations.</p> Signup and view all the answers

    What does a seasonal index of 0.84 for Wednesday indicate about meal servings?

    <p>Wednesday meal servings are 16% less than the daily average.</p> Signup and view all the answers

    Which statement about the coefficient of determination is correct?

    <p>A higher r² value means a poorer fit of the least squares line.</p> Signup and view all the answers

    How can the seasonal index for Friday (1.10) be interpreted regarding meal servings?

    <p>Friday serves 10% more than the average number of meals.</p> Signup and view all the answers

    What is the interpretation of the coefficient 0.422 in the least squares equation?

    <p>For every 10-point increase in HDI, life expectancy increases by 4.22 years.</p> Signup and view all the answers

    Which day of the week is expected to have the highest number of meals served based on the long-term averages?

    <p>Saturday</p> Signup and view all the answers

    Which of the following options accurately describes interpolation?

    <p>Using the least squares line to predict values that are substantially below the minimum HDI.</p> Signup and view all the answers

    How is the residual calculated for predicting life expectancy in Australia?

    <p>Observed life expectancy minus predicted life expectancy.</p> Signup and view all the answers

    What kind of trend is observed in the mean temperature time series data over the months?

    <p>Seasonality with irregular fluctuations.</p> Signup and view all the answers

    What can be inferred about the carbon dioxide emissions in relation to a country's level of human development?

    <p>Higher carbon emissions indicate better human development.</p> Signup and view all the answers

    Given the least squares line, which interpretation is accurate regarding the y-intercept of 43.0?

    <p>The value represents the average life expectancy across all countries.</p> Signup and view all the answers

    When interpreting the data, which of the following implications is valid regarding outliers?

    <p>Outliers only influence the correlation coefficient, not the predictions.</p> Signup and view all the answers

    Based on the least squares line, what would be the predicted life expectancy for a country with an HDI of 85?

    <p>77.8 years</p> Signup and view all the answers

    Which conclusion can be drawn about the relationship between life expectancy and HDI?

    <p>The relationship is positive and exhibits linear characteristics.</p> Signup and view all the answers

    Study Notes

    Question 7: Pyramid Height

    • Rectangular-based right pyramid ABCDE.
    • AB = DC = 24 cm, AD = BC = 10 cm, AE = BE = CE = DE = 28 cm.
    • Height OE needs to be calculated.
    • OE is approximately 24.8 cm.

    Question 8: Flag Area

    • String of seven flags: alternating black and white equilateral triangles.
    • Black flag edge length is double the white flag edge length.
    • Total area of black flags is four times the total area of white flags.

    Question 1: Blood Pressure and Age

    • Data on blood pressure (low, normal, high) and age (under 50, 50 or over) for 110 adults.
    • 11 adults under 50 have high blood pressure.
    • Percentage of adults under 50 with high blood pressure is approximately 19%.

    Question 2: Variable Types

    • Blood pressure (low, normal, high) is a nominal variable.
    • Age (under 50 years, 50 years or over) is an ordinal variable.

    Question 8: Job Allocation

    • Five children (Alan, Brianna, Chamath, Deidre, Ewen) assigned different jobs.
    • Time taken for each child to complete each job is given in a table.
    • Two possible job allocations minimize total time.
    • First child to finish could be either Deidre or Ewen.

    Question 1: Shaded Area

    • Diagram shows a 10cm x 12cm rectangle with a 5cm x 5cm square cut out.
    • Shaded area is 85 square centimeters.

    Question 9: Least Squares Line and Life Expectancy

    • Least squares line equation: life expectancy = 43.0 + 0.422 × HDI
    • Coefficient of determination: r² = 0.875
    • Statement "On average, life expectancy increases by 43.0 years for each 10-point increase in the Human Development Index" is not true.

    Question 10: Residual Calculation

    • Life expectancy in Australia (2011): 81.8 years, HDI: 92.9
    • Using the least squares line, the predicted life expectancy is approximately 82.2.
    • Residual is closest to -0.4.

    Question 12: Carbon Dioxide Emissions and HDI

    • There's an association between carbon dioxide emissions and HDI.
    • Countries with higher HDIs tend to have higher carbon dioxide emissions.

    Question 13: Time Series Plot

    • Time series plot shows mean temperature over time.
    • Pattern shows seasonality with irregular fluctuations.

    Question 14: Seasonal Index

    • Seasonal index for Wednesday is 0.84.
    • This means the number of meals served on Wednesday is 16% more than the daily average.

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    Related Documents

    Victorian Certificate of Education Further Mathematics Written examination 1 2016 PDF

    Description

    Test your knowledge on various geometry concepts including pyramids and flag areas, alongside basic statistics related to blood pressure and age. This quiz covers multiple topics, ensuring a comprehensive assessment. Dive into practical applications and mathematical reasoning!

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