VCE General Mathematics Practice Questions

The Brunswick Striders is a running club with 60 members. The club records fitness and training data for every member. (a) The resting heart rates of club members are approximately normally distributed, with a mean of 66 beats per minute (bpm) and a standard deviation of 8 bpm. (i) Using the 68-95-99.7% rule, determine the percentage of members expected to have a resting heart rate between 58 bpm and 82 bpm. (1 mark) (ii) Calculate the standardised score (z-score) for a member with a resting heart rate of 54 bpm. (1 mark) (b) The weekly training distances, in kilometres, of the 60 members have the following five-number summary: minimum = 12, Q1 = 24, median = 32, Q3 = 40, maximum = 68. Use an appropriate calculation to show that the maximum value of 68 km would be shown as an outlier on a boxplot of this data. (2 marks) (c) Eight members completed a 10-km race. Their average weekly training distance, x (km), and race time, y (minutes), are shown below. weekly distance (km): 20 24 28 32 36 40 44 48 race time (minutes): 57.8 56.1 54.6 52.4 51.9 49.2 47.6 47.1 Use your CAS to determine the equation of the least squares regression line that enables race time to be predicted from weekly training distance. Round the values of the intercept and the slope to three significant figures. (2 marks) (d) Interpret the slope of this regression line in terms of the variables race time and weekly training distance. (1 mark) (e) (i) Determine the value of the correlation coefficient, r, rounded to three decimal places. (1 mark) (ii) Determine the value of the coefficient of determination, as a percentage rounded to one decimal place, and interpret it in terms of the variables. (1 mark) (f) (i) Use the least squares regression line to predict the 10-km race time of a member whose average weekly training distance is 38 km. Round your answer to one decimal place. (1 mark) (ii) The member who trained 36 km per week ran the race in 51.9 minutes. Determine the residual value for this member, rounded to two decimal places. (1 mark) (g) The club also runs group fitness classes, and quarterly attendance is seasonal. The seasonal indices are: Q1 (Jan-Mar) 1.15 | Q2 (Apr-Jun) 0.95 | Q3 (Jul-Sep) 0.78 | Q4 (Oct-Dec) unknown (i) Determine the seasonal index for Quarter 4. (1 mark) (ii) The actual attendance in Q1 2026 was 2415. Determine the deseasonalised attendance for this quarter. (1 mark) (iii) A least squares trend line fitted to the deseasonalised attendance data is: deseasonalised attendance = 1980 + 28 x quarter number, where quarter number 1 is Q1 2025. Use this trend line to forecast the ACTUAL attendance in Q3 2027. Round to the nearest whole number. (2 marks)