An object is projected vertically into the air. Its height,
For how long is the object at a height of 300 metres or more above the ground?
- 4 seconds
- 6 seconds
- 8 seconds
- 10 seconds
Bivariate Data, SM-Bank 016
The scatterplot below shows the rainfall (in mm) and the percentage of clear days for each month of 2023.
An equation of the line of best fit for this data set is
- Using coordinates at the graph extremities or otherwise, draw this line on the scatterplot. (2 marks)
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- Describe this association in terms of strength and direction. (1 mark)
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Show Answers Only
i.
ii.
Show Worked Solution
i.
ii.
Bivariate Data, SM-Bank 015
The heights (in cm) and ages (in months) of a random sample of 15 boys have been plotted in the scatterplot below.
A line of best fit has been fitted to the data.
- State the independent variable in the graph. (1 mark)
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- Describe this association in terms of strength and direction. (2 marks)
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- Determine the gradient of the line of best fit, giving your answer correct to one decimal place. (2 marks)
-
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Bivariate Data, SM-Bank 014
The scatterplot below displays the mean age, in years, and the mean height, in centimetres, of 648 women from seven different age groups.
In an initial analysis of the data, a line of best fit is drawn, as shown.
- Describe this association in terms of strength and direction. (2 marks)
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- Determine the mean height predicted for a group of 65 year old women. (1 mark)
-
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Bivariate Data, SM-Bank 013
The scatterplot below plots male life expectancy (male) against female life expectancy (female) in 1950 for a number of countries.
A line of best fit has been fitted to the scatterplot as shown.
- State the dependent variable in the graph. (1 mark)
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- Determine the age at which males and females have the same life expectancy. (1 mark)
-
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Bivariate Data, SM-Bank 012
A teacher analysed the class marks of 15 students who sat two tests.
The test 1 mark and test 2 mark, all whole number values, are shown in the scatterplot below.
A line of best fit has been fitted to the scatterplot.
- If a student scored 34 in the first test, what is their expected mark in the second test. (1 mark)
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- The line of best fit shows the predicted test 2 mark for each student based on their test 1 mark.
- Determine the number of students whose actual test 2 mark was within two marks of that predicted. (1 mark)
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Bivariate Data, SM-Bank 011
The scatterplot below displays the resting pulse rate, in beats per minute, and the time spent exercising, in hours per week, of 16 students.
A line of best fit has been fitted to the data.
- If a student spends 8 hours exercising per week, determine the resting pulse rate predicted by the line of best fit. (1 mark)
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- Provide TWO descriptions of the association between the variables time spent exercising and resting pulse rate. (2 marks)
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Bivariate Data, SM-Bank 010
The scatterplot below shows the wrist circumference and ankle circumference, both in centimetres, of 13 people.
A line of best fit been drawn with ankle circumference as the independent variable.
- If a person has a wrist circumference of 18.5 centimetres, estimate the ankle circumference that is predicted by the line of best fit. (1 mark)
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- Explain why the
-intercept of this graph has no meaning in this context. (1 mark)
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Bivariate Data, SM-Bank 009
The height (in cm) and foot length (in cm) for each of eight Year 12 students were recorded and displayed in the scatterplot below.
A line of best fit has been fitted to the data as shown.
- Determine the predicted foot size of a student who is 176 centimetres tall. (1 mark)
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- Calculate the gradient of the line of best fit, giving your answer correct to two decimal places. (2 marks)
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- What is the equation of the line of best fit? (2 marks)
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Bivariate Data, SM-Bank 008 MC
Bivariate Data, SM-Bank 007 MC
Dr Chris measures the weights (in grams) and lengths (in cm) of 12 baby pythons.
The results were recorded and plotted in the scatterplot below. The line of best fit that enables the weight of the pythons to be predicted from their length has also been plotted.
The line of best fit predicts that the weight, in grams, of a python of length 30 cm would be closest to
Bivariate Data, SM-Bank 006
The lengths and diameters, in millimetres, of a sample of jellyfish selected were recorded and displayed in the scatterplot below.
A line of best fit for this data is shown.
- Determine the expected length of a jellyfish with a diameter of 12 millimetres. (1 mark)
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- Determine the expected diameter of a jellyfish with a length of 16 millimetres. (1 mark)
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Bivariate Data, SM-Bank 005
Each member of a group of males had his height and foot length measured and recorded. The results were graphed and a line of fit drawn.
- Why does the value of the
-intercept have no meaning in this situation? (1 mark)
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- George is 10 cm taller than his brother Harry. Use the line of fit to estimate the difference in their foot lengths. (1 mark)
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Bivariate Data, SM-Bank 004
The shoe size and height of ten students were recorded.
- Complete the scatter plot AND draw a line of best fit by eye. (2 marks)
- Use the line of best fit to estimate the height difference between a student who wears a size 7.5 shoe and one who wears a size 9 shoe. (1 mark)
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Show Worked Solution
i.
ii.
Bivariate Data, SM-Bank 003
Ahmed collected data on the age (
He created a scatterplot of the data and constructed a line of best fit to model the relationship between the age and height of males.
- Determine the gradient of the line of best fit shown on the graph. (1 mark)
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- Determine the equation of the line of best fit shown on the graph. (2 marks)
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- Use the line of best fit to predict the height of a typical 17-year-old male. (1 mark)
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- Why would this model not be useful for predicting the height of a typical 45-year-old male? (1 mark)
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Bivariate Data, SM-Bank 002
People are placed into groups to complete a puzzle. There are 9 different groups.
The table shows the number of people in each group and the amount of time, in minutes, for each group to complete the puzzle.
- Complete the scatterplot by adding the last four points from the table. (1 mark)
- Add a line of best fit by eye to the graph in part (a). (1 mark)
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- The graph in part (a) shows the association between the time to complete the puzzle and the number of people in the group.
- Identify the form (linear or non-linear), the direction and the strength of the association. (2 marks)
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Show Answers Only
a.
b.
c. `text(Form: linear)
Show Worked Solution
a.
b.
c.
Bivariate Data, SM-Bank 001
The graph shows a line of best fit describing the life expectancy of people born between 1900 and 2000.
- According to the graph, what is the life expectancy of a person born in 1932? (1 mark)
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- Determine the value of the gradient of the line of best fit. (2 marks)
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Depreciation, SMB-004
A new electric vehicle costs $46 000 and is depreciated using the reducing balance method by 15% of its value each year.
Find its value after four years, giving your answer to the nearest dollar. (2 marks)
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Depreciation, SMB-003 MC
A new car costs $30 000 and is depreciated using the reducing balance method by 20% of its value each year.
After three years its value is
Depreciation, SMB-002
Peter installed his new pool fence on 1 January 2013 at a cost of $12 000.
On 1 January of each year after 2013 its value is depreciated by 15% using the reducing balance method.
The value of the pool fence will be below $4000 for the first time on 1 January of what year? Show all working. (3 marks)
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Depreciation, SMB-001 MC
A new air-conditioning unit was purchased for $5000 on 1 January 2017.
On 1 January of each year after 2017 its value is depreciated by 20% using the reducing balance method.
The value of the air conditioner will be below $1500 for the first time on 1 January
- 2020
- 2021
- 2022
- 2023
Compound Interest, SMB-031
Camilla is considering a term deposit that pays 4.8% interest per annum, compounded monthly.
She calculates that if she invests in the term deposit, her money will be worth $9800 in 2 years' time.
Determine the amount that Camilla is planning to invest, giving your answer to the nearest cent. (2 marks)
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Compound Interest, SMB-030
Michelle decided to invest some of her money at a higher interest rate. She deposited $3000 in an account paying 8.2% per annum, compounding half yearly.
- Write down an expression involving the compound interest formula that can be used to find the value of Michelle’s $3000 investment at the end of two years. Find this value correct to the nearest cent. (2 marks)
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- How much interest will the $3000 investment earn over a four-year period?
Write your answer correct to the nearest cent. (2 marks)
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Compound Interest, SMB-029
The golf club’s social committee has $3400 invested in an account which pays interest at the rate of 4.4% per annum compounding quarterly.
- Show that the interest rate per quarter is 1.1%. (1 mark)
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- Determine the value of the $3400 investment after three years.
Write your answer in dollars correct to the nearest cent. (1 mark)
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- Calculate the interest the $3400 investment will earn over six years.
Write your answer in dollars correct to the nearest cent. (2 marks)
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Compound Interest, SMB-028
It is estimated that inflation will average 3.5% per annum over the next eight years.
If a new machine costs $60 000 now, calculate the cost of a similar new machine in eight years time, adjusted for inflation. Assume no other cost change.
Write your answer correct to the nearest dollar. (2 marks)
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Compound Interest, SMB-027 MC
An amount of $8000 is invested for a period of 4 years.
The interest rate for this investment is 7.2% per annum compounding quarterly.
The interest earned by the investment in the fourth year (in dollars) is given by
Compound Interest, SMB-026 MC
$10 000 is invested for five years. Interest is earned at a rate of 8% per annum, compounding quarterly.
Which one of the following calculations will give the total interest earned, in dollars, by this investment?
Compound Interest, SMB-025
$15 000 is invested for 12 months.
For the first six months the interest rate is 6.1% per annum compounding monthly.
After six months the interest rate increases to 6.25% per annum compounding monthly.
Calculate the total interest earned by this investment over 12 months, giving your answer to the nearest dollar. (4 marks)
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Compound Interest, SMB-024
$9000 is invested at a rate of 8% per annum compounding half yearly.
Determine the value, to the nearest dollar, of this investment after four years. (2 marks)
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Compound Interest, SMB-023 MC
$10 000 is invested at a rate of 10% per annum compounding half yearly.
The value, in dollars, of this investment after five years, is given by
Compound Interest, SMB-022 MC
The points on the graph below show the balance of an investment at the start of each quarter for a period of six years.
The same rate of interest applied for these six years.
In relation to this investment, which one of the following statements is true?
- interest is compounding annually and is credited annually
- interest is compounding annually and is credited quarterly
- simple interest is paid on the opening balance and is credited annually
- simple interest is paid on the opening balance and is credited quarterly
Compound Interest, SMB-021
Callum invests $20 000 in a term deposit account that adds 3.8% interest annually, calculated on the account balance at the end of each year.
Calculate the interest paid in the third year of Callum's investment. (3 marks)
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Compound Interest, SMB-020
Tim invests $3000 in a term deposit account that adds 6.5% interest annually, calculated on the account balance at the end of each year.
The interest paid in the fourth year is
Compound Interest, SMB-019
Kelly invests $8 000 at an interest rate of 7.5% per annum, compounding annually.
After how many years will her investment first be more than double its original value, giving your answer to the nearest year? (3 marks)
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Compound Interest, SMB-018 MC
Gerry invests $10 000 at an interest rate of 5.5% per annum, compounding annually.
After how many years will his investment first be more than double its original value?
- 12
- 13
- 14
- 15
Compound Interest, SMB-017
Ekamjot invests $13 000 for two years.
Interest is calculated at the rate of 7.2% per annum, compounding quarterly.
How much interest does Ekamjot earn from this investment, giving your answer to the nearest cent? (2 marks)
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Compound Interest, SMB-016 MC
Mary invests $1200 for two years.
Interest is calculated at the rate of 3.35% per annum, compounding monthly.
The amount of interest she earns in two years is closest to
Compound Interest, SMB-015
Amy invests $15 000 for 150 days.
Interest is calculated at the rate of 4.60% per annum, compounding daily.
Assuming that there are 365 days in a year, find the value of her investment after 150 days, giving your answer to the nearest dollar. (3 marks)
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Compound Interest, SMB-014
Sam and Charlie each invest $5000 for three years.
Sam’s investment earns simple interest at the rate of 7.5% per annum.
Charlie’s investment earns interest at the rate of 7.5% per annum compounding annually.
At the conclusion of three years, determine which investment has the highest value and by how much. (4 marks)
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Compound Interest, SMB-013
What amount must be invested now at 6% per annum, compounded quarterly, so that in eighteen months it will have grown to
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Compound Interest, SMB-012
Louise's investment earns 3.6% per annum, compounded quarterly.
She calculates that her investment will be worth $7400 in 4 years.
Determine the amount that Louise initially invests, giving your answer to the nearest cent. (2 marks)
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Compound Interest, SMB-011 MC
Marshall's investment earns 5% per annum, compounded annually.
He calculates that his investment will be worth $1100 in 3 years, to the nearest dollar.
The amount Marshall invests now is closest to
- $892
- $928
- $950
- $1008
Compound Interest, SMB-010
A bank's Compound Saver Account pays interest at 4% per annum, compounded quarterly.
Sacha deposits $6500 when he opens his Compound Saver Account and makes no further deposits or withdrawals.
What will be the balance in the account at the end of 1.5 years, to the nearest dollar? (2 marks)
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Compound Interest, SMB-009
Jill opens a Smartsave Account that pays interest at 5% per annum, compounded quarterly.
Jill deposits $700 when she opens the account and makes no further deposits or withdrawals.
What will be the balance in the account at the end of 3 years, to the nearest dollar? (2 marks)
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Compound Interest, SMB-008 MC
A bank's Maxi Saver Account pays interest at 6% per annum, compounded quarterly.
Jen opens a Maxi Saver Account and deposits $3000 into it.
Assuming no further deposits or withdrawals are made, what will be the balance in the account at the end of two years?
- $3120.00
- $3360.00
- $3379.48
- $4781.54
Compound Interest, SMB-007
Shannon invests $25 000 in an account that earns interest at 6% per annum, compounded monthly.
What is the future value of Shannon's investment, to the nearest dollar, after 2 years? (2 marks)
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Compound Interest, SMB-006
Natalie is saving for a netball hoop and invests $2200 in an account that earns interest at 5.5% per annum, compounded monthly.
What is the future value of Natalie's investment, to the nearest dollar, after 1.5 years? (2 marks)
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Compound Interest, SMB-005 MC
Roger invests $1400. He earns interest at 4% per annum, compounded monthly.
What is the future value of Roger's investment after 2.5 years?
- $1540.00
- $1546.98
- $3080.00
- $4540.76
Compound Interest, SMB-004
In Japan, a bowl of ramen cost 1000 Japanese yen in 2005. The cost of ramen has increased by 0.5% per annum since then.
Determine the cost of the same bowl of ramen in 2020 in Japanese yen, to the nearest yen. (2 marks)
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Compound Interest, SMB-003 MC
At the pump, one litre of diesel fuel cost 98 cents in NSW in 2003. The value of diesel fuel has increased by 4% per annum since then.
Which expression gives the value, in cents, of one litre of diesel at the pump in 2023?
Compound Interest, SMB-002
Samanda opens a bank account and deposits $5000 into it. Interest is paid at 4% per annum, compounding annually.
Assuming no further deposits or withdrawals are made, what will be the balance in the account at the end of three years? (2 marks)
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Compound Interest, SMB-001 MC
Resilia opens a bank account and deposits $2000 into it. Interest is paid at 4% per annum, compounding annually.
Assuming no further deposits or withdrawals are made, what will be the balance in the account at the end of two years?
- $2160.00
- $2163.20
- $2346.24
- $3920.00
Volume, SMB-016
The truncated cone, pictured below, is made by cutting a right cone of height 60 centimetres.
Find the volume of the truncated cone, giving your answer to the nearest cubic centimetre. (4 marks)
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Trigonometry, SMB-039
Gerry flies his helicopter from a heliport on a bearing of S50°W for 75 km until he stops at Town P which is due west of Town Q.
If Town Q is due south of the heliport, find the distance between the heliport and Town Q in kilometres, correct to two decimal places. (3 marks)
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Show Worked Solution
Trigonometry, SMB-038
Trigonometry, SMB-037
Express the compass bearing S30°E as a true bearing. (2 marks)
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Trigonometry, SMB-036
Express the compass bearing S60°W as a true bearing. (2 marks)
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Trigonometry, SMB-035 MC
Peter is standing 8 metres due west of Mary.
Bob is standing 8 metres due north of Mary.
Bob is facing north. He then turns anticlockwise so that he is facing Peter.
How many degrees does Bob turn through?
Show Worked Solution
Trigonometry, SMB-034
Statistics, STD1 S3 2023 HSC 19
The scatterplot shows the number of ice-creams sold,
- The data are modelled by the equation of the line of best fit given below.
- Sam used a particular temperature with this equation and predicted that 23 ice-creams would be sold.
- What was the temperature used by Sam, to the nearest degree? (2 marks)
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- In using the equation to make the prediction in part (a), was Sam interpolating or extrapolating? Justify your answer. (2 marks)
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