Aussie Maths & Science Teachers: Save your time with SmarterEd
The location of Sorong is `text(1°S 131°E)` and the location of Darwin is `text(12°S 131°E)`.
The graph shows the amounts charged by Company `A` and Company `B` to deliver parcels of various weights.
This radar chart was used to display the average daily temperatures each month for two different towns.
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Reece is preparing his annual budget for 2006.
His expected income is:
• $90 every week as a swimming coach
• Interest earned from an investment of $5000 at a rate of 4% per annum.
His planned expenses are:
• $30 every week on transport
• $12 every week on lunches
• $48 every month on entertainment.
Reece will save his remaining income. He uses the spreadsheet below for his budget.
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At the beginning of 2006, Reece starts saving.
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Moheb owns five red and seven blue ties. He chooses a tie at random for himself and puts it on. He then chooses another tie at random, from the remaining ties, and gives it to his brother.
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Copy the tree diagram into your writing booklet.
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| i. | `P(R)` | `= (#\ text(red ties))/(#\ text(total ties))` |
| `= 5/12` |
| ii. | |
iii. `Ptext((same colour))`
`= P(text(RR)) + P(text(BB))`
`= 5/12 × 4/11\ \ +\ \ 7/12 × 6/11`
`= 20/132 + 42/132`
`= 31/66`
What is the percentage increase in the number of bacteria? (1 mark)
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What is the number of bacteria after 15 hours? (1 mark)
\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \text{Time in hours $(t)$} \rule[-1ex]{0pt}{0pt} & \;\; 0 \;\; & \;\; 5 \;\; & \;\; 10 \;\; & \;\; 15 \;\; \\
\hline
\rule{0pt}{2.5ex} \text{Number of bacteria ( $n$ )} \rule[-1ex]{0pt}{0pt} & \;\; 100 \;\; & \;\; 193 \;\; & \;\; 371 \;\; & \;\; ? \;\; \\
\hline
\end{array}
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Use about half a page for your graph and mark a scale on each axis. (4 marks)
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i. `text(Percentage increase)`COMMENT: Common ADV/STD2 content in new syllabus.
`= (114 -100)/100 xx 100`
`= 14text(%)`
ii. `n = 100(1.14)^t`
`text(When)\ \ t = 15,`
| `n` | `= 100(1.14)^15` |
| `= 713.793\ …` | |
| `= 714\ \ \ text{(nearest whole)}` |
| iii. |  |
iv. `text(Using the graph)`
`text(The number of bacteria reaches 300 after)`
`text(approximately 8.4 hours.)`
The following graphs have been constructed from data taken from the Bureau of Meteorology website. The information relates to a town in New South Wales.
The graphs show the mean 3 pm wind speed (in kilometres per hour) for each month of the year and the mean number of days of rain for each month (raindays).
A clay brick is made in the shape of a rectangular prism with dimensions as shown.
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Three identical cylindrical holes are made through the brick as shown. Each hole has a radius of 1.4 cm.
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The shaded region represents a block of land bounded on one side by a road.
What is the approximate area of the block of land, using Simpson’s rule?
(A) `680\ text(m²)`
(B) `760\ text(m²)`
(C) `840\ text(m²)`
(D) `1360\ text(m²)`
| `A` | `≈ h/3[y_0 + 4y_1 + y_2]` |
| `≈ 20/3 [19 + (4 × 15) + 23]` | |
| `≈ 20/3 [102]` | |
| `≈ 680\ text(m²)` |
`=> A`
The diagram shows a spinner.
The arrow is spun and will stop in one of the six sections.
What is the probability that the arrow will stop in a section containing a number greater
than 4?
Tai uses the declining balance method of depreciation to calculate tax deductions for her business. Tai’s computer is valued at $6500 at the start of the 2003 financial year. The rate of depreciation is 40% per annum.
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Kirbee is shopping for computer software. Novirus costs `$115` more than
Funmaths. Let `x` dollars be the cost of Funmaths.
The diagram shows the points `A(text(−1) , 3)` and `B(2, 0)`.
The line `l` is drawn perpendicular to the `x`-axis through the point `B`.
| (i) | `A(-1,3)\ \ \ \ \ B(2,0)` |
| `AB` | `= sqrt( (x_2 – x_1)^2 + (y_2 – y_1)^2 )` |
| `= sqrt( (2+1)^2 + (0-3)^2 )` | |
| `= sqrt(9+9)` | |
| `= sqrt 18` | |
| `= 3 sqrt 2\ text(units)` |
| (ii) | `text(Gradient of)\ AB` | `= (y_2 – y_1)/(x_2 – x_1)` |
| `= (0 – 3)/(2 + 1)` | ||
| `= – 1` |
| (iii) | `text(S) text(ince Gradient)\ AB = – 1` |
`/_ABO = 45^@`
`:.\ text(Angle between)\ AB\ text(and)\ l`
`= 90 – 45`
`= 45^@`
| (iv) | `text(Equation of)\ AB\ text(has)\ m = -1,\ text(through)\ \ (2,0)` |
| `y – y_1` | `= m(x – x_1)` |
| `y – 0` | `= -1 (x – 2)` |
| `y` | `= -x + 2` |
`:.\ x + y – 2 = 0\ \ \ …\ text(as required)`
(v)
`text{Origin (0,0) satisfies the inequality}`
`:.\ text(Shaded area is below)\ x + y – 2 = 0`
| (vi) | `text(Equation of)\ l` |
| `x = 2` |
| (vii) | `m_(AC) xx m_(AB)` | `= -1\ \ \ (AC⊥AB)` |
| `m_(AC) xx -1` | `= -1` | |
| `m_(AC)` | `= + 1` |
`text(Equation of)\ AC\ text(has)\ \ m = 1,\ text(through)\ (-1, 3),`
| `y – y_1` | `= m(x – x_1)` |
| `y – 3` | `= 1 (x + 1)` |
| `y` | `= x + 4` |
`=>C\ text(lies on)\ y = x + 4`
`text(When)\ \ x = 2,\ \ y = 6`
`:. C\ (2, 6)`
Find the values of `x` for which `|\ x + 1\ |<= 5`. (2 marks)
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`text(Solution 1)`
`|\ x + 1\ |<= 5`
| `-5` | `≤x+1≤5` |
| `:.-6` | `≤x≤4` |
`text(Solution 2)`
`|\ x + 1\ |<= 5`
| `(x+1)^2` | `<= 5^2` |
| ` x^2 + 2x + 1` | `<= 25` |
| `x^2 + 2x – 24` | `<= 0` |
| `(x + 6)(x – 4)` | `<= 0` |
`:.\ -6 <= x <= 4`
A packet contains 12 red, 8 green, 7 yellow and 3 black jellybeans.
One jellybean is selected from the packet at random.
What is the probability that the selected jellybean is red or yellow? (2 marks)
Differentiate `x^4 + 5x^(−1)` with respect to `x`. (2 marks)
Solve `(x-5)/3-(x+1)/4 = 5`. (2 marks)
A salesman earns $200 per week plus $40 commission for each item he sells.
How many items does he need to sell to earn a total of $2640 in two weeks?
The angle of depression of the base of the tree from the top of the building is 65°. The height of the building is 30 m.
How far away is the base of the tree from the building, correct to one decimal place?
`text(Let)\ d =\ text(distance from base to tree)`
| `tan25^@` | `=d/30` | |
| `:.d` | `=30 xx tan25^@` | |
| `=13.98…\ text{m}` |
`=> B`
The probability of an event occurring is `9/10.`
Which statement best describes the probability of this event occurring?
There are 100 tickets sold in a raffle. Justine sold all 100 tickets to five of her friends. The number of tickets she sold to each friend is shown in the table.
Give a reason why Justine’s statement is NOT correct. (1 mark)
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The diagram shows the shape of Carmel’s garden bed. All measurements are in
metres.
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Calculate the volume of straw required. Give your answer in cubic metres. (2 marks)
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How many bags does she need to buy? (2 marks)
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Find the length of this fence to the nearest metre. (2 marks)
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The diagram is a scale drawing of a butterfly.
What is the actual wingspan of the butterfly?
This box-and-whisker plot represents a set of scores.
What is the interquartile range of this set of scores?
What is the area of the triangle to the nearest square metre?
This sector graph shows the distribution of 116 prizes won by three schools: X, Y and Z.
How many prizes were won by School X?
Use the set of scores 1, 3, 3, 3, 4, 5, 7, 7, 12 to answer Questions 6 and 7.
Question 6
What is the range of the set of scores?
Question 7
What are the median and the mode of the set of scores?
What is the correct expression for tan 20° in this triangle?
If `K = Ft^3`, `F = 5` and `t = 0.715`, what is the value of `K` correct to three significant figures?
Susan drew a graph of the height of a plant.
What is the gradient of the line?
A delivery truck when new was valued at $65 000.
The truck’s value depreciates at a rate of 22 cents per kilometre travelled.
After it has travelled a total distance of 132 600 km, the value of the truck will be
A. `$14\ 300`
B. `$22\ 100`
C. `$22\ 516`
D. `$29\ 172`
E. `$35\ 828`
An amount of $6500 is borrowed at a simple interest rate of 3.5% per annum.
The total interest paid over the period of the loan is $910.
The period of the loan is closest to
A. 2.5 years.
B. 3.5 years.
C. 3.8 years.
D. 4 years.
E. 4.9 years.
A plumber quoted $300, excluding GST (Goods and Services Tax), to complete a job.
A GST of 10% is added to the price.
The full price for the job will be
A. $3
B. $30
C. $303
D. $310
E. $330
A new kitchen in a restaurant cost $50 000. Its value is depreciated over time using the reducing balance method.
The value of the kitchen in dollars at the end of each year for ten years is shown in the graph below.
Which one of the following statements is true?
A. The kitchen depreciates by $4000 annually.
B. At the end of five years, the kitchen's value is less than $20 000.
C. The reducing balance depreciation rate is less than 5% per annum.
D. The annual depreciation rate increases over time.
E. The amount of depreciation each year decreases over time.
Tamara’s bank statement for September has been damaged by spilt ink as shown below.
Tamara’s Pay/Salary was deposited on 30 September.
What is the value of this deposit?
A. `$441.95`
B. `$442.20`
C. `$444.65`
D. `$785.70`
E. `$788.15`
`text(From table)`
`text(Balance after interest on 01 Sept)`
`= 2143.50 + 2.45`
`= 2145.95`
`text(Balance after Telstra payment)`
`= 2145.95 − 616.40`
`= 1529.55`
| `:.\ text(Salary)` | `= 1971.75 − 1529.55` |
| `= $442.2` |
`=> B`
A van is purchased for $56 000.
Its value depreciates at a rate of 42 cents for each kilometre that it travels.
The value of the van after it has travelled 32 000 km is
A. `$13\ 440`
B. `$26\ 880`
C. `$29\ 120`
D. `$32\ 480`
E. `$42\ 560`
An amount of $22 000 is invested for three years at an interest rate of 3.5% per annum, compounding annually.
The value of the investment at the end of three years is closest to
A. `$2310`
B. `$9433`
C. `$24\ 040`
D. `$24\ 392`
E. `$31\ 433`
An electrician charges $68 per hour to complete a job.
A Goods and Services Tax (GST) of 10% is added to the charge.
Including GST, the cost of a job that takes three hours is
A. $6.80
B. $20.40
C. $204.00
D. $210.80
E. $224.40
Mei’s starting salary is $65 000 per annum.
After the first year her salary will increase by 2.8%.
After the second year her salary will increase by a further 3.5%.
After this second increase, her salary will be closest to
A. $66 820
B. $68 690
C. $69 030
D. $69 160
E. $69 630
The selling price of a large tin of paint is $215.
After a 25% discount, the selling price of the tin of paint will become
A. $43.00
B. $53.75
C. $161.25
D. $190.00
E. $195.00
A bank approves a $90 000 loan for a customer.
The loan is to be repaid fully over 20 years in equal monthly payments.
Interest is charged at a rate of 6.95% per annum on the reducing monthly balance.
To the nearest dollar, the monthly payment will be
A. $478
B. $692
C. $695
D. $1409
E. $1579
The Domestics Cleaning Company provides household cleaning services.
For two hours of cleaning, the cost is $55.
For four hours of cleaning, the cost is $94.
The rule for the cost of cleaning services is
`text(cost) = a + b xx text(hours)`
where `a` is a fixed charge, in dollars, and `b` is the charge per hour of cleaning, in dollars per hour.
Using this rule, the cost for five hours of cleaning is
A. `$19.50`
B. `$97.50`
C. `$99.50`
D. `$113.50`
E. `$121.50`
The cost of hiring a plasterer is $86.00 per hour plus GST of 10%.
The cost of hiring a plasterer for four hours, including GST, is
A. $120.40
B. $309.60
C. $344.00
D. $352.60
E. $378.40
This month, a business charges $1500 to install a water tank.
Next month, the charge will increase by 3.5%.
The charge next month will be
A. `$45.00`
B. `$52.50`
C. `$1545.00`
D. `$1552.50`
E. `$1950.00`
This is a sketch of a sector of a circle.
Find the value of `theta` to the nearest degree.
(A) `47°`
(B) `48°`
(C) `68°`
(D) `69°`
Paul makes rulers. There is a fixed cost of $60 plus a manufacturing cost of $0.20 per ruler.
Last week Paul was able to break even by selling his rulers for $1 each.
The number of rulers Paul sold last week was
A. `50`
B. `75`
C. `90`
D. `120`
E. `150`
A builder's fee, `C` dollars, can be determined from the rule `C = 60 + 55n`, where `n` represents the number of hours worked.
According to this rule, the builder's fee will be
A. $60 for 1 hour of work.
B. $110 for 2 hours of work.
C. $500 for 8 hours of work.
D. $550 for 10 hours of work.
E. $1150 for 10 hours of work.
Kathy is a tutor who offers tutorial sessions for English and History students.
Part 1
An English tutorial session takes 1.5 hours.
A History tutorial session take 30 minutes.
Kathy has no more than 15 hours available in a week for tutorial sessions.
Let `x` represent the number of English tutorial sessions Kathy has each week.
Let `y` represent the number of History tutorial sessions Kathy has each week.
An inequality representing the constraint on Kathy’s tutorial time each week (in hours) is
A. `1.5x + 30y = 15`
B. `1.5x + 30y >= 15`
C. `1.5x + 30y <= 15`
D. `1.5x + 0.5y >= 15`
E. `1.5x + 0.5y <= 15`
Part 2
Kathy prefers to have no more than 18 tutorial sessions in total each week.
She prefers to have at least 4 English tutorial sessions.
She also prefers to have at least as many History tutorial sessions as English tutorial sessions.
Let `x` represent the number of English tutorial sessions Kathy has each week.
Let `y` represent the number of History tutorial sessions Kathy has each week.
The shaded region that satisfies all of these constraints is
The graph below shows the water temperature in a fish tank over a 12-hour period.
Part 1
Over the 12-hour period, the temperature of the tank is increasing most rapidly
A. during the first 2 hours.
B. from 2 to 4 hours.
C. from 4 to 6 hours.
D. from 6 to 8 hours.
E. from 8 to 10 hours.
Part 2
The fish tank is considered to be a safe environment for a type of fish if the water temperature is maintained between 24°C and 28°C.
Over the 12-hour period, the length of time (in hours) that the environment was safe for this type of fish was closest to
A. `1.5`
B. `5.0`
C. `7.0`
D. `8.5`
E. `10.5`
Part 3
The graph below can be used to determine the cost (in cents) of heating the fish tank during the first five hours of heating.
The cost of heating the tank for one hour is
A. `4\ text(cents.)`
B. `5\ text(cents.)`
C. `15\ text(cents.)`
D. `20\ text(cents.)`
E. `100\ text(cents.)`
A block of land is triangular in shape.
The three sides measure 36 m, 58 m and 42 m.
To calculate the area, Heron’s formula is used.
The correct application of Heron’s formula for this triangle is
The length of `RT` in the triangle shown is closest to
A. `17\ text(cm)`
B. `33\ text(cm)`
C. `45\ text(cm)`
D. `53\ text(cm)`
E. `57\ text(cm)`
For the triangle shown, the size of angle `theta` is closest to
A. `33°`
B. `41°`
C. `45°`
D. `49°`
E. `57° `
For an observer on the ground at `A`, the angle of elevation of a weather balloon at `B` is 37°.
`C` is a point on the ground directly under the balloon. The distance `AC` is 2200 m.
To the nearest metre, the height of the weather balloon above the ground is
A. `1324\ text(m)`
B. `1658\ text(m)`
C. `1757\ text(m)`
D. `2919\ text(m)`
E. `3655\ text(m)`
For the triangle shown, the value of `cos theta^@` is equal to
A. `6/10`
B. `6/8`
C. `8/10`
D. `10/8`
E. `8/6`
Calculate the cost of a call of duration `6` minutes and `20` seconds, given that there is a connection fee of `35` cents and a call rate of `37` cents per `30` second block or part thereof. (2 marks)
Murray is a photographer and has recently purchased an external hard drive with a `500 text(GB)` capacity.
If the average size of his photographic files is `4.0 text(MB)`, how many should he expect to fit on the hard drive? (2 marks)
Solve these simultaneous equations to find the values of `x` and `y`.
`y = 3x - 2`
`x + 2y + 18 = 0` (3 marks)
