A current of 4.0 A flows in a wire that is placed in a magnetic field of 0.75 T. The wire is 0.80 m long and is at an angle of 45° to the field.
Calculate the force on the wire. (2 marks)
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PHYSICS, M6 EQ-Bank 24
Negatively charged particles were accelerated from rest between a pair of parallel metal plates. The potential difference between the plates was varied, and the final velocity of the particles was measured for each variation.
The data in the table show the potential difference between the plates and the square of the corresponding final velocity of the particles.
\begin{array}{|c|c|}
\hline
\rule{0pt}{2.5ex}\textit{Potential difference}\ \text{(V)} \rule[-1ex]{0pt}{0pt}&\quad v^2\left(\times 10^9 \, \text{m}^2\, \text{s}^{-2}\right) \quad \\
\hline
\rule{0pt}{2.5ex}100\rule[-1ex]{0pt}{0pt}&0.8\\
\hline
\rule{0pt}{2.5ex}200\rule[-1ex]{0pt}{0pt}& 2.1\\
\hline
\rule{0pt}{2.5ex}300\rule[-1ex]{0pt}{0pt}& 3.1 \\
\hline
\rule{0pt}{2.5ex}400\rule[-1ex]{0pt}{0pt}& 4.1 \\
\hline
\rule{0pt}{2.5ex}500\rule[-1ex]{0pt}{0pt}& 5.2 \\
\hline
\end{array}
- Plot the data on the grid provided and draw a line of best fit.
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- A student hypothesised that the charged particles are electrons. Justify whether the student's hypothesis is correct or not. Support your answer using the data provided and relevant calculations.
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Show Answers Only
a.
b. The gradient of the line = `(v^2)/(V)`
Calculate the gradient (choose values close to limits):
| `text{gradient}` | `=((5.2-0.9) xx10^(9))/(500-100)` | |
| `=1.1 xx10^7 text{m}^2 text{s}^(-2) text{V}^(-1)` |
The change in kinetic energy is equal to the work done by the electric field on the charged particles:
| `W` | `=Delta K` | |
| `qV` | `=(1)/(2)mv^2` | |
| `(V^2)/(v)` | `=(2q)/(m)` |
Charge to mass ratio of the particles:
| `(q)/(m)` | `=(V^2)/(2v)` | |
| `=(text{gradient})/(2)` | ||
| `=5.4 xx10^6 text{C kg}^(-1)` |
Charge to mass ratio of an electron:
| `(q)/(m)` | `=(1.602 xx10^(-19))/(9.109 xx10^(-31))` | |
| `=1.8 xx10^(11) text{C kg}^(-1)` |
Therefore, the charged particles are not electrons.
Show Worked Solution
a.
b. The gradient of the line = `(v^2)/(V)`
Calculate the gradient (choose values close to limits):
| `text{gradient}` | `=((5.2-0.9) xx10^(9))/(500-100)` | |
| `=1.1 xx10^7 text{m}^2 text{s}^(-2) text{V}^(-1)` |
The change in kinetic energy is equal to the work done by the electric field on the charged particles:
| `W` | `=Delta K` | |
| `qV` | `=(1)/(2)mv^2` | |
| `(V^2)/(v)` | `=(2q)/(m)` |
Charge to mass ratio of the particles:
| `(q)/(m)` | `=(V^2)/(2v)` | |
| `=(text{gradient})/(2)` | ||
| `=5.4 xx10^6 text{C kg}^(-1)` |
Charge to mass ratio of an electron:
| `(q)/(m)` | `=(1.602 xx10^(-19))/(9.109 xx10^(-31))` | |
| `=1.8 xx10^(11) text{C kg}^(-1)` |
Therefore, the charged particles are not electrons.
PHYSICS, M6 EQ-Bank 22
An 'electron gun' like that used by JJ Thomson is shown.
Electrons leave the cathode and are accelerated towards the anode.
- Show that the acceleration of the electrons as they just leave the cathode is `4 × 10^(16) \ text{m s}^(-2)`. (2 marks)
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- Calculate the velocity of an electron as it reaches the anode. (2 marks)
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PHYSICS, M6 EQ-Bank 2 MC
What is the role of a transformer at a power station?
- To reduce heating in the transmission lines by stepping up the current
- To reduce heating in the transmission lines by stepping up the voltage
- To increase heating in the transmission lines by stepping up the current
- To increase heating in the transmission lines by stepping up the voltage
PHYSICS, M6 EQ-Bank 2 MC
A student performed an experiment using two identical, current-carrying metal rods connected to a power supply. Rod `A` was placed at different distances from Rod `B`, and the measurements on the electronic balance were recorded.
What is the dependent variable in this experiment?
- The current in `A`
- The length of the rods
- The mass recorded on the balance
- The distance between the two rods
BIOLOGY, M8 EQ-Bank 14
- Identify a disorder or disease, and describe how it affects the normal function of an organ. (2 marks)
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- Evaluate the effectiveness of a technology in managing the disorder or disease described in part (a). (4 marks)
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BIOLOGY, M7 EQ-Bank 23
The diagram shows the immune response after primary exposure to a pathogen.
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- On the diagram, continue the graph to show the immune response upon secondary exposure to the same pathogen. (2 marks)
- Using annotations on the diagram, explain the shape of the entire graph. (4 marks)
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Show Answers Only
a. & b.
Show Worked Solution
a. & b.
BIOLOGY, M8 EQ-Bank 5 MC
Which of the following is an example of an educational program to reduce the incidence of skin cancer?
- An advertising campaign on TV to promote sun safety
- Making sunscreen freely available at pools and beaches
- Increasing the availability of free skin checks
- Providing free training to doctors to help them diagnose skin cancers
BIOLOGY, M8 EQ-Bank 4 MC
An investigation was undertaken to examine the cause of lactose intolerance, a non-infectious condition found in some humans who cannot digest milk. The investigation found variation in the occurrence of lactose intolerance in human populations from different parts of the world.
What is this investigation an example of?
- A study of ecosystems
- A microbiological study
- An epidemiological study
- A study of the human immune system
BIOLOGY, M8 EQ-Bank 1 MC
What is the main focus of the study of epidemiology?
- Skin diseases
- Changes in the characteristics of a species
- Factors involved in the occurrence, prevalence and spread of disease
- How the body maintains its functions in response to variations in the environment
BIOLOGY, M8 EQ-Bank 2 MC
The diagram shows a homeostatic mechanism in a mammal.
Which row of the table describes what happens to the muscles and the arteriole walls in the skin when the core body temperature is below normal?
BIOLOGY, M7 EQ-Bank 12
A practical investigation is to be carried out to test for the microbes found in food.
Complete the table to show how to minimise risks that are likely to arise in carrying out this investigation. (3 marks)
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BIOLOGY, M7 EQ-Bank 2 MC
The runny nose and coughing that is symptomatic of having a cold is an example of the body's response to a pathogen.
How does this response protect the body?
- By heating the body to try to kill the virus
- By trying to spread the virus to other people
- By preventing the virus from entering the body
- By attempting to rapidly expel the virus from the airways
BIOLOGY, M6 EQ-Bank 22
The flow chart illustrates the effect of a point mutation on an organism.
- Outline the series of events from stages 2 to 4 that resulted in the faulty protein. (3 marks)
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- Describe how a type of mutagen may have caused the changes observed in stage 2. (2 marks)
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- Given the information in the chart shown, describe the effect caused by the mutation in stage 4 and the effect this would have on the organism. (3 marks)
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BIOLOGY, M6 EQ-Bank 3 MC
A New Zealand research team inserted a single gene into an onion to reduce the activity of the enzyme that makes your eyes water, resulting in an onion that you can cut without crying.
Which term best describes this team's process?
- Cloning
- Artificial pollination
- Genetic engineering
- Artificial insemination
BIOLOGY, M6 EQ-Bank 1 MC
A student was doing a literature review on biotechnology and wanted to see how biotechnology research could positively benefit people who suffered from Type 1 diabetes. He found several potential measures that were being explored to help people with diabetes.
Which of the following measures does NOT use biotechnology?
- Gene therapy in which genetic information is introduced into the cells of the pancreas
- The screening of genes to inform potential parents of the risk of their child developing Type 1 diabetes
- The use of auto-monitoring insulin pumps that can detect when a patient's insulin levels are dropping too low
- Collecting survey data on the prevalence of Type 1 diabetes in different communities to ensure insulin supplies are maintained at sufficient levels
BIOLOGY, M5 EQ-Bank 24
A non-infectious disease was observed in a mother and her four sons who live with her. She has no daughters. The father of these children does not have the disease and does not live with them. The woman's parents and her two sisters who live overseas do not have the disease.
A geneticist suspects that the disease is inherited.
- Draw the family pedigree for this disease. (3 marks)
- From the evidence, what indicates that the disease could be the result of a recessive allele and not be sex-linked? (2 marks)
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a.
b. Evidence disease is recessive and not sex-linked:
- Generation 1 parents do not have the disease but it is present in their daughter, meaning it must be recessive.
- If the disease was sex-linked, the same daughter who has the disease must have a father with the disease, however this is not the case.
Show Worked Solution
a.
b. Evidence disease is recessive and not sex-linked:
- Generation 1 parents do not have the disease but it is present in their daughter, meaning it must be recessive.
- If the disease was sex-linked, the same daughter who has the disease must have a father with the disease, however this is not the case.
BIOLOGY, M5 EQ-Bank 21
There are some significant differences in the form that DNA has in prokaryotic and eukaryotic cells.
In the space provided draw a labelled diagram demonstrating the difference in the form of DNA between prokaryotic and eukaryotic cells. (3 marks)
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Show Worked Solution
Points to note on images:
- Prokaryotic DNA is in the form of a loop
- Eukaryotic DNA has two loose ends and is tightly coiled in the body
BIOLOGY, M5 EQ-Bank 23
Students conducted preliminary experiments to analyse the DNA base composition of five different individuals.
The table shows the experimental data collected.
- On the grid provided, plot the % Guanine against % Adenine of the individuals analysed and draw a suitable line of best fit. (3 marks)
- Identify the relationship shown by the data. (1 mark)
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- Explain the relationship shown by the data. (3 marks)
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Show Answers Only
a.
b. Relationship: As the % of Adenine increases, the % of Guanine decreases.
c. Adenine/Guanine relationship
→ Because Adenine pairs with Thymine and Cytosine pairs with Guanine occurring to DNA base pairing rules, each should directly correlate to each other and account for the same % within the DNA composition of any species.
→ There are the only 4 components that make up all DNA composition. This also means that when comparing % of bases that do not pair, such as Adenine and Guanine, they must combine to form 50% of all DNA. This is evident when looking at individuals A and B, as well as C, D and E which are only off by 1-2%, most likely due to human error.
→ This always explains the relationship where an increase in Adenine (and Thymine) % will result in a decrease in Guanine (and Cytosine) % as the A and T pairs now occupy more space in the genome.
Show Worked Solution
a.
b. Relationship: As the % of Adenine increases, the % of Guanine decreases.
c. Adenine/Guanine relationship
→ Because Adenine pairs with Thymine and Cytosine pairs with Guanine occurring to DNA base pairing rules, each should directly correlate to each other and account for the same % within the DNA composition of any species.
→ There are the only 4 components that make up all DNA composition. This also means that when comparing % of bases that do not pair, such as Adenine and Guanine, they must combine to form 50% of all DNA. This is evident when looking at individuals A and B, as well as C, D and E which are only off by 1-2%, most likely due to human error.
→ This always explains the relationship where an increase in Adenine (and Thymine) % will result in a decrease in Guanine (and Cytosine) % as the A and T pairs now occupy more space in the genome.
BIOLOGY, M5 EQ-Bank 22
- The following data shows the average amount of Human Chorionic Gonadotropin (hCG) produced by pregnant women.
\begin{array}{|c|c|}
\hline \rule{0pt}{2.5ex}\text {Weeks of pregnancy} \rule[-1ex]{0pt}{0pt} & h C G\,\text{(ng/mL)} \\
\hline \rule{0pt}{2.5ex}0 \rule[-1ex]{0pt}{0pt}& 0 \\
\hline \rule{0pt}{2.5ex}4 \rule[-1ex]{0pt}{0pt}& 85 \\
\hline \rule{0pt}{2.5ex}8 \rule[-1ex]{0pt}{0pt}& 185 \\
\hline \rule{0pt}{2.5ex}12 \rule[-1ex]{0pt}{0pt}& 185 \\
\hline \rule{0pt}{2.5ex}16 \rule[-1ex]{0pt}{0pt}& 80 \\
\hline \rule{0pt}{2.5ex}20 \rule[-1ex]{0pt}{0pt}& 65 \\
\hline \rule{0pt}{2.5ex}24 \rule[-1ex]{0pt}{0pt}& 60 \\
\hline \rule{0pt}{2.5ex}28 \rule[-1ex]{0pt}{0pt}& 65 \\
\hline \rule{0pt}{2.5ex}32 \rule[-1ex]{0pt}{0pt}& 75 \\
\hline \rule{0pt}{2.5ex}36 \rule[-1ex]{0pt}{0pt}& 65 \\
\hline \rule{0pt}{2.5ex}40 \rule[-1ex]{0pt}{0pt}& 35 \\
\hline
\end{array}
Use the information provided to graph the levels of hCG in a normal pregnancy. (3 marks)
- Describe the role and changes in levels of a hormone in pregnancy. (3 marks)
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a. Levels of hCG in a normal pregnancy
b. The role and changes in levels of hormones in pregnancy.
- Progesterone is a sex hormone which is initially secreted by the corpus leuteum after ovulation to thicken the endometrium for implantation.
- Once the placenta has developed, it then increases the progesterone levels which maintain the pregnancy.
- Progesterone levels eventually drop in the last stage of pregnancy to facilitate delivery.
Answers could also include information about other hormones including:
- Oestrogen
- hCG
Show Worked Solution
a. Levels of hCG in a normal pregnancy
b. The role and changes in levels of hormones in pregnancy.
- Progesterone is a sex hormone which is initially secreted by the corpus leuteum after ovulation to thicken the endometrium for implantation.
- Once the placenta has developed, it then increases the progesterone levels which maintain the pregnancy.
- Progesterone levels eventually drop in the last stage of pregnancy to facilitate delivery.
Answers could also include information about other hormones including:
- Oestrogen
- hCG
BIOLOGY, M5 EQ-Bank 2 MC
A student completed a genetics exercise by preparing a Punnett square. `T` represents a dominant allele and `t` represents a recessive allele.
What were the likely genotypes of these parents?
- Both parents were homozygous.
- Both parents were heterozygous.
- Parent 1 was homozygous, Parent 2 was heterozygous.
- Parent 1 was heterozygous, Parent 2 was homozygous.
BIOLOGY, M5 EQ-Bank 4 MC
A student constructed a model of meiosis as shown. However, there is an error in the model.
Which aspect of this model does NOT fit with observations of meiosis?
- Separation of chromatids has not been shown in the model.
- The chromosomes have not independently assorted in stage 2 .
- The chromosomes in stage 4 should have duplicated before stage 5 .
- The chromosomes have undergone crossing over before sister chromosome alignment in stage 3 .
PHYSICS, M8 EQ-Bank 22
Einstein's equation `E = mc^(2)` is one of the most important equations in the history of physics.
Justify this statement. (7 marks)
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PHYSICS, M8 EQ-Bank 3 MC
A 5-gram sample of radioactive strontium-90 decayed over time. The graph shows the mass of strontium-90 remaining from the initial sample as a function of time.
What is the approximate value of the decay constant, in `\text{year}^(-1)`, for strontium-90?
- 0.006
- 0.011
- 0.014
- 0.025
PHYSICS, M8 EQ-Bank 4 MC
Which of the following is true in relation to Millikan's oil drop experiment?
\begin{align*}
\begin{array}{l}
\rule{0pt}{2.5ex} \ \rule[-1ex]{0pt}{0pt}& \\
\rule{0pt}{2.5ex}\textbf{A.}\\
\text{}\rule[-1ex]{0pt}{0pt}&\text{}\\
\rule{0pt}{2.5ex}\textbf{B.}\\
\text{}\rule[-1ex]{0pt}{0pt}&\text{}\\
\rule{0pt}{2.5ex}\textbf{C.}\rule[-1ex]{0pt}{0pt}\\
\rule{0pt}{2.5ex}\textbf{D.}\rule[-1ex]{0pt}{0pt}\\
\end{array}
\begin{array}{|l|l|}
\hline
\rule{0pt}{2.5ex}\textit{Aim of the experiment}\rule[-1ex]{0pt}{0pt}& \textit{Type of field used in experiment} \\
\hline
\rule{0pt}{2.5ex}\text{Measure the charge-to-mass} &\text{Electric and magnetic}\\
\text{ratio of electrons}\rule[-1ex]{0pt}{0pt}&\text{}\\
\hline
\rule{0pt}{2.5ex}\text{Measure the charge-to-mass} & \text{Magnetic}\\
\text{ratio of electrons}\rule[-1ex]{0pt}{0pt}&\text{}\\
\hline
\rule{0pt}{2.5ex}\text{Measure the charge of electrons}\rule[-1ex]{0pt}{0pt}& \text{Electric and magnetic} \\
\hline
\rule{0pt}{2.5ex}\text{Measure the charge of electrons}\rule[-1ex]{0pt}{0pt}& \text{Electric} \\
\hline
\end{array}
\end{align*}
PHYSICS, M8 EQ-Bank 2 MC
After DC voltage was applied to an apparatus containing hydrogen gas, the hydrogen separated into streams of oppositely charged particles.
What could be concluded from this observation?
- Hydrogen gas conducts electricity.
- Hydrogen is the simplest element.
- Hydrogen atoms have components.
- Hydrogen atoms have a neutral charge.
PHYSICS, M8 EQ-Bank 1 MC
A Hertzsprung-Russell diagram is shown.
In which region would a star have the same surface temperature as a star on the main sequence?
- `P`
- `Q`
- `R`
- `S`
PHYSICS, M5 EQ-Bank 4 MC
A torque is applied to a nut, using a wrench.
Which change will increase the magnitude of applied torque?
- Increasing the angle between the applied force and the wrench
- Decreasing the angle between the applied force and the wrench
- Increasing the distance between the nut and the point of application of the force
- Decreasing the distance between the nut and the point of application of the force
Proof, EXT2 P2 EQ-Bank 11
A sequence is given by the recursive formula
`a_1=10, \ a_(n+1)=3a_n+4` for `n>=1`
Using mathematical induction to show the formula for the general term of the sequence is
`a_n=4(3^n)-2` (3 marks)
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Calculus, EXT1 C3 EQ-Bank 12
Solve `dy/dx=2x^2-3x` given that when `x=3`, `y=-1`. (2 marks)
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Calculus, EXT1 C3 EQ-Bank 8
A researcher estimates the number of brumbies in a National Park after `t` years can be modelled by the equation
`B(t)=(18\ 000)/(1+4e^(-t))`
- Sketch the function `B(t)` over the first four years of the research. (2 marks)
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- Calculate when the brumby population should reach 13 000, giving your answer to 2 decimal places. (1 mark)
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- Show that `B^(′)(t)=(72\ 000e^t)/(e^t+4)^2` (2 marks)
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- What is the maximum growth rate of the brumby population? (3 marks)
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Show Answers Only
-
- `2.34\ text{years}`
- `text{Proof (See Worked Solutions}`
- `4500\ text{brumbies per year}`
Show Worked Solution
i.
ii. `text {Find}\ t\ text{when}\ \ B(t)=13\ 000`
| `13\ 000` | `=(18\ 000)/(1+4e^(-t))` | |
| `13\ 000(1+4e^(-t))` | `=18\ 000` | |
| `1+4e^(-t)` | `=18/13` | |
| `4e^(-t)` | `=5/13` | |
| `e^(-t)` | `=5/52` | |
| `-t` | `=ln(5/52)` | |
| `t` | `=2.34\ text{years (2 d.p.)}` |
iii. `text{Show}\ \ B^(′)(t)=(72\ 000e^t)/(e^t+4)^2`
`B(t)=18\ 000(1+4e^(-t))^(-1)`
| `B^(′)(t)` | `=-1*-1*4e^(-t)*18\ 000(1+4e^(-t))^-2` | |
| `=(72\ 000)/(e^t(1+4e^(-t))^2)` | ||
| `=(72\ 000)/(e^t(1+4/e^t)^2)` | ||
| `=(72\ 000)/(e^t((e^t+4)/e^t)^2)` | ||
| `=(72\ 000)/(e^t/(e^t)^2*(e^t+4)^2)` | ||
| `=(72\ 000e^t)/(e^t+4)^2\ \ text{… as required}` |
iv. `B^(′)(t)=72\ 000e^t(e^t+4)^(-2)`
`text{Using product rule:}`
| `B^(′′)(t)` | `=72\ 000e^t(e^t+4)^(-2)+(-2e^t)(e^t+4)^(-3)72\ 000e^t` | |
| `=72\ 000e^t(1/(e^t+4)^2-(2e^t)/(e^t+4)^3)` | ||
| `=72\ 000e^t((e^t+4-2e^t)/(e^t+4)^3)` | ||
| `=72\ 000e^t((4-e^t)/(e^t+4)^3)` |
`text{Find}\ t\ text{when}\ \ B^(′′)(t)=0:`
| `4-e^t` | `=0` | |
| `e^t` | `=4` | |
| `t` | `=ln4` | |
| `=1.386…\ text{years}` |
`text{Checking concavity changes:}`
`text{Since}\ e^t>0, (e^t+4)^3>0\ \ text{for all}\ t:`
`text{At}\ t=1, 4-e^1=1.28>0\ \ =>\ \ B^(′′)(1)>0`
`text{At}\ t=2, 4-e^2=-3.4<0\ \ =>\ \ B^(′′)(2)<0`
`B^(′)(ln4)=\ text{Max growth rate}`
| `B^(′)(ln4)` | `=(72\ 000e^(ln4))/(e^(ln4)+4)^2` | |
| `=(72\ 000xx4)/((4+4)^2)` | ||
| `=4500\ text{brumbies per year}` |
Calculus, EXT1 C3 EQ-Bank 6
The population of Myna birds in a national park is decreasing at a rate proportional to the population at that time.
- Write a differential equation that describes the situation. (1 mark)
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- If the population was originally 1300 and decreased to 1040 after 5 years, find the expected population after 10 years. (3 marks)
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Proof, EXT2 P2 EQ-Bank 2
`n` lines are drawn in a 2-dimensional plane such that no three lines are concurrent and no two lines are parallel.
`S_n` is the number of regions into which these lines divide the plane with the diagram illustrating that `S_3=7`
- In a similar way, draw diagrams that illustrate `S_1, S_2` and `S_4`. (1 mark)
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- Using the results in part (i), make a conjecture about the general formula for `S_n`. (2 marks)
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- Use mathematical induction to prove the formula from part (ii). (3 marks)
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Show Worked Solution
i. `S_1=2` `S_2=4`
`S_4=11`
ii. `text{Consider the pattern above:}`
`S_1=2,\ \ S_2=S_1+2`
`S_3=S_2+3,\ …\ , S_n=S_(n-1)+n`
| `S_n` | `=S_(n-1)+n` | |
| `=S_(n-2)+(n-1)+n` | ||
| `=S_(n-3)+(n-2)+(n-1)+n` | ||
| `vdots` | ||
| `=S_1+(2+3+…+(n-1)+n)` | ||
| `=S_0+(1+2+…+(n-1)+n)` | ||
| `=1+(1+2+…+(n-1)+n)` |
`=>text{AP where}\ \ a=1, l=n, n=n`
| `S_n` | `=1+n/2(1+n)` | |
| `=(2+n(n+1))/2` | ||
| `=(n^2+n+2)/2` |
iii. `text{Prove}\ \ S_n=(n^2+n+2)/2\ \ text{for}\ \ n>=0`
`text{If}\ \ n=1`
`text{LHS}\ =S_1=2`
`text{RHS}\ = (1^2+1+2)/2=2=\ text{LHS}`
`:.\ text{True for}\ n=1.`
`text{Assume true for}\ \ n=k:`
`text{i.e.}\ S_k=(k^2+k+2)/2`
`text{Prove true for}\ \ n=k+1:`
`text{i.e.}\ S_(k+1)=((k+1)^2+(k+1)+2)/2=(k^2+3k+4)/2`
`text{Consider the line}\ d_4\ text{added below that crosses 3 existing lines}`
`text{and creates 4 new regions.}`
`text{Similarly, the line}\ d_(k+1)\ text{will cross}\ k\ text{existing lines and}`
`text{create}\ (k+1)\ text{new regions.}`
| `S_(k+1)` | `=S_k+k+1` | |
| `=(k^2+k+2)/2+k+1` | ||
| `=(k^2+k+2+2k+2)/2` | ||
| `=(k^2+3k+4)/2` | ||
| `=\ text{RHS}` |
`:.\ text{True for}\ \ n=k+1`
`:.\ text{Since true for}\ n=1,\ text{by PMI, true for integers}\ n>=1`
Vectors, EXT2 V1 EQ-Bank 14
Use vector methods to find the coordinates of the point that divides the interval joining the points `A(7,-3,0)` and `B(2,2,-10)` in the ratio `2:3`. (3 marks)
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Vectors, EXT2 V1 EQ-Bank 12
Two planes are flying in directions given by the vectors `-200underset~i+400underset~j-3underset~k` and `300underset~i+250underset~j+underset~k`.
A person in the flight control centre is plotting their paths on a map.
Calculate the acute angle between their projected flight paths, giving your answer correct to one decimal place. (2 marks)
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Vectors, EXT2 V1 EQ-Bank 9
A parallelogram is formed by joining the points `P(-2,1,4), Q(1,4,5), R(0,2,3)` and `S(a,b,c)`.
Use vector methods to find `a,b` and `c`. (2 marks)
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Show Worked Solution
`text{Opposite sides of a parallelogram are equal and parallel.}`
`=> vec(PQ)=vec(SR)`
`vec(PQ)=((1+2),(4-1),(5-4))=((3),(3),(1))`
`vec(SR)=((-a),(2-b),(3-c))`
`text{Equating coordinates:}`
`-a=3\ \ =>\ \ a=-3`
`2-b=3\ \ =>\ \ b=-1`
`3-c=1\ \ =>\ \ c=2`
Vectors, EXT2 V1 EQ-Bank 7
In triangle `ABC`, `M` is the midpoint of `AC` and `N` is the midpoint of `AB`.
Use vector methods to prove that
- `MN=1/2CB` (2 marks)
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- `MN` is parallel to `CB` (1 mark)
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Show Worked Solution
i.
`vec(AC)+vec(CB)+vec(BA)=0\ \ \ text{(resultant vector ends at starting point)}`
`vec(CB)=-(vec(AC)+vec(BA))`
`text(S)text(ince)\ M\ text (and)\ N\ text(are midpoints:)`
| `vec(MN)` | `=-1/2vec(AC)-1/2vec(BA)` | |
| `=-1/2(vec(AC)+vec(AB))` | ||
| `=1/2vec(CB)\ \ text(… as required)` |
ii. `text{If}\ \ vec(u) = kvec(v)\ \ (k\ text{scalar})\ \ =>\ \ vec(u)\ text{||}\ vec(v)`
`vec(MN)=1/2vec(CB)\ \ text{(see (i))`
`:.MN\ text{||}\ RCB`
Vectors, EXT2 V1 EQ-Bank 6
Use vector methods to find the coordinates of the point that divides the interval joining the points `A(-1,3,2)` and `B(7,-1,-6)` in the ratio `1:3`. (3 marks)
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Vectors, EXT2 V1 EQ-Bank 5
Use two vector methods to locate the midpoint of the interval joining the points `A(3,-2,1)` and `B(5,4,-3)`. (3 marks)
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Vectors, EXT2 V1 EQ-Bank 3
If `underset ~a = 3 underset ~i-underset ~j` and `underset ~b = −2 underset ~i + 6 underset ~j + 2underset ~k`
- Calculate `underset ~a-1/2underset ~b` (2 marks)
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- Find `hat underset ~b` (2 marks)
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BIOLOGY, M7 2014 HSC 5 MC
In which of the following cases would bacteria be described as pathogens?
- Bacteria reducing lung function in mammals
- Bacteria in the human gut assisting digestion
- Bacteria producing insulin as a result of genetic engineering
- Bacteria in the mouth preventing growth of harmful bacteria
PHYSICS, M5 EQ-Bank 5 MC
An object is projected upwards from the ground, and follows a path as represented in the diagram.
Which of the following describes the projectile's horizontal and vertical acceleration at point `Y` ?
- Both the horizontal and vertical acceleration are zero.
- Both the horizontal and vertical acceleration are `9.8 \ text{m s}^(-2)`.
- The horizontal acceleration is `9.8 \ text{m s}^(-2)` and the vertical acceleration is zero.
- The horizontal acceleration is zero and the vertical acceleration is `9.8 \ text{m s}^(-2)`.
PHYSICS, M5 EQ-Bank 1 MC
Some students were testing the hypothesis that launching a projectile at an angle of 45° will give the maximum horizontal range.
Which experimental setup will best test the hypothesis?
ENGINEERING, AE 2017 HSC 6 MC
The diagram shows an aerofoil.
Which condition needs to be achieved for lift to occur?
- Pressure 1<Pressure 2
- Pressure 1= Pressure 2
- Pressure 1> Pressure 2
- Pressure 1+ Pressure 2=0
ENGINEERING, TE 2017 HSC 2 MC
Which of the following is the circuit symbol for a diode?
ENGINEERING, CS 2018 HSC 23b
The steel used in the chassis members was tested.
The load–extension graph represents the data collected during the testing of a specimen of the steel.
Before testing, the specimen was 1020 mm long with a cross-sectional area of 100 mm².
- Calculate Young's modulus for this steel. (4 marks)
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- Describe the physical changes that occur in the specimen tested in part (i) when a 20 kN load is applied and then removed, compared to when a 30 kN load is applied and then removed. (2 marks)
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ENGINEERING, PPT 2018 HSC 21b
Outline the benefits of using electric motors to power self-driving vehicles. (3 marks)
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ENGINEERING, AE 2018 HSC 17 MC
Aircraft skins can be constructed using either fibre metal laminate (FML) or sheet aircraft-grade aluminium alloy.
FML is preferred in this application because it has
- higher density and lower Young's modulus.
- higher density and improved fatigue resistance.
- higher strength-to-weight ratio and lower Young's modulus.
- higher strength-to-weight ratio and improved fatigue resistance.
ENGINEERING, PPT 2018 HSC 8 MC
In which of the following do all of the processes require plastic deformation to achieve a final shape?
- Brazing, casting, rolling
- Brazing, soldering, welding
- Extruding, casting, forging
- Extruding, pressing, rolling
ENGINEERING, PPT 2018 HSC 7 MC
An arrangement of resistors is shown.
What is the total resistance of this arrangement of resistors?
- `33 Omega`
- `50 Omega`
- `150 Omega`
- `300 Omega`
ENGINEERING, CS 2018 HSC 5 MC
Two types of bridge are shown.
What are the two types of bridge design shown?
- Suspension bridge and masonry arch
- Suspension bridge and masonry beam
- Reinforced concrete arch and masonry arch
- Reinforced concrete arch and masonry beam
ENGINEERING, TE 2018 HSC 21d
Digital logic controls a self-driving vehicle's brakes.
Brakes will be applied when all of the following conditions are met:
-
- the motor is on
- the vehicle is in motion
- either sensor 1 or sensor 2 is activated.
Explain how the logic gates, labelled 1, 2 and 3 in the circuit below, control the vehicle's brakes. (3 marks)
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BIOLOGY, M8 2019 HSC 33c
A large epidemiological study was conducted. It used historical data to investigate the association between Herpes simplex virus (HSV) infection and dementia. Dementia is caused by a variety of brain illnesses. Alzheimer's disease is the most common cause of dementia.
The study used the records of 8362 patients with HSV infection and 25086 randomly selected sex- and age-matched control patients without HSV infection. Some of the patients with HSV had been treated with antiviral medication.
The graph below shows some results of the study.
- Describe the trends shown in the data. (3 marks)
ENGINEERING, TE 2019 HSC 27a
A telecommunications tower with repeater transmitters is shown. The tower is assembled from many individual parts.
Explain why detailed drawings are used in the design and manufacture of these individual parts. (2 marks)
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ENGINEERING, TE 2019 HSC 22a
A telecommunications engineer has designed a tower that is to support two mobile repeater transmitters. It is to be located in an urban community.
Outline responsibilities the engineer has when placing the tower within a local community. (3 marks)
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ENGINEERING, CS 2019 HSC 11 MC
The table shows materials that have been used to build civil structures over time.
Which row of the table shows the use of the materials in the correct historical order?
ENGINEERING, PPT 2019 HSC 7 MC
A box sits on a horizontal surface. The box begins to slip when this surface is tilted to 28 degrees.
What is the coefficient of friction between the box and the surface?
- 0.280
- 0.469
- 0.532
- 0.883
ENGINEERING, TE 2019 HSC 3 MC
Which AND gate shows the correct output for its given inputs?
ENGINEERING, AE 2019 HSC 1 MC
Which Australian aeronautical innovation is commonly used to record in-flight data?
- Altimeter
- Pitot tube
- Black box
- Transponder
PHYSICS, M8 2015 HSC 33d
The position of the Sun, star `W` and star `Z` are shown on the H-R diagram.
The curves `A` and `B` show intensity versus frequency for star `W` and the Sun, measured from the same distance.
- Identify which curve (`A` or `B`) represents star `W` and justify your choice. (2 marks)
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- Account for differences between stars `W` and `Z` that can be deduced from the H-R diagram. (3 marks)
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