Number and Algebra, NAPK21v1
MATRICES, FUR2 2020 VCAA 3
An offer to buy the Westmall shopping centre was made by a competitor.
One market research project suggested that if the Westmall shopping centre were sold, each of the three centres (Westmall, Grandmall and Eastmall) would continue to have regular shoppers but would attract and lose shoppers on a weekly basis.
Let `S_n` be the state matrix that shows the expected number of shoppers at each of the three centres `n` weeks after Westmall is sold.
A matrix recurrence relation that generates values of `S_n` is
`S_(n+1) = T xx S_n`
`{:(quad qquad qquad qquad qquad qquad qquad qquad text(this week)),(qquad qquad qquad qquad qquad qquad quad \ W qquad quad G qquad quad \ E),(text(where)\ T = [(quad 0.80, 0.09, 0.10),(quad 0.12, 0.79, 0.10),(quad 0.08, 0.12, 0.80)]{:(W),(G),(E):}\ text(next week,) qquad qquad S_0 = [(250\ 000), (230\ 000), (200\ 000)]{:(W),(G),(E):}):}`
 Calculate the state matrix, `S_1`, to show the expected number of shoppers at each of the three centres one week after Westmall is sold. (1 mark)
Using values from the recurrence relation above, the graph below shows the expected number of shoppers at Westmall, Grandmall and Eastmall for each of the 10 weeks after Westmall is sold.
 What is the difference in the expected weekly number of shoppers at Westmall from the time Westmall is sold to 10 weeks after Westmall is sold?
Give your answer correct to the nearest thousand. (1 mark)
 Grandmall is expected to achieve its maximum number of shoppers sometime between the fourth and the tenth week after Westmall is sold.
Write down the week number in which this is expected to occur. (1 mark)
 In the long term, what is the expected weekly number of shoppers at Westmall?
Round your answer to the nearest whole number. (1 mark)
MATRICES, FUR2 2020 VCAA 1
The three major shopping centres in a large city, Eastmall `(E)`, Grandmall `(G)` and Westmall `(W)`, are owned by the same company.
The total number of shoppers at each of the centres at 1.00 pm on a typical day is shown in matrix `V`.
`qquad qquad qquad {:(qquad qquad qquad \ E qquad qquad G qquad qquad \ W),(V = [(2300,2700,2200)]):}`
 Write down the order of matrix `V`. (1 mark)
Each of these centres has three major shopping areas: food `(F)`, clothing `(C)` and merchandise `(M)`.
The proportion of shoppers in each of these three areas at 1.00 pm on a typical day is the same at all three centres and is given in matrix `P` below.
`qquad qquad qquad P = [(0.48), (0.27), (0.25)] {:(F),(C),(M):}`
 Grandmall’s management would like to see 700 shoppers in its merchandise area at 1.00 pm.
If this were to happen, how many shoppers, in total, would be at Grandmall at this time? (1 mark)
 The matrix `Q = P xx V` is shown below. Two of the elements of this matrix are missing.
`{:(quad qquad qquad qquad \ E qquad qquad G qquad qquad W), (Q = [(1104, \ text{___}, 1056 ), (621,\ text{___}, 594), (575, 675, 550)]{:(F),(C), (M):}):}`

 Complete matrix `Q` above by filling in the missing elements. (1 mark)
 The element in row `i` and column `j` of matrix `Q` is `q_(ij)`.
What does the element `q_23` represent? (1 mark)
The average daily amount spent, in dollars, by each shopper in each of the three areas at Grandmall in 2019 is shown in matrix `A_2019` below.
`qquad qquad A_2019 = [(21.30), (34.00), (14.70)] {:(F),(C),(M):}`
On one particular day, 135 shoppers spent the average daily amount on food, 143 shoppers spent the average daily amount on clothing and 131 shoppers spent the average daily amount on merchandise.
 Write a matrix calculation, using matrix `A_2019`, showing that the total amount spent by all these shoppers is $9663.20 (1 mark)
 In 2020, the average daily amount spent by each shopper was expected to change by the percentage shown in the table below.
Area food clothing merchandise Expected change increase by 5% decrease by 15% decrease by 1%
The average daily amount, in dollars, expected to be spent in each area in 2020 can be determined by forming the matrix product
`qquad qquad A_2020 = K xx A_2019`
Write down matrix `K`. (1 mark)
CORE, FUR2 2020 VCAA 8
Samuel has a reducing balance loan.
The first five lines of the amortisation table for Samuel’s loan are shown below.
Interest is calculated monthly and Samuel makes monthly payments of $1600.
Interest is charged on this loan at the rate of 3.6% per annum.
 Using the values in the amortisation table
 i. calculate the principal reduction associated with payment number 3 (1 mark)
 ii. calculate the balance of the loan after payment number 4 is made.
 Round your answer to the nearest cent. (1 mark)
 Let `S_n` be the balance of Samuel’s loan after `n` months.
 Write down a recurrence relation, in terms of `S_0, S_(n+1)` and `S_n`, that could be used to model the monthtomonth balance of the loan. (1 mark)
CORE, FUR2 2020 VCAA 6
The table below shows the mean age, in years, and the mean height, in centimetres, of 648 women from seven different age groups.
 What was the difference, in centimetres, between the mean height of the women in their twenties and the mean height of the women in their eighties? (1 mark)
A scatterplot displaying this data shows an association between the mean height and the mean age of these women. In an initial analysis of the data, a line is fitted to the data by eye, as shown.
 Describe this association in terms of strength and direction. (1 mark)
 The line on the scatterplot passes through the points (20,168) and (85,157).
Using these two points, determine the equation of this line. Write the values of the intercept and the slope in the appropriate boxes below.
Round your answers to three significant figures. (1 mark)
mean height = 

+ 

× mean age 
 In a further analysis of the data, a least squares line was fitted.
The associated residual plot that was generated is shown below.
The residual plot indicates that the association between the mean height and the mean age of women is nonlinear.
The data presented in the table in part a is repeated below. It can be linearised by applying an appropriate transformation to the variable mean age.
Apply an appropriate transformation to the variable mean age to linearise the data. Fit a least squares line to the transformed data and write its equation below.
Round the values of the intercept and the slope to four significant figures. (2 marks)
CORE, FUR2 2020 VCAA 4
The age, in years, body density, in kilograms per litre, and weight, in kilograms, of a sample of 12 men aged 23 to 25 years are shown in the table below.
Age (years) 
Body density 
Weight 

23  1.07  70.1  
23  1.07  90.4  
23  1.08  73.2  
23  1.08  85.0  
24  1.03  84.3  
24  1.05  95.6  
24  1.07  71.7  
24  1.06  95.0  
25  1.07  80.2  
25  1.09  87.4  
25  1.02  94.9  
25  1.09  65.3 
 For these 12 men, determine
 i. their median age, in years (1 mark)
 ii. the mean of their body density, in kilograms per litre. (1 mark)
 A least squares line is to be fitted to the data with the aim of predicting body density from weight.
 i. Name the explanatory variable for this least squares line. (1 mark)
 ii. Determine the slope of this least squares line.
 Round your answer to three significant figures. (1 mark)
 What percentage of the variation in body density can be explained by the variation in weight?
 Round your answer to the nearest percentage. (1 mark)
CORE, FUR2 2020 VCAA 3
In a study of the association between BMI and neck size, 250 men were grouped by neck size (below average, average and above average) and their BMI recorded.
Fivenumber summaries describing the distribution of BMI for each group are displayed in the table below along with the group size.
The associated boxplots are shown below the table.
 What percentage of these 250 men are classified as having a below average neck size? (1 mark)
 What is the interquartile range (IQR) of BMI for the men with an average neck size? (1 mark)
 People with a BMI of 30 or more are classified as being obese.
 Using this criterion, how many of these 250 men would be classified as obese? Assume that the BMI values were all rounded to one decimal place. (1 mark)
 Do the boxplots support the contention that BMI is associated with neck size? Refer to the values of an appropriate statistic in your response. (2 marks)
CORE, FUR2 2020 VCAA 2
The neck size, in centimetres, of 250 men was recorded and displayed in the dot plot below.
 Write down the modal neck size, in centimetres, for these 250 men. (1 mark)
 Assume that this sample of 250 men has been drawn at random from a population of men whose neck size is normally distributed with a mean of 38 cm and a standard deviation of 2.3 cm.
 i. How many of these 250 men are expected to have a neck size that is more than three standard deviations above or below the mean?
 Round your answer to the nearest whole number. (1 mark)
 ii. How many of these 250 men actually have a neck size that is more than three standard deviations above or below the mean? (1 mark)
 The fivenumber summary for this sample of neck sizes, in centimetres, is given below.
`qquad`
Use the fivenumber summary to construct a boxplot, showing any outliers if appropriate, on the grid below. (2 marks)
CORE, FUR2 2020 VCAA 1
Body mass index (BMI), in kilograms per square metre, was recorded for a sample of 32 men and displayed in the ordered stem plot below.
 Describe the shape of the distribution. (1 mark)
 Determine the median BMI for this group of men. (1 mark)
 People with a BMI of 25 or over are considered to be overweight.
 What percentage of these men would be considered to be overweight? (1 mark)
Geometry, NAPXp124059v02
Geometry, NAPXp124059v01
Heath is making a square pyramid using plastic balls and sticks.
How many more sticks does Heath need to finish the square pyramid?
1  2  3  4  5 





Algebra, NAPXp116602v02
Jordan lives in Perth and receives 10 cents for every glass bottle she recycles at the depot.
Jordan takes 33 glass bottles to the depot.
How much money will she receive?
33 cents  $3.30  $33.00  $333 




Algebra, NAPXp116602v01
Jardine lives in Adelaide and receives 5 cents for every plastic bottle he delivers to the recycling depot.
Jardine delivers 18 plastic bottles.
How much money will he receive?
$900  $90  $9.00  $0.90 




Algebra, MET1 2013 VCAA 5b
Solve the equation `3^(– 4x) = 9^(6  x)` for `x`. (2 marks)
Algebra, MET1 SMBank 12
Solve the equation `log_2(x1) = 8` for `x`. (2 marks)
Mechanics, SPEC2 2020 VCAA 5
Two objects, each of mass `m` kilograms, are connected by a light inextensible strings that passes over a smooth pulley, as shown below. The object on the platform is initially at point A and, when it is released, it moves towards point C. The distance from point A to point C is 10 m. The platform has a rough surface and, when it moves along the platform, the object experiences a horizontal force opposing the motion of magnitude `F_1` newtons in the section AB and a horizontal force opposing the motion of magnitude `F_2` newtons when it moves in the section BC.
 On the diagram above, mark all forces that act on each object once the object on the platform has been released and the system is in motion. (2 marks)
The force `F_1` is given by `F_1 = kmg, \ k ∈ R^+`.
 i. Show that an expression for the acceleration, in `text(ms)^(−2)`, of the object on the platform, in terms of `k`, as it moves from point A to point B is given by `(g(1  k))/2`. (2 marks)
 ii. The system will only be in motion for certain values of `k`.
 Find these values of `k`. (1 mark)
Point B is midway between points A and C.
 Find, in terms of `k`, the time taken, is seconds, for the object on the platform to reach point B. (2 marks)
 Express, in terms of `k`, the speed `v_B`, in `text(ms)^(−1)`, of the object on the platform when it reaches point B. (2 marks)
 When the object on the platform is at point B, the string breaks. The velocity of the object at point B is `v_B = 2.5\ text(ms)^(−1)`. The force that opposes motion from point B to point C is `F_2 = 0.075 mg + 0.4 mv^2`, where `v` is the velocity of the object when it is a distance of `x` metres from point B. The object on the platform comes to rest before point C.
 Find the object's distance from point C when it comes to rest. Give your answer in metres, correct to two decimal places. (4 marks)
Calculus, SPEC2 2020 VCAA 3
Let `f(x) = x^2e^(−x)`.
 Find an expression for `f′(x)` and state the coordinates of the stationary points of `f(x)`. (2 marks)
 State the equation(s) of any asymptotes of `f(x)`. (1 mark)
 Sketch the graph of `y = f(x)` on the axes provided below, labelling the local maximum stationary point and all points of inflection with their coordinates, correct to two decimal places. (3 marks)
Let `g(x) = x^n e^(−x)`, where `n ∈ Z`.
 Write down an expression for `g″(x)`. (1 mark)
 i. Find the nonzero values of `x` for which `g″(x) = 0`. (1 mark)
 ii. Complete the following table by stating the value(s) of `n` for which the graph of `g(x)` has the given number of points of inflection. (2 marks)
Vectors, SPEC2 2020 VCAA 1
A particle moves in the `x\ – y` plane such that its position in terms of `x` and `y` metres at `t` seconds is given by the parametric equations
`x = 2sin(2t)`
`y = 3cos(t)`
where `t >= 0`
 Find the distance, in metres, of the particle from the origin when `t = pi/6`. (2 marks)
 i. Express `(dy)/(dx)` in terms of `t` and, hence, find the equation of the tangent to the path of the particle at `t = pi` seconds. (3 marks)
 ii. Find the velocity, `underset ~ v`, in `text(ms)^(−1)`, of the particle when `t = pi`. (2 marks)
 iii. Find the magnitude of the acceleration, in `text(ms)^(−2)`, when `t = pi`. (2 marks)
 Find the time, in seconds, when the particle first passes through the origin. (1 mark)
 Express the distance, `d` metres, travelled by the particle from `t = 0` to `t = pi/6` as a definite integral and find this distance correct to three decimal places. (2 marks)
Number, NAPXp116616v04
Justin owns a collection of action figures which is more than 674 action figures and less than 764.
Which of these numbers could represent the number of action figures that Justin owns?
792  724  648  772 




Number, NAPXp116616v03
Eric owns a book which has more than 258 pages but less than 285 pages
Which of these could represent the number of pages in Eric’s book?
287  294  249  262 




Number, NAPXp116602v04
Number, NAPXp116602v03
Vectors, SPEC2 SMBank 23
Calculus, SPEC2 2020 VCAA 1 MC
The `y`intercept of the graph of `y = f(x)`, where `f(x) = ((x  a)(x + 3))/((x  2))`, is also a stationary point when `a` equals
 `−2`
 `−6/5`
 `0`
 `6/5`
 `2`
GRAPHS, FUR1 2020 VCAA 3 MC
The delivery fee for a parcel, in dollars, charged by a courier company is based on the weight of the parcel, in kilograms.
This relationship is shown in the step graph below for parcels that weigh up to 20 kg.
Which one of the following statements is not true?
 The delivery fee for a 4 kg parcel is $20.
 The delivery fee for a 12 kg parcel is $26.
 The delivery fee for a 13 kg parcel is the same as the delivery fee for a 20 kg parcel.
 The delivery fee for a 10 kg parcel is $14 more than the delivery fee for a 2 kg parcel.
 The delivery fee for a 12 kg parcel is $18 more than the delivery fee for a 2 kg parcel.
GRAPHS, FUR1 2020 VCAA 2 MC
At a school concert, the entry fee for adults was different from the entry fee for children.
The entry fee for three adults and four children was $67.00
The entry fee for two adults and five children was $57.50
Let `x` be the entry fee for an adult.
Let `y` be the entry fee for a child.
A pair of simultaneous equations that could be used to represent the situation above is
A.  `3x + 2y = 57.5`  B.  `3x + 2y = 67` 
`4x + 5y = 67`

`4x + 5y = 57.5`


C.  `3x + 4y = 57.5`  D.  `3x + 4y = 67` 
`2x + 5y = 67`

`2x + 5y = 57.5`


E.  `4x + 3y = 67`  
`5x + 2y = 57.5`

GEOMETRY, FUR1 2020 VCAA 2 MC
GEOMETRY, FUR1 2020 VCAA 1 MC
Each year begins on 1 January.
The location that begins each year first is
 Kathmandu (28° N, 85° E).
 Cairo (30° N, 31° E).
 Kabul (34° N, 69° E).
 Nairobi (1° S, 37° E).
 Port Moresby (9° S, 147° E).
NETWORKS, FUR1 2020 VCAA 4 MC
NETWORKS, FUR1 2020 VCAA 2 MC
NETWORKS, FUR1 2020 VCAA 1 MC
A connected planar graph has seven vertices and nine edges.
The number of faces that this graph will have is
 1
 2
 3
 4
 5
MATRICES, FUR1 2020 VCAA 1 MC
The matrix `[(1, 0, 0), (0, 1, 1), (1, 0, 1)]` is an example of
 a binary matrix.
 an identity matrix.
 a triangular matrix.
 a symmetric matrix.
 a permutation matrix.
CORE, FUR1 2020 VCAA 21 MC
The following recurrence relation can generate a sequence of numbers.
`T_0 = 10, qquad T_(n + 1) = T_n + 3`
The number 13 appears in this sequence as
 `T_1`
 `T_2`
 `T_3`
 `T_10`
 `T_13`
CORE, FUR1 2020 VCAA 6 MC
A percentaged segmented bar chart would be an appropriate graphical tool to display the association between month of the year (January, February, March, etc.) and the
 monthly average rainfall (in millimetres).
 monthly mean temperature (in degrees Celsius).
 annual median wind speed (in kilometres per hour).
 monthly average rainfall (below average, average, above average).
 annual average temperature (in degrees Celsius).
CORE, FUR1 2020 VCAA 13 MC
The times between successive nerve impulses (time), in milliseconds, were recorded.
Table 1 shows the mean and the fivenumber summary calculated using 800 recorded data values.
Part 1
The difference, in milliseconds, between the mean time and the median time is
 10
 70
 150
 220
 230
Part 2
Of these 800 times, the number of times that are longer than 300 milliseconds is closest to
 20
 25
 75
 200
 400
Part 3
The shape of the distribution of these 800 times is best described as
 approximately symmetric.
 positively skewed.
 positively skewed with one or more outliers.
 negatively skewed.
 negatively skewed with one or more outliers.
Calculus, SPEC1 2020 VCAA 7
Consider the function defined by
`f(x) = {({:mx + n,:}, x < 1), ({: frac{4}{(1 + x^2)},:}, x >= 1):}`
where `m` and `n` are real numbers.
 Given that `f(x)` and `f prime(x)` are continuous over `R`, show that `m = 2` and `n = 4`. (2 marks)
 Find the area enclosed by the graph of the function, the xaxis and the lines `x = 0` and `x = sqrt 3`. (3 marks)
Calculus, EXT1 C2 2020 SPEC1 6
Let `f(x) = tan^(1) (3x  6) + pi`.
 Show that `f prime(x) = 3/(9x^2  36x + 37)`. (1 mark)
 Hence, show that the graph of `f` has a point of inflection at `x = 2`. (2 marks)
 Sketch the graph of `y = f(x)` on the axes provided below. Label any asymptotes with their equations and the point of inflection with its coordinates. (2 marks)
Calculus, SPEC1 2020 VCAA 6
Let `f(x) = arctan (3x  6) + pi`.
 Show that `f prime(x) = 3/(9x^2  36x + 37)`. (1 mark)
 Hence, show that the graph of `f` has a point of inflection at `x = 2`. (2 marks)
 Sketch the graph of `y = f(x)` on the axes provided below. Label any asymptotes with their equations and the point of inflection with its coordinates. (2 marks)
Calculus, EXT1 C2 2020 SPEC1 2
Evaluate `int_(1)^0 (1 + x)/sqrt(1  x)\ dx`, using the substitution `u=1x`. (3 marks)
Calculus, EXT2 C1 2020 SPEC1 2
Evaluate `int_(1)^0 (1 + x)/sqrt(1  x)\ dx`. (3 marks)
Calculus, MET1 2020 VCAA 7
Consider the function `f(x) = x^2 + 3x + 5` and the point `P(1, 0)`. Part of the graph `y = f(x)` is shown below.
 Show the point `P` is not on the graph of `y = f(x)`. (1 mark)
 Consider a point `Q(a, f(a))` to be a point on the graph of `f`.
 Find the slope of the line connecting points `P` and `Q` in terms of `a`. (1 mark)
 Find the slope of the tangent to the graph of `f` at point `Q` in terms of `a`. (1 mark)
 Let the tangent to the graph of `f` at `x = a` pass through point `P`.
Find the values of `a`. (2 marks)
 Give the equation of one of the lines passing through point `P` that is tangent to the graph of `f`. (1 mark)
 Find the value of `k`, that gives the shortest possible distance between the graph of the function of `y = f(x  k)` and point `P`. (2 marks)
Calculus, MET1 2006 ADV 2aii
Differentiate with respect to `x`:
Let `y=sin x/(x + 1)`. Find `dy/dx `. (2 marks)
Calculus, MET1 2013 VCAA 1b
Let `f(x) = e^(x^2)`.
Find `f prime (3)`. (3 marks)
Calculus, MET1 2010 VCAA 1b
For `f(x) = log_e (x^2 + 1)`, find `f prime (2)`. (2 marks)
Calculus, MET1 2009 ADV 2b
Let `y=ln(3x^3 + 2)`.
Find `dy/dx`. (2 marks)
Calculus, MET1NHT 2018 VCAA 1b
Let `y= (x + 5) log_e (x)`.
Find `(dy)/(dx)` when `x = 5`. (2 marks)
Calculus, MET1 2017 VCAA 1b
Let `g(x) = (2  x^3)^3`.
Evaluate `g prime (1)`. (2 marks)
Functions, EXT1 F1 2020 MET1 6
`f(x) = 1/sqrt2 sqrtx`, where `x in [0,2]`
 Find `f^(−1)(x)`, and state its domain. (2 marks)
The graph of `y = f(x)`, where `x ∈ [0, 2]`, is shown on the axes below.
 On the axes above, sketch the graph of `f^(−1)(x)` over its domain. Label the endpoints and point(s) of intersection with `f(x)`, giving their coordinates. (2 marks)
Probability, 2ADV S1 2012 MET1 2
A car manufacturer is reviewing the performance of its car model X. It is known that at any given sixmonth service, the probability of model X requiring an oil change is `17/20`, the probability of model X requiring an air filter change is `3/20` and the probability of model X requiring both is `1/20`.
 State the probability that at any given sixmonth service model X will require an air filter change without an oil change. (1 mark)
 The car manufacturer is developing a new model. The production goals are that the probability of model Y requiring an oil change at any given sixmonth service will be `m/(m + n)`, the probability of model Y requiring an air filter change will be `n/(m + n)` and the probability of model Y requiring both will be `1/(m + n)`, where `m, n ∈ Z^+`.
Determine `m` in terms of `n` if the probability of model Y requiring an air filter change without an oil change at any given sixmonth service is 0.05. (2 marks)
Probability, MET1 2020 VCAA 2
A car manufacturer is reviewing the performance of its car model X. It is known that at any given sixmonth service, the probability of model X requiring an oil change is `17/20`, the probability of model X requiring an air filter change is `3/20` and the probability of model X requiring both is `1/20`.
 State the probability that at any given sixmonth service model X will require an air filter change without an oil change. (1 mark)
 The car manufacturer is developing a new model. The production goals are that the probability of model Y requiring an oil change at any given sixmonth service will be `m/(m + n)`, the probability of model Y requiring an air filter change will be `n/(m + n)` and the probability of model Y requiring both will be `1/(m + n)`, where `m, n ∈ Z^+`.
Determine `m` in terms of `n` if the probability of model Y requiring an air filter change without an oil change at any given sixmonth service is 0.05. (2 marks)
Calculus, MET1 2020 VCAA 1b
Evaluate `f′(1)`, where `f: R > R, \ f(x) = e^(x^2  x + 3)`. (2 marks)
Calculus, MET1 2020 VCAA 1a
Let `y = x^2 sin(x)`.
Find `(dy)/(dx)`. (1 mark)
Proof, EXT2 P1 SMBank 15
Prove `sqrt5 + sqrt3 > sqrt14` by contradiction. (2 marks)
Complex Numbers, EXT2 N1 SMBank 9
Let `z = sqrt3  3 i`
 Express `z` in modulusargument form. (2 marks)
 Find the smallest integer `n`, such that `z^n + (overset_z)^n = 0`. (3 marks)
Complex Numbers, EXT2 N1 SMBank 1 MC
Which of the following is the complex number ` sqrt3 + 3 i`?
 `2 sqrt3 e^(frac{i pi}{3})`
 `2 sqrt3 e^(frac{i 2pi}{3})`
 `12 e^(frac{i pi}{3})`
 `12 e^(frac{i 2pi}{3})`
Complex Numbers, EXT2 N1 2004 HSC 2b
Let `alpha = 1 + i sqrt3` and `beta = 1 + i`.
 Find `frac{alpha}{beta}`, in the form `x + i y`. (1 mark)
 Express `alpha` in modulusargument form. (3 marks)
 Given that `beta` has the modulusargument form
`beta = sqrt2 (cos frac{pi}{4} + i sin frac{pi}{4})`.
find the modulusargument form of `frac{alpha}{beta}`. (1 mark)  Hence find the exact value of `sin frac{pi}{12}` (1 mark)
Complex Numbers, EXT2 N2 EQBank 1
`z = sqrt2 e^((ipi)/15)` is a root of the equation `z^5 = alpha(1 + isqrt3), \ alpha ∈ R`.
 Express `1 + isqrt3` in exponential form. (2 marks)
 Find the value of `alpha`. (1 mark)
 Find the other 4 roots of the equation in exponential form. (3 marks)
Complex Numbers, Ext2 N1 EQBank 9
Calculate the value of `(e^((ipi)/3)  e^(−(ipi)/3))/(2i)`. (2 marks)
Complex Numbers, EXT2 N1 EQBank 5 MC
In which quadrant of the complex plane is the complex number `4e^((i16)/3)` found?
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