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#### sweetiepi

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##### Difficult Questions from past VCAA papers!
« on: October 28, 2016, 09:37:31 am »
+18
I know these are already posted in the Methods Exam discussion, however these may prove useful to later years, as well, so I'm going to add them here.

2015:
Question 4c (41% got both marks) Asks for average value
Question 6b (37% got both marks) Conditional probability, combing with normal distributions
Question 7b (36% got all three marks) was solving an equation for t
Question 8c (28% got a mark) “if events A and B are independent, calculate \(\ Pr A union B) “
Question 9bi (28% got two marks) Finding the probability it came from a particular place
Question 9bii (19% got this mark) “If the probability that this egg came from farm B is 0.3, find the value of p.”
Question 10a (20% got the mark) Finding a coordinate in terms of \(\ \Theta)
Question 10b (16% received a mark) Finding the gradient of the tangent at above coordinate
Question 10cii (47% got this correct) Finding “d” in terms of \(\ \Theta)
Question 10d (11% got all 3 marks) Finding the min value of \( \Theta) in which the area is a minium

2014:
Question 5c (21% got all 3 marks) Asks us to find the area enclosed within the graph and another line.
Question 6 (44% got both marks) This was solving a log equation for x.
Question 7 (38% got the full 3 marks) This was a find the antiderivative question.
Question 8a (48% got the 2 marks) Determining the median of a probability density function
Question 8b (24% got both marks) Using conditional probability
Question 9bi (44% received 2 marks) Was finding a probability given that the probability of something else was x.
Question 9bii (27% had the full two marks) Finding the probability that the event happened, with conditional probability
Question 10a (30% received the 3 marks) Finding two values in the equation of a curve.
Question 10bi (32% got this mark) Finding an expression of “v” in terms of “u”
Question 10bii (9% of the cohort received these two marks) Find the minimum total shaded area
Question 10biii (8% of the cohort received this mark) Finding the max total shaded area

2013:
Question 3 (42% got the full 2 marks) Finding a function with its derivative.
Question 4 (47% got the full 2 marks) Solving a trig equation for x
Question 6 (16% got all 3 marks) Finding “a” from the function’s average value.
Question 7a (46% got each of the 3 marks) Finding “p” in a probability distribution
Question 7bi (29% got both marks) Finding the expected value of the distribution
Question 7bii (32% got this mark) Finding the probability the “X” is greater than the expected value
Question 8 (21% got all 3 marks) Finding the expected value of a continuous function via integration by recognition.
Question 9b (46% got both marks) Sketching the graph of an absolute function – no longer on the study design.
Question 9ci (16% got the full 2 marks) Finding the rule of a function after transformations- albeit in reference to a modulus function.
Question 9cii (39% got the mark) Finding the domain of the function
Question 10b (26% got the full 3) Finding the maximum area of a triangle and the max value of x
Question 10c (7% bagged the full 3 marks) Finding the area of the region bound by the function and a line segment

2012:
Question 2 (27% got the 2 marks) Finding an antiderivative of a function
Question 4c (3% of the cohort got all 3 marks) Finding a probability of an event happening
Question 5a (46% got the full 3 marks) Sketching a graph of a modulus function- no longer on the course
Question 5bii (26% got both marks) Finding the image of a graph under transformations (even though it relates to a modulus function)
Question 8a (34% bagged the 2 marks) Finding the probability between two values for a normal distribution in terms of “q”
Question 8b (45% received the 3 marks) Finding the value of a pronumeral in the pdf, so that the probability of “X” being less than or equal to the pronumeral is equal to \(\ 5/8 )
Question 9b (45% got the 3 marks) Integration by recognition to find the value of an antiderivative.
Question 10aii (18% got the mark) Finding the value of a pronumeral so that a stationary point is a positive number
Question 10b (22% got all 3 marks) Finding the value of a pronumeral where the tangent, at x= -6 passes through the origin

2011:
Question 1b (44% got both marks) Find the derivative of a function and find the value of the derivative at a point
Question 2a (43% got the mark) Find an antiderivative of a function
Question 2b (28% received all 3 marks) Solve the equation for x
Question 3b (31% bagged both marks) Solve a trig function for x
Question 4b (10% received 2 marks) State the max function where f(g(x)) is defined
Question 5a (18% received the full 2 marks) Find the probability that “X” is less than 3.5. (Requires integration of a modulus function- modulus in no longer in the course)
Question 5b (14% received the 2 marks) Conditional probability- be mindful that it still involves a modulus here
Question 6a (25% received all 3 marks) Find the value of a pronumeral where there infinitely many solutions
Question 6b (33% received the mark) Find the value of a pronumeral where there is a unique solution
Question 7aii (41% got the mark) In terms of “p”, find the probability of obtaining two heads and a tail from a biased coin (where Pr(H) = “p”)
Question 7b (18% got the mark) If the probability of obtaining 3 heads = the probability of obtaining two heads and a tail, find “p”
Question 8a (38% both marks) Calculate Pr(A’ intersection B) when Pr(A union B) = \(\ ¾)
Question 8b (44% got the mark) Calculate Pr(A’ intersection B) when A and B are mutually exclusive
Question 9 (16% received all 4 marks) Find the value of a and m if the area of the shaded region is 64
Question 10c (28% were awarded the 2 marks) Find the derivative and hence show “BD”=2”CD”
Question 10d (5% were awarded the mark) Find the max value of L if a= \(\ 3 \root5)

2010
Question 2b (30% were awarded all 3 marks) Find a pronumeral given the an antiderivative equals the \(\ ln(p) )
Question 4b (39% were given both marks) Solve the trig equation for x
Question 5b (31% got both marks) Find a pronumeral such that a normal distribution value equals a standard normal value.
Question 6 (23% received 3 marks) Find the values of a, b, c using the matrix transformations
Question 7a (49% got all 3 marks) Find the value of a in a continuous probability distribution function.
Question 8 (32% got all 3 marks) Find the value of “p” in the discrete probability distribution
Question 9b (20% were given all 3 marks) Find the area of the shaded region in the form \(\ a*ln(b) +c)
Question 10 (35% were awarded each of the 4 marks) Find the values of a, c and d where the tangent of the curve y=x \(\ 1/2) is y=ax-1 at (9, c)
Question 11a (11% received both marks) “Find h in terms of r”
Question 11b (47% received this mark) “find S in terms of r”
Question 11c (10% of the cohort got 2 marks) “find the value of r for which S is a maximum”

2009:
Question 1b (37% got 3 marks) Find a derivative and substitute in a value
Question 2a (25% received 2 marks) Find an antiderivative
Question 2b (48% received the full 3 marks) Using a definite integral to find the antiderivative
Question 3 (38% received 3 marks) Find the inverse function
Question 4 (41% received 3 marks) Solve the trig equation
Question 5c (40% received both marks) “Given that the sum of the numbers on the two balls is 5, what is the probability that the second ball drawn is numbered 1?”
Question 8 (37% got 3 marks) “the tangent to the graph f at point x=a passes through (0,0)” find the value of k in terms of a.
Question 9 (22% got 4 marks) Solve the log equation for x
Question 10a (27% got 4 marks) Linear approximation/euler’s formula- not seen in an exam since then. (Believed to be only in specialist now)
Question 10b (8% got this mark) Explain why this approximate value is greater than the exact value for \(\ \cuberoot 8.06)

2008:
Question 3 (41% awarded 2 marks) Solve the trig equation
Question 4a (49% received 2 marks) Find “k” in a probability density function
Question 4b (27% received 3 marks) Standard conditional probability question
Question 5 (47% got 3 marks) Find “C” when the area between the function and line x=C is \(\ 5/2)
Question 6a (40% given the mark) What is the domain of the derivative function?
Question 7b (49% got both marks) “Jane drives to work on two consecutive days.What is the probability that the number of traffic lights that are red is the same on both days?”
Question 8 (39% received 3 marks) Find the probability that “Jean-Paul” goes to the Cino on exact two of the next three Fridays.
Question 9a (35% bagged the 2 marks) Find an expression for y in terms of x
Question 9b (31% received the 2 marks) What is the expression of the total surface area?
Question 9c (30% received the 3 marks) Find the value of x so that the area is a minimum
Question 10a (45% got 2 marks) Find the inverse of the function and it’s domain.
Question 10b (19% got the mark) Sketch f(f-1(x)) for it’s max domain
Question 10c (20% awarded 2 marks) find f(-f-1(2x)) in the form \(\ (ax)/(bx+c) )

2007:
Question 2b (41% received 2 marks) Find the derivative and sub in a value
Question 3a (25% got 3 marks) Sketch the derivative function
Question 3b (45% got this mark) Write the domain of the derivative function
Question 4 (42% got the full 3 marks) Standard related rates question- related rates is now only in specialist.
Question 5 (26% got both marks) “what is the probability that more than two of these customers order coffee?”
Question 6a (31% got that mark) Calculate \(\ Pr(A’ intersection B) ) when \(\ Pr(A intersection B) = 1/8))
Question 6b (23% got this mark) Calculate \(\ Pr(A’ intersection B) ) when A and B are mutually exclusive
Question 7 (28% bagged the 3 marks) Standard integration by recognition question
Question 8a (45% gained these 2 marks) Solve the trig equation for x
Question 8b (20% gained 2 marks) Calculate the smallest possible value of x for which g(x) is a max
Question 9a (44% got 2 marks) Find the equation of the normal to the graph where it crosses the y-axis.
Question 9b (27% awarded 3 marks) Find the exact area of the shaded region
Question 10 (33% awarded 3 marks) Find k when the area bounded between y=kx\(\ ½) and x=9 is 27.
Question 11a (49% awarded both marks) “Find the probability that the flight departs on time”
Question 11b (19% got 2 marks) Sneaky conditional probability question
Question 12 (20% got 4 marks) Find the coordinates of P and the minimum length when the length from O to P is a minimum.

2006:
Question 2b (45% got the mark) Find the domain of the inverse function
Question 3b (29% got the full 3 marks) Find the derivative when x= \(\ \pi/6)
Question 4b (14% got the 3 marks) Sketch the function and label the axes intercepts and their coordinates. Also label endpoints.
Question 5b (45% got the mark) Find the probability between two numbers on a normal distribution
Question 5c (27% had 2 marks) Conditional probability question, tucked neatly into a normal distribution problem
Question 6a (46% bagged 2 marks) Find the probability
Question 6b (39% awarded 2 marks) If “X” is greater or equal to a equals \(\ 5/8), find a
Question 7b (35% got a mark) Asks for range in regards to a- definitely out of the course as modulus isn’t in the 2016-2018 design
Question 8 (29% got 4 marks) Find the value of a in a normal
Question 9a (37% got this mark) Find the Area of the rectangle in terms of a
Question 9b (21% got all 3 marks) Find the max value of A and the value of a at that point.

Exam 2: Multiple-Choice
2015 MCQ
Question 3 (20%) A rule for a function question
Question 9 (37%) Finding the expected value of a function
Question 11 (24%) A transformations question
Question 16 (22%) A “which one is true?” question
Question 18 (48%) Another “which of the following is true” question
Question 21 (37%) A two graphs will no points of intersect for which values
Question 22 (35%) A which of the following represents this best

2014 MCQ
Question 13 (43%) What is the domain of the function?
Question 14 (45%) A conditional probability question
Question 15 (44%) “the max value of x is closest to”
Question 16 (46%) “The value of integral is…”
Question 20 (44%) Average value question
Question 21 (28%) Max area of a shape
Question 22 (37%) Probability of an event happening ratios

2013 MCQ
Question 7 (37%) A max value for pronumeral question
Question 11 (47%) A tangent to the graph question
Question 12 (35%) The value of the derivative at a point
Question 15 (25%) “Let h be a function with an average value of 2 over the interval [0, 6]. The graph could be”
Question 16 (21%) “Which one of the following definite integrals could be used to find the area of the shaded region?”
Question 17 (49%) Conditional probability problem
Question 18 (35%) “Which one is true for all values of x?”
Question 20 (25%) Matrices and transformations
Question 21 (29%) A cubic has no stationary points when…
Question 22 (47%) What is the value of the standard deviation (in a normal distribution)

2012 MCQ
Question 4 (45%) “The derivative of the composite function is”
Question 8 (49%) “The gradient of the graph is negative for”
Question 16 (34%) The value of a pronumeral for one solution question
Question 17 (43%) Linear equations question with matrix (matrix n/a anymore woo!), no solution problem
Question 18 (30%) A “which is false” question
Question 19 (45%) A possible rule question
Question 20 (19%) Calculate the probability question
Question 22 (32%) What does this function have?

2011 MCQ
Question 13 (45%) A normal distribution problem- find the mean
Question 14 (44%) Find the area of the shaded region
Question 16 (41%) A which is not true question
Question 17 (48%) Find the equation of the normal
Question 19 (43%) Approximation question – I personally haven’t see this since the 2009 exam 1.
Question 21 (15%) Independent events question
Question 22 (45%) What is the log expression equal to?

2010 MCQ:
Question 7 (47%) Simultaneous equations problem, infinitely many solutions
Question 12 (44%) Probability (binomial) problem
Question 18 (45%) A which statement is true question
Question 20 (25%) An integration by recognition question
Question 21 (43%) A probability question
Question 22 (29%) A find the rule question

2009 MCQ:
Question 1 (49%) Simultaneous equations problem, a unique solution
Question 9 (49%) Find the equation of the tangent
Question 17 (31%) Sample space question
Question 20 (34%) Number of solutions question
Question 21 (43%) Local maximum question
Question 22 (45%) Area bounded by question

2008 MCQ:
Question 4 (49%) Finding what a definite integral equals to
Question 6 (45%) Simultaneous equations question, infinitely many solutions
Question 9 (38%) Transformations matrices
Question 10 (45%) The range of a function
Question 12 (44%) Finding the value of a substitution
Question 15 (7%) Sample space question
Question 18 (36%) Transformations question

2007 MCQ:
Question 5 (36%) Simultaneous linear equations- looking for a unique solution
Question 6 (39%) Finding the range of a function
Question 17 (47%) A ‘find the function that satisfies’ question
Question 21 (27%) Finding x such that question
Question 22 (37%) Graph of combined functions question

2006 MCQ:
Question 10 (48%) A rate of increase question- pretty sure this got turfed out of the course
Question 13 (33%) Transformations with matrices
Question 17 (37%) A possible rule for a function question
Question 19 (35%) A simultaneous linear equations problem: looking for no solutions

Exam 2: Extended Response
2015 Extended Response:
Question 2a (33% got the 2 marks) Finding an angle between the tangent and a point (to the nearest degree)
Question 2b (44% got the 2 marks) Find the maximum downwards slope of the road
Question 2c (33% got all 3 marks) Find the coordinates of M (to 2 decimal places)
Question 2d (21% got all 3 marks) Find the value of the pronumeral and the lengths “MN and “PQ”
Question 2e (49% got all 3 marks) Find the x-coordinates (to 2 decimal places) of the points where the curve meets the parabola
Question 3aii (47% got both marks) Find the probability that an “orange has a diameter greater than 7cm”
Question 3dii (35% got both marks) Find the smallest sample so that Pr(X=x)>0.5
Question 4a (36% got this mark) “What is the value of a?”
Question 4c (41% got both marks) Find two transformations that map y=f(x) onto y=h(x)
Question 4di (12% got the 2 marks) Find the area enclosed by the graphs if “n” is even
Question 4dii (9% received 2 marks) Find the area enclosed by the graphs is “n” is odd
Question 5aiv (43% bagged both 2 marks) Find the average rate of change over an interval
Question 5ci (4% received both marks) Find a set of possible values for the pronumeral such that the minimum of the function occurs at t=0
5cii (4% received both marks) Find a set of possible values for the pronumeral such that the minimum of the function occurs at t=5
Question 5d (11% awarded both marks) Find the value of a pronumeral when the volume is at a local minimum.

2014 Extended Response
Question 1d (29% awarded 2 marks) Find the “fraction of time” when the “population” was less than n(10)
Question 2d (42% received the mark) Find the value of “h” when “S” is a minimum
Question 2f (22% bagged all 3 marks) find the derivative in terms of “h”
Question 2g (40% received a mark) “Find the rate of which the height of the cylinder will be decreasing” – This is related rates, pretty sure it’s out of the course
Question 2h (9% received both marks) “Find the year that the top of the statue will just be exposed”
Question 3cii (26% awarded 2 marks) “Find the values of t1 and t2
Question 3d (29% received 3 marks) Find the value of the pronumeral is the max “concentration” was 0.74mg/L at t=0.5hours
Question 4a (43% got this mark) “What is the minimum height”
Question 4b (47% got both marks) How many “basil plants” need to be moved?
Question 4d (25% snagged both marks) “Find the max height”
Question 4e (23% received both marks) “Find the minimum value”
Question 4fii (48% got 2 marks) Calculate the value of p
Question 4g (43% got 2 marks) Find the probability that the fifth pot made is smooth- uses transition matrices- out of the course
Question 5a (48% got 2 marks) “Express x 4 – 8x in the form x(x – a) ((x + b)2 + c )
Question 5b (37% got the mark) “Describe the translation”
Question 5ci (7% got a mark) Find the values of d such that the graph of y = f(x+d ) has one positive x-axis intercept
Question 5cii (19% received this mark) “Find the values of d such that the graph of y = f(x+d ) two positive x-axis intercepts.”
Question 5d (17% were awarded this mark) “Find the value of n for which the equation g x n ( ) = has one solution.”
Question 5ei (24% snagged 2 marks) Find the value of
Question 5eii (10% snagged that mark) Find “u” and “v” if “u+v=1”
Question 5fi (22% got that mark) “Find the equation of the tangent”
Question 5fii (11% received all 3 marks) “Find the equations of the tangents”

2013 Extended Response
Question 1d (45 got 2 marks) How long is the time great/equal to 26?
Question 1fi (10% got 2 marks) Find the values of the pronumerals
Question 1fii (12% got that mark) Find the coordinates of “P’ “
Question 2aii (39% got all 3 marks) “What is the probability that more than 15 complete “S” in less than 3 mins” – conditional probability!
Question 2ci (46% bagged 2 marks) Find the expected value
Question 2cii (42% got the 2 marks) How many are expected to finish “S”?
Question 3di (21% correctly got the 2 marks) Find the coordinate
Question 3dii (17% got 2 marks) Find the length
Question 3f (44% got 2 marks) Find the value of x when V is at a max
Question 3g (35% got 2 marks) If “m=10”, find the max speed of the “train”
Question 3h (25% got both marks) if the V max is 120, what is “m”?
Question 4aii (26% got all 3 marks) “Evaluate the area of the shaded region”
Question 4b (15% bagged all 3 marks) Find the positive x-coordinate of “Q” for which “OQ” is a min and find the min distance
Question 4c (6% snagged these 2 marks) Find the gradient of the tangent
Question 4di (3% gained 2 marks) Find the rule “A(k)” that gives the area of the shaded region
Question 4dii (3% gained 2 marks) Find the max area of the shaded region
Question 4diii (2% gained these 2 marks) Find the min area of the shaded region

2012 Extended Response
Question 1b (38% received the full 2 marks) Find the possible values of x if V(x) > 0
Question 1d (45% received both marks) Find the exact values of x and h for a max volume
Question 2a (43% got all 3 marks) Sketch the graph, label with asymptotes and coordinates of intercepts
Question 2c (10% received 2 marks) Find the equation of the tangent
Question 2d (14% received all 4 marks) Find the coordinates of the points on the graph so that the tangents intersect at (-1, 7/2)
Question 2e (8% snagged both marks) Find the values of a, c, d using the matrices transformations technique
Question 3aii (48% got 2 marks) A binomial question
Question 3bi (32% awarded 3 marks) A transition matrix question- transition matrices are out of our study design!
Question 3bii (30% given 2 marks) Yet another matrix question- is out of course.
Question 3c (13% of the cohort got 2 marks) Yet another probability question- sort of like combinatorics.
Question 3d (12% snagged all 4 marks) A normal/binomial distribution question
Question 4cii (17% received 3 marks) Related rates question- that’s out of the course
Question 4e (11% got 2 marks) Continuation of rates question
Question 4f (11% got that mark) continuation of rates question
Question 5aiii (36% received a mark) Find the total area
Question 5bi (34% awarded 2 marks) Find the x-coordinate
Question 5bii (11% received a mark) Find a set of values of “a” so that the graphs have two distinct points of interesection
Question 5c (11% got 2 marks) Find the value of a.

2011 Extended Response
Question 1a (20% received the full 3 marks) A related rates question
Question 1dii (29% received both marks) continuation of the related rates question
Question 2b (37% awarded 3 marks) Find the mean
Question 2cii (30% awarded 2 marks) Find the value of a so the probability=0.7
Question 2e (9% snagged all 3 marks) Sneaky conditional probability question
Question 3aii (47% got 1 mark) Explain why the derivative is always greater or equal to 5
Question 3bi (9% got 1 mark) What are the possible values of m if p has stationary points?
Question 3bii (20% got a mark) if p has an inverse, what are the values of m?
Question 3di (30% bagged 3 marks) Find c when g has 1 stationary point
Question 3dii (9% bagged 3 marks) when g and g-1 intersect, find the value of k
Question 4a (39% got this one in the bag and got 3 marks) Find the length
Question 4bi (36% got this correct and were given 3 marks) Find the derivative and then find the coordinates
Question 4bii (30% got 2 marks) Find the length of the pipeline from the desal plant to the village
Question 4c (11% got all 3 marks) Find the total time taken to get to the desal plant
Question 4dii (22% got 2 marks) Find the coordinates to get to the desal plant in min time
Question 4e (17% got 2 marks) Find the value of k to get to the desal plant in minimum time from (1,0)
Question 4f (1% got full marks) Find the value of k from camp to desal in minimum time.

2010 Extended Response
Question 1aii (44% got 3 marks) A sketch the inverse question
Question 1aiv (41% received both marks) A calculate the area bound between the two graphs question
Question 1bv (30% snagged both marks) Find the exact value of p on the tangent if (-1, 0) lies on it
Question 2a (49% got 2 marks) A matrix probability question- pretty sure this is out of the course
Question 2di (36% received all 3 marks) Another matrix probability question
Question 2dii (10% received all 4 marks) Find the expected value
Question 2e (15% got 3 marks) Calculate the minimum number of “statues”
Question 3b (42% got 2 marks) Find the equation for the total surface area
Question 3c (26% got 2 marks) Find the height of the “pyramid” in terms of x
Question 3d (22% got that mark) Find the volume of the pyramid
Question 3e (17% got all 4 marks) Find the derivative
Question 3f (12% awarded 2 marks) Find the possible values for x
Question 4b (38% snagged 3 marks) In terms of “a” and “b”, what is a stationary point of f?
Question 4c (47% gained that mark) For what value of “a” does f have no stationary points?
Question 4d (14% received 2 marks) Find “a” in terms of “b” if f has one stationary point
Question 4e (37% received 1 mark) What is the max number of stationary points for f?
Question 4f (3% received 3 marks) Find the value of p is there is a stationary point at (1,1) and (p,p)

2009 Extended Response
Question 1eii (13% got 2 marks) Find the derivative
Question 1eiii (17% got 3 marks) Sketch the graph of the derivative
Question 2aii (33% got 2 marks) Show that pronumerals equal values
Question 2bii (41% got this mark) Find the length of the tunnel
Question 2c (35% received a mark) Find k in terms of w
Question 2d (30% awarded 2 marks) Find w
Question 2e (23% snagged 2 marks) Find the exact distance
Question 3ci (42% got a mark) Standard conditional probability question
Question 3cii (4% received both marks) Binomial question
Question 3d (22% got 3 marks) Find the standard deviation
Question 3g (23% got 2 marks) Find the smallest sample size so that p is less than 0.45
Question 4ai (32% received 1 marks) Show that “h=2r”
Question 4aii (40% got a mark) Find an expression for the volume
Question 4b (40% got 2 marks) Find the derivative and the rate that it is increasing (the related rates are gone from the study design)
Question 4cii (47% awarded the mark) Find the height when it is increasing- related rates, see above
Question 4dii (25% got 1 mark) Find an expression for the height of the acid in terms of t (more related rates)
Question 4ei (34% snagged the mark) More related rates
Question 4eii (16% awarded 2 marks) The end of the related rates question!!

2008 Extended Response
Question 1bii (46% got all 3 marks) Standard probability question
Question 1biii (17% received 3 marks) A matrix probability question- out of course
Question 1biv (46% awarded a mark) Another matrix probability question
Question 1ci (43% got 2 marks) Sketch the probability density function
Question 2aii (37% snagged 2 marks) A gradient question
Question 2ci (27% got 2 marks) Express the area of the region bounded by…
Question 2cii (26% got 2 marks) What value of “a” does the area equal 7?
Question 2ciii (11% received this mark) Explain why “a<e”
Question 2d (9% of the cohort got these 2 marks) Find the values of “m” and “n” such that the two integrals equal the numbers
Question 3e (33% got that mark) “Show that he gets to the camp in time to get to the antidote”
Question 3f (43% received 2 marks) What are the coordinates of “A” and “C”?
Question 3g (22% got 2 marks) Find the equation of the curve
Question 3h (16% awarded a mark) “How many days does he need to take a capsule”?
Question 4aiii (39% got all 3 marks) Sketch the equation of the normal
Question 4b (30% awarded 2 marks) Find the values of x
Question 4c (37% awarded 2 marks) Find the exact value of a
Question 4dii (40% snagged both marks) Solve the equation
Question 4e (26% got both marks) Sketch the graph

2007 Extended Response
Question 1c (33% received 2 marks) Find the value of r so that the surface area is a minimum
Question 1d (3% awarded 2 marks) Find the max possible surface area of the “can”
Question 2a (44% got a mark) “What is the value of m”
Question 2b (37% got 3 marks) Sketch the graph
Question 2c (48% received 2 marks) What is the minimum
Question 2d (41% got 1 mark) Find the time
Question 2e (35% bagged 2 marks) What length of time
Question 2fii (49% bagged a mark) Find the length of time
Question 2g (14% got 3 marks) “Show that it is possible for him to recover the diamond successfully and state how much time he has to spare”
Question 3a (49% snagged 2 marks) Find the value of x where “g(x)” is a max
Question 3bii (48% got 2 marks) Find the total area of the shaded regions
Question 3c (33% got 2 marks) Find the maximum value of “|f(x)-g(x)|”
Question 3di (13% got 2 marks) State two transformations
Question 3dii (13% received 2 marks) Find a cubic polynomial
Question 4a (26% got 2 marks) Explain why “a=1 and b=-1”
Question 4cii (15% got 2 marks) Sketch and label the inverse function
Question 4di (26% got 2 marks) a show that question that involves substitution
Question 4dii (29% awarded that mark) another show that question that involves substitution
Question 5a (22% got the full 2 marks) Sketch the graph
Question 5c (43% got both marks) Standard conditional probability question
Question 5d (37% got the full 2 marks) Binomial probability question
Question 5e (25% got both marks) A standard probability question
Question 5fi (15% got 2 marks) Find the max value
Question 5fii (9% received 2 marks) Find when the max occurs

2006 Extended Response
Question 1c (17% got 2 marks) Find the exact value of “m”- a tangent problem
Question 1d (15% got 2 marks) Find the general solution for the trig equation, when the function equals 1.
Question 2aii (36% received 2 marks) A probability question where a tree diagram would be useful
Question 2b (46% received a mark) A transition matrix question
Question 2e (35% awarded 2 marks) A binomial question
Question 2f (33% got 2 marks) Find the median
Question 3e (13% scored all 4 marks) Find the values of “k” for the equation given
Question 4bi (41% scored 2 marks) Find “q” in terms of “p”
Question 4bii (34% scored a mark) Find “f(1)” in terms of “p”
Question 4biii (27% awarded a mark) Find the value of “a” for which “f’(a)=0”
Question 4biv (26% bagged 2 marks) If “a=17/3” find p and q
Question 4e (31% snagged 3 marks) Find the values “a” and “b”
Question 4f (28% got all 4 marks) Find the shaded area

Enjoy!

(Math mods- feel free to place in the right section. )
2017-2019: Bachelor of Pharmaceutical Science (Formulation Science)
2020: Bachelor of Pharmaceutical Science (Honours) Read my uni journey here!

#### keerthanasl

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##### Re: Difficult Questions from past VCAA papers!
« Reply #1 on: September 15, 2021, 11:27:04 am »
0
This is INCREDIBLE. Thank you!