Following a trend with the difficult questions lists (as seen in the bio discussion), I've compiled a list of the most difficult questions for the exam 1s from 2006 to 2015!
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*Some of the questions are no longer relevant to the study design, but still included for fun!
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 \(Pr A \cup B \) “
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= \(\sqrt[3]{5}\)
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 \(\sqrt[3]{8.06}\)
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 \(Pr(A’ \cap B \)) when \(Pr(A \cap B) = 1/8\)
Question 6b (23% got this mark) Calculate \(Pr(A’ \cap B)\) 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.
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Topic: Mathematical Methods (CAS) Exam Discussion (Read 7284 times)