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March 29, 2024, 11:47:51 pm

Author Topic: Difficult Questions from past VCAA papers- Spesh  (Read 5012 times)  Share 

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sweetiepi

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Difficult Questions from past VCAA papers- Spesh
« on: October 30, 2016, 11:29:47 am »
+13
I did the methods difficult questions thread , and I've decided to give spesh some lovin' too, so I made yet another huge list, from all the exams from 2006-2015. ;D

Exam 1: Short Answer

2015
Question 4a (40% got 3 marks) Finding the solutions to a complex number equation
Question 4b (44% got 1 mark) Finding the solutions to a complex number equation
Question 5 (37% got 3 marks) Volume/Solids of revolution question
Question 7a (34% got 3 marks) Solving a trig equation/double angle formula question
Question 7b (11% got 2 marks) Solving a trig equation/identities/double angle question
Question 8a (47% got 2 marks) Integration by substitution
Question 8d (23% got 2 marks) Finding the area enclosed by a graph
Question 9c (16% got 2 marks) Finding the angle between two tangents

2014
Question 1b (42% got 2 marks) Find the acute angle that a makes with the x axis
Question 2b (42% got 2 marks) Sketch the path of the particle
Question 4 (48% got 3 marks) Find the normal and it’s gradient at a point
Question 5b (48% got 3 marks) Integration by substitution
Question 5c (45% got 1 mark) Integration by substitution
Question 6b (37% got 4 marks) Find the volume in a solid of revolution
Question 7a (4% got 1 mark) Find the range of an \(arctan(x)\) function
Question 7c (26% got 3 marks) Evaluate the area enclosed in the graph between two lines
Question 8ai (44% got 2 marks) Resolve the forces on the body question
Question 8b (40% got 1 mark)  Demonstrate that \(tan(\Theta)\) is greater than \(\sec(\Theta)\)
Question 8c (25% got 3 marks) Find the maximum value of \(\Theta\)

2013
Question 2 (47% got 4 marks) Partial fractions integration question
Question 4b (46% got 2 marks) Sketch the graph of an \(\arccos(x)\) function
Question 4c (47% got 2 marks) Find the gradient of the tangent at a point
Question 5b (41% got 3 marks) Differential equations question
Question 6 (40% got 4 marks) Implicit differentiation question
Question 7b (22% got 2 marks) Sketch the path of the particle
Question 7c (29% got 2 marks) Find the speed of the particle
Question 8 (23% got 4 marks) Complex solutions question
Question 9 (29% got 4 marks) Volume/Solids of revolution

2012
Question 1 (46% got 2 marks) Finding an antiderivative/There was a need to split the fraction into 2 parts
Question 2 (11% got 3 marks) Finding all the solutions to a trig equation
Question 3a (44% got 3 marks) Finding the roots of a complex equation
Question 3b (33% got 1 mark) Plotting roots onto an argand diagram
Question 4b (44% got 1 mark) Finding the max value of T that can be applied
Question 4c (40% got 1 mark) Finding the value of T required to move the object
Question 5 (44% got 3 marks) Standard double derivative question
Question 6 (45% got 3 marks) Implicit differentiation/find the tangent to the curve
Question 7 (41% got 3 marks) Find the area bound/integration by substitution question
Question 8 (28% got 3 marks) Find the acceleration question
Question 9b (38% got 2 marks) A Pythagoras’s theorem question/finding the speed of the particle
Question 9c (35% got 2 marks) find the derivative/chain rule question
Question 9d (13% got 2 marks) Find the angle question
Question 10aii (33% got 1 mark) A find the domain question
Question 10b (13% got 3 marks) compound angle question

2011
Question 1 (39% got 3 marks) Find the antiderivative/partial fractions question
Question 2 (49% got 3 marks) Differential equation question
Question 3b (49% got 3 marks) Sketch the relation
Question 4 (23% got 3 marks) Find the argument of z/complex number question
Question 6 (47% got 2 marks) Antiderivative question/integration by substitution
Question 7b (41% got 3 marks) Find the value of “m” so that the system remains in equilibrium
Question 8 (27% got 3 marks) Find the coordinates of intersection between two graphs
Question 9ci and ii (41% got 2 marks) Find the value of one vector minus another and then find a value of “m” for linear dependence
Question 11 (46% got 3 marks) Solids of revolution/find the volume question

2010
Question 2b (23% got 4 marks) Solving a differential equation
Question 3c (30% got 3 marks) Find the area of a triangle
Question 5 (35% got 3 marks) find the double derivative and substitute a value
Question 6 (34% got 3 marks) Integration by substitution question
Question 7 (33% got 3 marks) Differential equation question
Question 8b (37% got 3 marks) Finding the speed of a particle at a certain time
Question 8c (20% got 1 mark) finding \(\tan(\theta)\) at a point of time
Question 9a (44% got 3 marks) Sketch the graph of the equation
Question 9b (33% got 3 marks) gradient of the equation/implicit differentiation question
Question 10 (23% got 4 marks) Find the area bounded

2009
Question 3 (38% got 3 marks) Resolve the vector into its two components- parallel and perpendicular to another vector
Question 4 (32% got 4 marks) Double angle question/complex number question
Question 5c (22% got 2 marks) Find the gradient of the curve
Question 7 (23% got 4 marks) Find the velocity from the acceleration question
Question 8b (31% got 3 marks) Find the area bound by a graph and two lines
Question 9a (34% got 3 marks) Solve the differential equations
Question 9b (44% got 2 marks) Apply Euler’s method question
Question 10a (34% got 2 marks) Find the domain and range of “f”
Question 10b (23% got 3 marks) Find the derivative of “f”

2008
Question 1 (19% got 5 marks) Sketch the graph question
Question 2 (48% got 2 marks) Find the normal to graph/implicit differentation
Question 3 (16% got 3 marks) Find “m/n” so that the vectors are linearly dependent
Question 4 (23% got 3 marks) Double angle formula question
Question 5a (48% got 2 marks) Find the acceleration of the particle
Question 5b (34% got 3 marks) Find the position equation
Question 6 (47% got 3 marks) Solve the differential equation
Question 7 (32% got 3 marks) Lami’s theorem question
Question 8b (27% got 2 marks) Find the coordinates of “D” so that the shape is a parallelogram
Question 8c (36% got 1 mark) Show that the shape is a rectangle
Question 9a (28% got 1 mark) Find the bounded area
Question 9b (37% got 3 marks) Find the volume of the solid of revolution
Question 10a (41% got 1 mark) Complex number question
Question 10c (3% got 4 marks) Roots of a complex polynomial question

2007
Question 2b (42% got 2 marks) Find other solutions for the complex polynomial
Question 3 (43% got 3 marks) Find the tangent to the curve/implicit differentiation
Question 4 (35% got 4 marks) Find the volume/Solids of revolution
Question 6c (22% got 2 marks) Sketch the path of the particle
Question 7a (36% got 2 marks) Euler’s method question
Question 7b (33% got 2 marks) Solve the differential equation
Question 8a (29% got 2 marks) Slope fields question
Question 8b (46% got 3 marks) Solve the differential equation
Question 8c (13% got 1 mark) Sketch the curve
Question 9 (18% got 3 marks) Find the acceleration
Question 10 (20% got 3 marks) Double angle formula question

2006
Question 2 (45% got 4 marks) Solve the differential equation
Question 3a (39% got 3 marks) Sketch the graph
Question 3b (22% got 4 marks) Find the bounded area
Question 4b (42% got 2 marks) Calculate the tension
Question 5a (22% got 4 marks) Double/compound angle question
Question 5b (28% got 2 marks) tan-1 question
Question 6c (49% got 2 marks) Volume/solids of revolution question
Question 7b (31% got 2 marks) Sketch the graph
Question 8 (31% got 4 marks) Find the antiderivative/integration by substitution
Question 9b (16% got 3 marks) Solve the complex quadratic equation

Exam 2: Multiple Choice

2015 MCQ
Question 4 (43%) Equation of a hyperbola
Question 6 (43%) Finding a relation that has a graph that passes through a point in the complex plane
Question 9 (47%) A complex number/Argand diagram question
Question 13 (47%) Slope field question
Question 15 (49%) Direction of vector in relation to another
Question 16 (23%) Equilibrium system question
Question 17 (48%) The cosine of an angle question
Question 22 (42%) Find the time taken for the ball to hit max height.

2014 MCQ
Question 18 (45%) Force diagram question
Question 19 (49%) Force/velocity question
Question 22 (49%) Velocity graph to determine distance question

2013 MCQ
Question 3 (47%) Find the values of 3 pronumerals in an equation
Question 4 (43%) Values of 2 pronumerals if two graphs intersect 3 times
Question 22 (38%) Equation of motion

2012 MCQ
Question 6 (37%) Complex number question/argand diagram
Question 12 (48%) Volume of solid of revolution
Question 19 (44%) Statics of a particle

2011 MCQ
Question 1 (34%) The number of asymptotes a graph has
Question 8 (49%) Roots of a complex equation
Question 16 (25%) Gradient of a curve/implicit differentiation

2010 MCQ
Question 10 (2 options were accepted) (12% for the first option and 28% for the second option) Argand diagram/complex circles
Question 11 (40%) Slope field question
Question 22 (40%) velocity/force question

2009 MCQ
Question 2 (43%) Intersection of two graphs question
Question 8 (47%) Complex numbers question
Question 10 (23%) Integration by substitution question
Question 13 (38%) Differential equation question
Question 17 (30%) Vector diagram question
Question 19 (48%) Statics/Motion question

2008 MCQ
Question 2 (42%) equation of a circle question
Question 4 (26%) De Moivre’s question
Question 9 (40%) Slope field question
Question 12 (45%) The value of a definite integral
Question 15 (36%)  Magnitude of force question
Question 17 (43%) Collinear points question
Question 22 (45%) velocity from acceleration question

2007 MCQ
Question 1 (49%) Product of gradients of asymptotes question
Question 5 (48%) The equation of this graph question
Question 9 (38%) Roots on an Argand diagram
Question 12 (27%) Kinematics question
Question 14 (37%) Differential equations question
Question 15 (37%) Vector perpendicular question
Question 20 (43%) Force diagram question
Question 22 (45%) Acceleration question

2006 MCQ
Question 5 (39%) Roots to a complex equation
Question 10 (47%) Differential equations
Question 11 (40%) Slope field question
Question 12 (35%) Acceleration of a particle
Question 16 (49%) A unit vector that is perpendicular



Exam 2: Extended Response

2015 Extended Response
Question 1d (36% got 2 marks) Sketch the graph and its inverse
Question 2aiv (44% got 3 marks) Find the points of intersection of the line and the circle/complex number question
Question 2bi (21% got 3 marks) Find the roots of “z1” and “z2” in the complex equation.
Question 2bii (23% got 1 mark) Find the argument.
Question 3e (20% got 3 marks) Find an antiderivative and then find the area
Question 4aii (33% got 2 marks) Find the angle of elevation
Question 4b (43% got 1 mark) Find the time that the position of the object is above where it started
Question 4d (39% got 2 marks) Find the speed of the object
Question 5di (30% got 2 marks) Solve the differential equation
Question 5div (12% got 3 marks) Write and solve the definite integral

2014 Extended Response
Question 2c (9% got 3 marks) Finding the value of “k” where two points form a line to a curve/complex number
Question 3a (41% got 5 marks) Find the vector resolutes, parallel and perpendicular to another vector.
Question 3biii (37% got 2 marks) Find the values of “\(\alpha\)” and “\(\beta\)”
Question 4c (32% got 2 marks) Using a definite integral in combination to related rates
Question 4d (12% got 5 marks) Related rates question
Question 5bi (46% got 2 marks) Label and show the forces on the two objects
Question 5biii (36% got 3 marks) Find the time that one object collides with another

2013 Extended Response
Question 1b (41% got 3 marks) Find the values of “t” at a certain gradient
Question 2a (20% got 3 marks) Sketch two complex graphs on the argand diagram
Question 2b (15% got 3 marks) Find the intersections between the two graphs
Question 2f (41% got 2 marks) Find the area of the shaded region
Question 3a (30% got 2 marks) Verifying by substitution/differential equation
Question 3di (9% got 2 marks) Find the derivative question
Question 3dii (38% got 2 marks) Find the coordinates at a point of inflection
Question 3e (39% got 2 marks) Sketch the function
Question 4b (40% got 3 marks) Resolve a vector into two vector components, one that is parallel to and another that is perpendicular to another vector
Question 4d (44% got 2 marks) Find the angle between two vectors
Question 4eiii (10% got 1 mark) Simplify the expression of vectors
Question 5a (38% got 3 marks) Find the derivative of “r(t)” and the min and max speeds
Question 5b (15% got 2 marks) Find the times when a=0
Question 5c (29% got 2 marks) Find the time it takes for the object to hit the water
Question 5d (39% got 1 mark) Find the horizontal distance the object travels prior to hitting the water
Question 5e (23% got 3 marks) Find the distance when the coefficient of friction equals a value
Question 5f (34% got 1 mark) Find the minimum coefficient of friction to prevent the object from sliding back down

2012 Extended Response
Question 1b (42% got 4 marks) Sketch the curve
Question 1d (47% got 3 marks) Find the gradient of the curve at a point/implicit differentiation
Question 2d (44% got 2 marks) Find the area of the shaded region of the circle/complex number/argand diagram question
Question 2ei (25% got 3 marks) Arg/trig question
Question 2eii (36% got 1 mark) Find the value of n for z1
Question 3ei (34% got 2 marks) What is the expression of distance travelled by the object during motion
Question 3eii (30% got 1 mark) Find the total distance travelled by the object
Question 4a (49% got 1 mark) Find the height of an object to the origin.
Question 4b (34% got 3 marks) Find the acceleration of the object
Question 4c (34% got 2 marks) Find the speed of the object
Question 4d (46% got 2 marks) Find the Cartesian equation of the path
Question 4e (29% got 3 marks) Find the times the object is x distance away from the origin
Question 5b (49% got 2 marks) Constant acceleration question
Question 5c (23% got 2 marks) another constant acceleration question
Question 5dii (49% got 2 marks) Find the time it takes for the object to come to rest
Question 5diii (37% got 3 marks) Find the distance it takes for the object to come to rest

2011 Extended Response
Question 1di and dii (25% got 3 marks) Find the equation of the straight line/complex equation
Question 1ei and eii (32% got 3 marks) Shade the area on the graph and find its area
Question 2a (41% got 2 marks) Integration question
Question 2e (30% got 3 marks) Find the distance
Question 3bi and 3bii (41% got 3 marks) Write and evaluate the volume of the object/solids of revolution
Question 4e (41% got 3 marks) Find the acceleration
Question 4f (25% got 4 marks) Find the masses if the equilibrium remains
Question 5a (29% got 1 mark) What is the equation of the concentration
Question 5b (45% got 2 marks) What is the differential equation
Question 5ci and cii (11% got 4 marks) Find “x’(t)” and verify by substitution that “x(t)” satisfies the initial condition and the differential equation
Question 5d (46% got 3 marks) Sketch the graph
Question 5e (11% got 2 marks) Inflow/outflow question

2010 Extended Response
Question 1b (44% got 3 marks) Prove that this quadrilateral is a parallelogram.
Question 1dii (49% got 3 marks) Use a vector method to prove that one line is perpendicular to another line
Question 2d (35% got 2 marks) Find the coefficient of friction.
Question 2e (36% got 3 marks) Find the velocity of an object after x time
Question 3a (5% got 3 marks) Verify that a value satisfies the differential equation and the initial condition
Question 3di, ii, iii (28% got 3 marks) Sketch the graphs on the axes for each situation
Question 3eii (17% got 1 mark) “Use the definition of k to interpret your answer to part i. in the context of the population model”
Question 4a (4% got 3 marks) Sketch the function
Question 4bi (47% got 2 marks) Write the definite integral for a solid of revolution
Question 4bii (43% got 1 mark) Find the value of the integral
Question 4c (37% got 3 marks) Simple calculus question
Question 4d (30% got 2 marks) specify the domain for the hybrid function
Question 4e (19% got 2 marks) Sketch the hybrid function
Question 5b (45% got 3 marks) De Moivre’s Theorem question
Question 5c (18% got 3 marks) Polar form question
Question 5d (13% got 3 marks) Argument question

2009 Extended response
Question 1d (49% got a mark) Calculate the average speed
Question 1f (18% got 3 marks) Finding the time in a motion question
Question 2c (40% got 1 mark) Argument/complex question
Question 2d (44% got 3 marks) Finding the Cartesian points of intersection between a complex equation and a normal equation
Question 2f (25% got 2 marks) Finding the area between the points of intersection
Question 3c (40% got 1 mark) Find the time in a i/j r(t) equation problem
Question 3f (29% got 2 marks) Find the magnitude of acceleration
Question 3gi (28% got 2 marks) Find a definite integral
Question 4c (29% got 2 marks) Using the quadratic formula question
Question 4dii (45% got 1 mark) Finding the volume
Question 4e (18% got 3 marks) Related rates question
Question 5c (47% got 1 mark) Finding the terminal velocity
Question 5d (49% got 1 mark) Find the time it takes for an object reaches x velocity
Question 5e (41% got 2 marks) Find the distance from the velocity equation question
Question 5f (30% got 2 marks) Find the depth of the object at x velocity
Question 5g (12% got 3 marks) Find the distance from x to 0

2008 Extended Response
Question 1bi (37% got 1 mark) Find the polynomial equation for the points of inflection
Question 1bii (46% got 2 marks) Find two coordinates of points of inflection
Question 1c (43% got 2 marks) Sketch the graph
Question 1dii (33% got 2 marks) Integration by substitution
Question 1diii (26% got 2 marks) General antiderivative question
Question 2d (30% got 2 marks) Find the time needed for an object to reach x speed
Question 2eii (40% got 2 marks) Resolving forces question
Question 2eiii (28% got 2 marks) Find the value of tan(x)
Question 2eiv (27% got 1 mark) Find the tension force
Question 3aii (32% got 1 mark) Find the Cartesian equation
Question 3b (19% got 2 marks) Sketch the path
Question 3c (10% got 2 marks) Find the time that the object takes to complete a full circuit
Question 3d (31% got 2 marks) Find the speed
Question 3ei (19% got 1 mark) Write a definite integral
Question 3eii (8% got 1 mark) Find the distance
Question 4cii (39% got 1 mark) “How many foxes are on the island at this time?”
Question 4dii (39% got 2 marks) Implicit differentiation question
Question 4e (9% got 3 marks) Determine the min and max values
Question 5b (47% got 2 marks) Plot roots onto an argand diagram
Question 5c (33% got 3 marks) Find the points of intersection/complex equations
Question 5d (38% got 3 marks) Sketch the curves on the argand diagram
Question 5e (37% got 2 marks) Shade the region
Question 5f (6% got 2 marks) Find the area of the shaded region

2007 Extended Response
Question 1d (48% got 2 marks) Find the roots of the complex polynomial
Question 1e (48% got 2 marks) Find the Cartesian equation
Question 1f (28% got 1 mark) Find “z-bar” satisfies a relation
Question 1g (28% got 2 marks) Shade the region on the Argand diagram
Question 3c (42% got 3 marks) Find the acceleration
Question 3e (14% got 4 marks) Find the angle
Question 4c (11% got 2 marks) Find the angle
Question 4d (20% got 2 marks) Find the time the object reaches a certain distance
Question 4e (18% got 2 marks) Find the distance
Question 5b (31% got 1 mark) “Explain why v will never equal 16”
Question 5d (38% got 3 marks) Find the distance
Question 5e (15% got 3 marks) Write an equation to find the time
Question 5f (8% got 1 mark) Find the time

2006 Extended Response
Question 1e (22% got 3 marks) Find an expression for the rate of change
Question 1f (28% got 1 mark) Find the exact depth for which its surface is a maximum
Question 2c (16% got 2 marks) Find the cosine of and angle, using a vector method
Question 2d (20% got 3 marks) Find another angle and hence show that both angles are supplementary
Question 3bii (34% got 2 marks) Write down a pair of equations to resolve the two unknowns
Question 3biii (42% got 1 mark) Find one unknown
Question 3ci (38% got 1 mark) Write down the equation of motion
Question 3cii (18% got 3 marks) Write a definite integral for the distance
Question 3ciii (20% got 1 mark) Find the distance
Question 4ci (21% got 1 mark) Find the double derivative
Question 4cii (8% got 2 marks) Find the y-coordinate of any points of inflection
Question 4d (28% got 1 mark) Sketch the path on the slope field
Question 4e (16% got 2 marks) Euler’s method question
Question 5aii (15% got 1 mark) Write the complex equation for a straight line that runs through two points
Question 5b (29% got 3 marks) Double angle formula question
Question 5c (37% got 2 marks) Find the exact value of another trig function
Question 5d (49% got 2 marks) Evaluate a complex number to a power
Question 5e (12% got 2 marks) Find which values of n that the complex number is real

Good luck to all! :)
2017-2019: Bachelor of Pharmaceutical Science (Formulation Science)
2020: Bachelor of Pharmaceutical Science (Honours) Read my uni journey here!

heids

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Re: Difficult Questions from past VCAA papers- Spesh
« Reply #1 on: October 30, 2016, 06:37:09 pm »
+2
Awesome work, insanipi!  Much appreciated, though ofc we know that *you* don't actually find any of these difficult ;)
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MightyBeh

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Re: Difficult Questions from past VCAA papers- Spesh
« Reply #2 on: October 30, 2016, 07:10:13 pm »
+1
You're actually crazy, where did you get the tie to do this? Great stuff tho :-*
VCE: Further Maths | Methods | Specialist | Literature | Software Development | Classics
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sweetiepi

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Re: Difficult Questions from past VCAA papers- Spesh
« Reply #3 on: October 30, 2016, 07:24:54 pm »
+3
Awesome work, insanipi!  Much appreciated, though ofc we know that *you* don't actually find any of these difficult ;)
Oh totes ;)

You're actually crazy, where did you get the tie to do this? Great stuff tho :-*
Hence the *insani* part of u/name :P
I literally sit down and isolate myself to write stuff like this down. :P (Plus I made the list so I could concentrate on what is usually the problem areas :P )


It's not like I'm not using it to study too! Plus I was thinking of doing the same with Physics + Chem, maybe...
2017-2019: Bachelor of Pharmaceutical Science (Formulation Science)
2020: Bachelor of Pharmaceutical Science (Honours) Read my uni journey here!