ATARMAxxing · Specialist Mathematics
SACE Specialist Mathematics Practice Exams with Worked Solutions
20 full-length papers · worked solutions for every question
The 20 practice exams inside the SACE Specialist Mathematics Mastery Pack, each set out like the real paper with a separate worked-solution guide. Open any paper to see what it covers.
- Induction proof of a divisibility result
- Fifth roots of a complex number in exact rcis form
- Rational function with an oblique asymptote
- Closest point on a line in space to a given point
- Logistic differential equation reaching a limiting population
- Induction proof for a closed form of a finite sum
- Repeated multiplication by a complex number as dilation and rotation
- Inverse of a restricted cubic sketched on supplied axes
- Plane through three points using a cross product
- Volume of revolution about the y-axis
- Induction proof of an nth derivative pattern
- Circle and ray loci intersecting in the Argand plane
- Domain of a square-root composition
- Row reduction showing three planes meet along a line
- Arc length of a trigonometric parametric path
- De Moivre's theorem proved by induction
- Real quadratic factor built from a given complex zero
- Absolute-value composition sketched from a given cubic
- Angle between a line and a plane
- Newton's law of cooling as a separable equation
- Induction proof for a product formula
- Roots of unity summing to zero and a regular polygon
- Reciprocal of a quadratic and its vertical asymptotes
- Distance between two parallel planes
- Repeated integration by parts for an exponential integrand
- Induction proof for a sum of cubes
- Triangle inequality applied to a sum of complex numbers
- Derivative of an inverse found by implicit differentiation
- Shortest distance between two skew lines
- Free-flight model with a clearance condition
- Induction proof for a telescoping sum
- Solving z^n = c and plotting the solution set
- Rational function with a removable discontinuity
- Vector proof that the medians of a triangle are concurrent
- Slope field with a solution curve drawn from a given point
- Induction proof of divisibility by 7
- Division in polar form and the resulting rotation
- Reciprocal of a trigonometric function sketched over one period
- Cartesian equation of a plane from a normal and a point
- Partial fractions with distinct linear factors
- Induction step written correctly in P(k) and P(k+1) notation
- Region bounded by a modulus inequality and an argument inequality
- Composite of an absolute value with a rational function
- Point of intersection of a line and a plane
- Area between two curves requiring a substitution
- Induction proof for a sum of odd squares
- Remainder theorem used to find two unknown coefficients
- Horizontal line test and a restricted inverse
- System of three planes with no solution
- Implicit differentiation of a conic-like relation
- Induction applied to a trigonometric power identity
- Cube roots of a complex number and the triangle they form
- Sketching y = 1/f(x) from a supplied graph of f
- Area of a triangle in space by cross product
- Related rates for a cone being filled
- Induction proof for a sum of a quadratic series
- Conjugate root theorem applied to a real quartic
- Rational function with a cubic numerator
- Foot of the normal from a point to a plane
- Volume of revolution with a trigonometric integrand
- Induction proof for a geometric-type sum
- Perpendicular bisector written as an equation in z
- Domain of a composition involving a reciprocal
- Row operations giving infinitely many solutions
- Arc length of a pendulum-style parametric path
- Induction proof of a derivative pattern for a trigonometric function
- Multiplication by i as an anticlockwise right-angle rotation
- Inverse of a restricted sine function with its exact domain
- Angle between two planes
- Separable differential equation in a mixing context
- Induction proof of divisibility by 9
- Sixth roots of unity and the area of the regular hexagon
- Sketching y = f(|x|) and y = |f(x)| from one graph
- Vector proof that the angle in a semicircle is a right angle
- Inverse-trigonometric integral after completing the square
- Induction proof for a sum involving alternating signs
- Product of two complex numbers written in polar form
- Rational function crossing its horizontal asymptote
- Plane parallel to two given direction vectors
- Logistic model solved with a supplied partial-fraction identity
- Induction proof for the nth derivative of a linear-exponential product
- Quartic solved from one supplied complex zero
- Composition defined only on a restricted interval
- Distance from a point to a plane by the standard formula
- Area between a curve and its inverse
- Induction proof for a sum of consecutive integers squared
- Family of circles written in terms of z and n
- Inverse of a rational function and its asymptotes
- Three planes meeting in a single point
- Velocity, speed and tangent for a parametric path
- Induction proof of divisibility by 6
- Fifth roots of a complex number and a quadrilateral area
- Reciprocal of an absolute-value function
- Plane through three points with an area comparison
- Implicit differentiation giving the equation of a tangent
- Induction proof for a sum involving powers of 2
- Ray from a point meeting a circle in the Argand plane
- Rational function with a repeated linear factor in the denominator
- Parameter deciding the solution type of a linear system
- Trigonometric parameterisation of an ellipse with speed and acceleration
Included in the SACE Specialist Mathematics Mastery Pack
20 full-length practice exams with worked solutions, 20 revision notes, 64 practice questions and 200 flashcards.
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