**Mathematics**

“This test assesses year-level appropriate mathematical knowledge (quoted by the SEU however over the years it has been known to be unreasonably harsh) Numbers, measurement, space and data are assessed.”Mathematics was the subtest where most students tended to struggle on. It comprised of 60 questions with a time limit of 30 minutes. You don't need to answer all questions without blindly guessing to attain a superior for this exam. A raw score of 35/60 may be high enough to get a superior. The questions in the mathematics subtest can be solved systematically, whereas numerical assessed your ability to reason with numbers in a logical approach. If you have your year 10 maths under your belt you should do well on this exam. The content list below may seem like a long list, but if you dedicate enough time into studying for it, it's definitely manageable. Also note sometimes it's easier substituting the options when answering the questions, or solving by trial and error. And especially for mathematics, don't spend too much time on one question, and when blindly guessing consider look-alike options (whether they are look-alike because they share similar factors, properties etc..) Usually one of the look-alike options will be correct. Remember, don't be overwhelmed by the questions presented in the maths exam as well, if you struggle chances are there are a lot of other students struggling as well.

**Content Descriptors**Number and algebra: - Financial Maths

• Simple interest

• Compound interest

• Loan repayment

• Contribution of money

• Deprecation

- Scientific notation and set builder notation

• Notations such as R, Z, N, Q, P (R=real numbers, Z=integers, N=natural numbers, Q=rational numbers, P=irrational numbers.)

• Union and intersection (∪ / ∩) (or / and)

• Elements (∈)

• Scientific notation (know how to express each number in sci note./standard form etc.)

- Logarithms/Exponentials

• Basic logarithm such as log3 27=3

• Conversion between bases (eg. decimal to binary etc.)

- Parabolas

• Vertex form

• General form

• Discriminator

• Sketching and identifying important features (x/y intercept, vertex/turning point)

• Finding the turning point from just equation (-b/2a, f(-b/2a))

- Quadratics

• Expand (apply algebraic identities)

• Factorise (know your shortcuts)

• Solve for pronumeral

• Complete the square

- Polynomials

• Factor and remainder theorem (questions like which is not a factor of <insert algebraic expression>)

• Function notation (brief understanding how to sketch polynomials, parabola etc.)

• Find the degree of a polynomial

• Factorise, expand and solve

- Linear and non linear relationships

• Simultaneous equations (when two equations intersect) - (substitution and elimination)

• Midpoints

• Equations of perpendicular and parallel lines

• Distance formula (distance between two coordinates)

• Inverse and direct proportion and ratios/rates

• Inequalities (compound, quadratic, absolute value, linear)

• Know how to graph basic quadratics, linear equations and inequalities

• Know how to solve basic cubic equations (can easily solve by just subbing the options)

- Surds and roots

• Multiply and divide surds

• Add and subtract surds

• Order surds (largest to smallest etc..)

• Simplify surds

• Convert surds/roots into exponents (eg.2=21/2)

• Rationalise the denominator

- Algebraic Identities (

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• Exponential rules (a^m * a^n=a^(m+n), aman=a(m-n), (a^m)^n=a(mn), etc..) & fractional indices

• Difference of squares a^2-b^2=(a+b)(a-b)

• Difference of cubes a^3-b^3=(a-b)(a^2+ab+b^2)

• Memorise expansions of expressions such as (a+b)^2, (a-b)^2, etc..

Measurement and geometry: - Triangle Similarities and Congruence

• Triangle proportionality theorem

• Midsegment theorem

• Angle bisector theorem

- Circle Theorems

• Angle and chord properties of circles

• Cyclic Quadrilaterals

• Inscribed triangles

• Tangents

• General theorems;

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• Solve right-angled problems using Pythagoras' Theorem and Trigonometry

• Angle of elevation and depression

• SOH CAH TOA (Sine/sin, Cosine/cos, Tangent/tan)

• Exact values Sin(90°)=1, Cos(60°)=0.5 etc..

- Units of measurement

• Convert metric units of speed, capacity, volume and area.

• Solve problems involving volume, surface area, area, perimeter.

• Solve distance and time problems

• Basic kinematics (find time when two objects meet opp/same direction)

- Geometric Properties

• Sum of interior and exterior angles

• Number of diagonals in a polygon

• Angles in transversal and parallel lines (co interior, corresponding, alternate)

• Quadrilateral Properties

Statistics and probability: - Sets and data

• Interquartile range

• Mean

• Median

• Mode

- Collection of data

• Venn diagram

• Contingency table

• Bar graphs

• Line graphs

• Box plots

• Stem and leaf plots

- Probability

• Conditional Probability

• Card, dice and coin probability

• Tree diagrams

• Experiments with and without replacement

• Permutations and combinations

• Selections involving identical items