This powerpoint is on Unit 1 Topic 1 of the 2025 Specialist Maths Syllabus for QLD. It covers the topic of Combinatorics and focusses the following dot points: •Use the inclusion-exclusion principle formulas to determine the number of elements in the union of two and the union of three sets. •|A∪B|=|A|+|B|−|A∩B| •|A∪B∪C|=|A|+|B|+|C|−|A∩B|−|A∩C|−|B∩C|+|A∩B∩C| •Use the multiplication principle. •Use the addition principle. •Define and use permutations. •Use factorial notation. •Use the notation nPr to represent the number of ways of selecting r objects from n distinct objects where order is important. •nPr=“n!” /"(n-r)!" =n×(n−1)×(n−2)×…×(n−r+1) •Solve problems that involve permutations. •Solve problems that involve permutations with restrictions including repeated objects, specific objects grouped together and selection from multiple groups. •Define and use combinations. •Use the notation (nr) and nCr to represent the number of ways of selecting r objects from n distinct objects where order is not important. •nCr=(nr)=n!r!(n−r)! •Solve problems that involve combinations. •Solve problems that involve combinations with restrictions including specific objects grouped together and selection from multiple groups. •Model and solve problems that involve permutations and combinations including probability problems, with and without technology.

This powerpoint is on Unit 1 Topic 3 of the 2025 Specialist Maths Syllabus for QLD. It includes animation to represent that vectors and a lot of diagrams with worked examples. It covers the topic of Representation of vectors in two dimensions and covers the following dot points: •Examine examples of vectors including displacement, velocity and force. •Understand the difference between a scalar and a vector including distance and displacement, speed and velocity, and magnitude of force and force. •Understand and use vector notation: (AB) ⃗, ▁c, d, and unit vector notation n ̂. •Use ordered pair notation (x,y) and column vector notation (x¦y) to represent a position vector in two dimensions. •Define and use the magnitude and direction of a vector. •Calculate and use a unit vector, n ̂, in the plane. •Understand and use vector equality. •Represent and use a scalar multiple of a vector. •Use the triangle rule to represent the resultant vector from the sum and difference of two vectors. •Represent a vector in the plane using a combination of the sum, difference and scalar multiple of other vectors. •Define and use unit vectors and the perpendicular unit vectors i ̂ and j ̂ . •Express a vector in Cartesian (component) form using the unit vectors i ̂ and j ̂ . •Understand and express a vector in the plane in polar form using the notation (r,θ). •Calculate and use a unit vector, n ̂, in the plane, n ̂=n/|n| •Convert between Cartesian form and polar form, with and without technology. •Understand and use the Cartesian form and polar form of a vector.

This is a powerpoint introducing students to the notation and definitions required for proofs. It covers the following dot points from the QLD 2025 Specialist Maths Unit 1 Syllabus: •Define and use set notation of number systems, including integers (Z), positive integers (Z+), negative integers (Z−), rational numbers (Q), irrational numbers (Q’), and real numbers ®. •Express rational numbers as terminating or eventually recurring decimals and vice versa. •Use the quantifiers ‘for all’ (∀) and ‘there exists’ (∃). •Use the set notation symbol ‘is an element of’ (∈). •Use implication, converse, equivalence, negation, contrapositive. •Use the symbols for implication ( ⇒ ), equivalence ( ⟺ ), and equality ( = ). •Use proof by contradiction. •Prove irrationality by contradiction. •Use examples and counterexamples. •Prove results involving integers, e.g. proving that the product of two consecutive odd numbers is an odd number and 5n2+3n+6 ∀n∈Z is an even number.

This powerpoint is on Unit 2 Topic 5: Matrices of the Specialist Maths 2025 Syllabus for QLD. It covers the topic of Matrix arithmetic and algebra and focusses on the following dot points: •Understand the matrix definition and notation. •Define and use addition and subtraction of matrices, scalar multiplication, matrix multiplication, multiplicative identity and multiplicative inverse. •Use matrix algebra properties, including •A+B=B+A (commutative law for addition) •A+ 0 =A (additive identity) •A+(−A)= 0 (additive inverse) •AI=A=IA (multiplicative identity) •A(B+C)=AB+AC (left distributive law) •(B+C)A=BA+CA (right distributive law) •Recognise that matrix multiplication in general is not commutative. •Define and use addition and subtraction of matrices, scalar multiplication, matrix multiplication, multiplicative identity and multiplicative inverse. •Use matrix algebra properties, including •AA−1=I=A−1A (multiplicative inverse) •Calculate the determinant and multiplicative inverse of 2×2 matrices, with and without technology. •If A=[abcd] then det(A)=ad−bc •A−1=[abcd)]^(-1)=1/(det⁡(A)) [d,-b,-c,a)] , det(A)≠0 •Use matrix algebra to solve matrix equations that involve matrices of up to dimension 2×2, including those of the form AX=B, XA=B and AX+BX=C, with and without technology •Model and solve problems that involve matrices of up to dimension 2×2, including the solution of systems of linear equations, with and without technology.

Specialist Maths Unit 1 Exam (Topics 2–5) with Complete Teacher Toolkit This comprehensive exam resource is designed for Unit 1 of Specialist Mathematics, covering Topics 2–5 inclusively. It includes: ✔ Full Exam Paper – professionally formatted and ready to use ✔ Detailed Solutions – for accurate and efficient marking ✔ Marking Guide – ensures consistency and saves time ✔ Markbook with RAG Rating – track student performance at a glance ✔ Teacher Analysis Tools – identify strengths and areas for improvement Perfect for assessing understanding and supporting data-driven teaching!

This powerpoint covers Unit 1 Topic 4: Algebra of vectors in two dimensions in the 2025 QLD Specialist Maths syllabus. It covers the following dot points: •Examine and use addition and subtraction of vectors in Cartesian form. •Define and use multiplication by a scalar of a vector in Cartesian form. •Examine properties of parallel and perpendicular vectors and determine if two vectors are parallel •Determine a vector between two points. •Define and use a vector representing a section of a line segment, including the midpoint of a line segment. •Resolve vectors into (i ) ̂and j ̂ components. •Define and use the scalar (dot) product. •a⋅b=|a||b|cos(θ) •(a_1¦a_2 )∙(b_1¦b_2 )=a_1 b_1+a_2 b_2 •Apply the scalar product to vectors expressed in Cartesian form. •Examine properties of parallel and perpendicular vectors and determine if two vectors are parallel or perpendicular. •Define and use scalar and vector projections of vectors. •scalar projection of a on b : |a|cos(θ)=a⋅ b ̂ •vector projection of a on b : |a|cos(θ)b ̂=(a⋅ b)b ̂=((a⋅b)/(b⋅b) “)b” • Model and solve problems that involve displacement, force, velocity and relative velocity using the above concepts. • Model and solve problems that involve motion of a body in equilibrium situations, including vector applications related to smooth inclined planes (excluding situations with pulleys and connected bodies).

Give your students the confidence to succeed in their PSMT with this complete, curriculum-aligned assessment package designed for the QCAA Senior Mathematics Specialist Syllabus. This resource takes the stress out of planning, scaffolding, and marking by providing everything teachers and students need for a high-quality Problem-Solving and Modelling task. What’s included? Full PSMT Assessment Task Complete task ready to stick your school logo on and hand out. This task is based on Unit 1 Topic 1: Combinatorics and focuses on designing a game. Teacher guide This outlines what students could include in their PSMT helping you to support any questions on possible assumptions, observations, modelling requirements, verifying, evaluating, and strengths and limitation. This can help you tailor your teaching prior to the assessment task. Student Sample Structure scaffold This helps the students to structure their PSMT but also includes some tips on what maths to include and how to run their simulation. ISMG Interpretation guide This document is staff and student facing. It helps you to explain to student what is expected of them in each section and in each mark boundary. Perfect for self assessment for students before handing in their drafts.