NSW · NESAQ&A
Maths Extension 1Q&A by dot point
A short Q&A bank for every NSW Maths Extension 1 syllabus dot point. Each question and answer is drawn directly from our worked dot-point page, so you can scan key concepts before opening the long-form answer.
Calculus (ME-C1, C2, C3)
- Model unrestricted growth and decay with and solve the resulting separable differential equation14Q&A pairs
- Apply integration by substitution to evaluate definite and indefinite integrals, including reverse chain rule cases14Q&A pairs
- Integrate functions whose antiderivative involves , or14Q&A pairs
- Differentiate inverse trigonometric functions and integrate functions that involve them13Q&A pairs
- Model projectile motion in two dimensions using parametric equations and find range, maximum height, time of flight and trajectory equation15Q&A pairs
- Solve related-rates problems by linking two changing quantities via an equation and differentiating with respect to time13Q&A pairs
- Solve separable first-order differential equations of the form by separating variables and integrating both sides14Q&A pairs
- Calculate volumes of revolution about the x-axis and y-axis using the disc method13Q&A pairs
Combinatorics (ME-A1)
- State and use the binomial theorem, identify general and specific terms, and relate it to Pascal's triangle15Q&A pairs
- Use the combination formula to count unordered selections, including with restrictions and complementary counting15Q&A pairs
- Use the multiplication principle and the permutation formula to count ordered arrangements, including restrictions and repeated elements15Q&A pairs
- State and apply the pigeonhole principle in counting and existence problems14Q&A pairs
Functions (ME-F1, ME-F2)
- Sketch curves given parametrically, eliminate the parameter to obtain Cartesian equations, and use parametric form for circles, parabolas and lines12Q&A pairs
- Apply the division algorithm for polynomials and use the remainder and factor theorems to identify and verify factors and roots11Q&A pairs
- Sketch polynomial functions using leading-term behaviour, intercepts and the multiplicity of each root12Q&A pairs
- Solve polynomial and rational inequalities by factoring and analysing the sign of each factor across critical values14Q&A pairs
- Use the relationships between roots and coefficients (Vieta's formulas) for polynomials of degree two, three and four11Q&A pairs
Proof (ME-P1)
- Prove divisibility statements involving an integer parameter using mathematical induction13Q&A pairs
- Apply mathematical induction to prove general statements about a recursive sequence, a property of a formula, or a recursive procedure12Q&A pairs
- Prove inequalities involving an integer parameter using mathematical induction11Q&A pairs
- Prove identities for sums of series using the principle of mathematical induction15Q&A pairs
Statistical Analysis (ME-S1)
- Define a Bernoulli random variable, compute its mean and variance, and recognise scenarios that fit the model11Q&A pairs
- Define the binomial distribution , state its probability mass function, and find its mean and variance14Q&A pairs
- Compute exact probabilities for the binomial distribution including , , , and use complementary counting15Q&A pairs
- Use the normal approximation to approximate binomial probabilities for large13Q&A pairs
Trigonometric Functions (ME-T1, T2, T3)
- Express in the form or and use this to solve equations and find extreme values10Q&A pairs
- Write general solutions to trigonometric equations using the period and the symmetries of , and14Q&A pairs
- Define and sketch the inverse trigonometric functions , and , including their domains and ranges12Q&A pairs
- Use the product-to-sum and sum-to-product identities to simplify trigonometric expressions and integrals11Q&A pairs
- Use the sum and difference identities for sine, cosine and tangent to expand or simplify trigonometric expressions11Q&A pairs
- Use the t-formula (Weierstrass substitution) to express , and as rational functions of12Q&A pairs
Vectors (ME-V1)
- Use vector methods to prove geometric properties, including parallelism, perpendicularity, midpoint and ratio division15Q&A pairs
- Write parametric vector equations of lines and convert between vector and Cartesian forms14Q&A pairs
- Compute the scalar product of two vectors in component or geometric form and use it to find the angle between vectors and test orthogonality11Q&A pairs
- Perform vector arithmetic with vectors in the plane, including component and column-vector notation, and find the magnitude and unit vector14Q&A pairs
- Compute the scalar and vector projection of one vector onto another and interpret it geometrically13Q&A pairs