Original post by tangotangopapa2What are some resources to practice maths section for the PAT other than past papers?The questions asked in PAT have quite a different nature compared to other and usually questions are of following properties/categories:1) Often simple questions involving mental arithmetic is asked e.g. 2023^2 - 2022^2, (3.12)^5 correct to one decimal place.2) Coordinate geometry of line includes, finding slope of line passing through two points or finding equation of the line passing through one point and having slope this (you need to find slope, e.g. perpendicular to another line). Coordinate geometry of circle is often asked but some of the questions that might put us off is like this: Find equation of line/lines tangent to the circle/curve and passing through this point (usually outside point).3) Simple questions testing properties of logarithms.4) Trigonometric equations; finding solution in a given interval. (Usually Pythagorean Identity has to be used and then quadratic equation has to be solved. Obviously, some extraneous results should be omitted). Some knowledge of inverse trigonometric function. e.g evaluate cos(tan^-1(sin(cot^-1x)))5) Arithmetic and geometric sequence and series, including finding sum of infinite geometric series.6) Factoring polynomials (degree 3 or 4) and finding all roots.7) Simple application of binomial expansion formula (Knowledge of Pascal's triangle is enough).8) Calculus: Rate of change e.g. If Rate of change of volume of water in cylinder is this, then what is the rate of change of height. Finding maxima/minima. Some harder questions like: Maximise area of rectangle of given perimeter. Simple knowledge of concavity, increasing/decreasing functions etc. is asked.9) Calculus: Finding area by integration. Finding definite integrals. Usually you either have to split expression into partial fractions or use algebraic substitution.10) Solving rational inequalities. Simple cautions to ensure no sign flip if you multiply equation by certain terms is often required.edit: I forgot this. 11) Probability theory: Simple probability questions. Sometimes one may have to use conditional probability formula but never binomial/Possion/Nomal distribution formula. One type of tricky question is: 3 special dice (each can give score of 1-8) are rolled. The score is calculated as Ad1 + Bd2 + Cd3 + D where A,B,C and D are constants and d1-3 are individual score of the die. Find the constants so that : - The score ranges from 1-512 and each score has equal probability.12) Roots of quadratic equation and their properties is assumed.13) Simple algebraic manipulation eg. If a= x^2 + y ^2 and b = 2xy express x and y in terms of a and b.14) Geometry. 95% of the time the question involves circle inscribed by polynomials ( most often equilateral triangle or square). You usually have to find the ratio of areas of two separate regions in the figure.15) The hardest of all. Curve sketching. Questions range from trivial to extremely challenging. You might have to use properties of transformation of graph. Sketch graphs of completely different/complicated functions. Sketch graphs of y = f(x) +/- g(x), y = f(x)g(x) or f(x)/g(x) where you know the graph of y = f(x) and y=g(x) separately. Sometimes you might have to sketch inequalities like. -2 < y/x < 4 or 0< y/x^2 < 6pi.MAT questions/ Senior Maths Challenge questions/ BMO questions don't have above mentioned properties. They deal with hard number theory, combinatorics, different type of algebra problems and provide very little help in brushing up above type of problems. So, what might help me to practice these type of problems? Thanks in advance.