Advanced Starters:Algebraic Product: Finding the value of the ex Angle Thinking: Find the range of possible angles, x, for which tan x > cos x > sin x [Topic(s): Trigonometry Inequalities] Average Cycling Speed: Work out the average speed of two journeys. The obvious answer is not the correct answer. [Topic(s): Average speed] Back To The Factory: Find all the numbers below 1000 which have exactly 20 factors [Topic(s): Factors, Possibilities, Prime, Number] Best Dice: Which of the unusual dice would you choose to give you the best chance of winning the prize? [Topic(s): Probability] Biased Coin: Use a biased coin to obtain a fair result [Topic(s): Probability] Cheryl's Birthday: Use a process of elimination to work out the correct date from the clues given. [Topic(s): Logic] Coordinate Distance: Find k given that(2,k) is 13 units away from (10,9) [Topic(s): Coordinate Geometry, Quadratics, Coordinates] Cuboid: Find the dimensions of a cuboid matching the description given [Topic(s): Measures] Divisible by 11: Can you prove that a three digit number whose first and third digits add up to the value of the second digit must be divisible by eleven? [Topic(s): Algebra, Place Value] Fence Optimisation: Find the length of a rectangle enclosing the largest possible area. [Topic(s): Differentiation Calculus Optimisation] Fermi Problem: The classic Fermi problem using standard estimation techniques [Topic(s): Fermi, Estimate, Standard Form] Find The Radius: Find the radius of the circle from the small amount of information provided. [Topic(s): Geometry Trigonometry Algebra] Four Fraction Division: Explain why the answer to a series of fraction divisions is a whole number. [Topic(s): Fractions] Grandmother: How far would grandma have travelled after a suitably large number of days given her walking regime? [Topic(s): Sequences and series] Hands Together: The hands of a clock are together at midnight. At what time are they next together? [Topic(s): Angles, Speed] How Many Left Handers?: Work out the number of members if the probability of lefthanded members being randomly selected is given. [Topic(s): Probability] Maximum Product: Two numbers add up to 10. What's the largest possible product they could have? [Topic(s): Optimise Differentiate Calculus] Multiple of sum of digits: What number is six times the sum of its digits? [Topic(s): Number] Nine Digit Numbers: How many different nine digit numbers are their that contain each of the digits from one to nine? [Topic(s): Number] Other Child's Gender: What is the probability that the other child is also a boy? [Topic(s): Probability] Paper Ratio: Calculate the ratio of the sides of an A4 sheet of paper without any measuring. [Topic(s): Ratio] Parallel Graphs: Determine from their equations which of the straight line graphs are parallel and perpendicular. [Topic(s): Graphs, Coordinate Geometry] Penny Bags: Can you place 63 pennies in bags in such a way that you can give away any amount of money (from 1p to 63p) by giving a selection of these prepacked bags? [Topic(s): Puzzle, Binary] Piece of String: Find where a piece of string should be cut to form a circle and a square of equal areas. [Topic(s): Equations, Problem Solving] Pizza Slice: A problem which can be solved by considereing the areas of a triangle and a sector of a circle. [Topic(s): Mensuration, Area, Trigonometry] Restrained Flea: How many different places could the flea find itself after 8 footlong jumps either north, south, east or west? [Topic(s): Loci, Combinations] Reverse Connection: Find a general rule for the difference between a two digit number and that same number with the digits reversed. [Topic(s): Algebra, Place Value] Road Connections: Design roads to connect four houses that are on the corners of a square, side of length one mile, to minimise the total length of the roads. [Topic(s): Calculus Trigonometry] Same Series Sum: Find an arithmetic series and a geometric series that have the same sum of the first five terms. [Topic(s): Sequences and series] Same Three Digits: Find ex Simplify: Simplify an algebraic fraction [Topic(s): Indices] Sphere Hole: Find the volume of the remaining part of a sphere after a 10cm cylindrical hole has been drilled through it. [Topic(s): Volume, Mensuration] Three Right Triangles: Calculate the lengths of the unlabelled sides of these rightangled triangles. [Topic(s): Similarity] TriJunction: A real life situation that can be analysed with the use of a tree diagram. [Topic(s): Tree diagrams, probability] Two real numbers: The sum of the reciprocals of two real numbers is 1, and the sum of their cubes is 4. What are they? [Topic(s): Simultaneous Equations] Unfinished Game: Share the prize in a fair ratio according to the probability of each player willing. [Topic(s): Ratio, Probability] Unlucky Seven Eleven: Follow the instructions to multiply a chosen number then explain the result you get. [Topic(s): Number, Place Value] Vowel Code: How many ways can you create a code for the vowels by assigning to each vowel a different vowel? [Topic(s): Codes, Permutations] X Divided by 2Y: Why do different calculators not agree on the order of operations? [Topic(s): BIDMAS Substitution Calculator] Zero Even: Prove that zero is an even number. [Topic(s): Proof]

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