Transum Maths Software

Advanced Maths Lesson Starters

Here is a list of advanced Maths lesson starters suitable for students studying for A Level, IB, Advanced placement etc.

In addition, many of the 'Starter of the Day' activities are easily developed for the more able student.

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Advanced Starters:

Algebraic Product: Finding the value of the expression is easier than you think!  [Topic(s): Algebra]


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]


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]


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 left-handed 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 foot-long 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 expressions which contain indices and evaluate to numbers containing the same digits.  [Topic(s): Puzzle, Indices, Problem Solving]


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 right-angled triangles.  [Topic(s): Similarity]


Tri-Junction: 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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