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]
Barmy BIDMAS: A misleading way of stating the answer to a simple calculation. [Topic(s): BIDMAS Factorial]
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]
Difference Cipher: Find the mathematical word from the cipher [Topic(s): code, cipher, number]
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]
Double or Half?: At ten percent change per day is doubling achieved faster than halving? [Topic(s): Percentages]
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 left-handed members being randomly selected is given. [Topic(s): Probability]
Key Eleven: Prove that a four digit number constructed in a certain way will be a multiple of eleven. [Topic(s): Number, Proof, Algebra]
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 Perimeter: Find the perimeter of a folded sheet of A4 paper as described in this short video. [Topic(s): Perimeter, Surds, Ratio]
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]
Quad Midpoints: What shape is created when the midpoints of the sides of a quadrilateral are joined together? [Topic(s): Geometry, Proof, Vectors]
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 ex
Simplify: Simplify an algebraic fraction [Topic(s): Indices]
Speed Circles: Find the diameters of the circles in the corners of the square. [Topic(s): Mensuration Circles]
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]
Square in Rectangle: Find the area of a square drawn under the diagonal of a rectangle [Topic(s): Algebra, area, similar triangles]
Tan 22.5: Find an exact value for tan 22.50 without using a calculator. [Topic(s): Trigonometry]
Test Scores: Explore the misconception that when adding fractions you add both the numerators and the denominators [Topic(s): Fractions]
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]
Weather Reports: Which five different integers multiply together to give 12? [Topic(s): Prime Factors, Negative numbers]
What Question?: Write down all the possible questions that could have been asked if this was the diagram provided in a mathematics textbook. [Topic(s): Trigonometry]
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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Exam Style Questions
Still looking for an Advanced Starter? Try an Exam Style Question. There are hundreds to choose from.
Yes past paper questions can make ideal Lesson Starters. Have them projected onto your whiteboard and your students can start working as soon as they sit down. The (I)GCSE Higher/Extended and the IB questions have fully worked solutions that you can reveal line by line when you go through the questions with the class. All this saves you valuable time at the beginning of your lesson.
Here are some questions I like as Starters to get you going:
Two circles just fit side by side in a larger circle. What fraction of the larger circle do they cover? more...
One is added to the product of two consecutive positive even numbers. Show that the result is a square number. more...
The diagrams below show a sequence of patterns made from red and yellow tiles. more...
This Venn diagram shows the relationship between the sets of numbers. more...
Twitter and the media were buzzing with comments about a particular question about Hanna's sweets. more...
Calculate the area of the front face of the dart board. more...
A restaurant offers 6 starters, 14 main courses and 5 different desserts. more...
Find the length of the elastic band that fits around three crayons. more...
The graph shows the height of water in a container over a period time. more...
This draft emoji design includes a circle and a kite. more...
Minerva's Revenge is the longest rollercoaster in the Funville Theme Park. more...
Windthrup bought a car for £9500 which depreciated by 6% in the first year. more...
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