Other tags that relate to Cocked Hat
Graphing software and graphical calculators. Mathematical reasoning & proof. Expanding and factorising quadratics. Turning points. Graph sketching. Maths Supporting SET. Symmetry. Biology. Functions and their inverses. Quadratic equations.There are 37 results
Broad Topics > Algebraic expressions, equations and formulae > Quadratic equations
Cocked Hat
Age 16 to 18
Challenge Level
Sketch the graphs for this implicitly defined family of functions.
Polar Flower
Age 16 to 18
Challenge Level
This polar equation is a quadratic. Plot the graph given by each factor to draw the flower.
Erratic Quadratic
Age 16 to 18
Challenge Level
Can you find a quadratic equation which passes close to these points?
Implicitly
Age 16 to 18
Challenge Level
Can you find the maximum value of the curve defined by this expression?
Mega Quadratic Equations
Age 16 to 18
Challenge Level
What do you get when you raise a quadratic to the power of a quadratic?
Always Two
Age 14 to 18
Challenge Level
Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.
Bird-brained
Age 16 to 18
Challenge Level
How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.
Quad Solve
Age 16 to 18 Short
Challenge Level
Can you solve this problem involving powers and quadratics?
Symmetrically So
Age 16 to 18
Challenge Level
Exploit the symmetry and turn this quartic into a quadratic.
Halving the Triangle
Age 16 to 18
Challenge Level
Draw any triangle PQR. Find points A, B and C, one on each side of the triangle, such that the area of triangle ABC is a given fraction of the area of triangle PQR.
Resistance
Age 16 to 18
Challenge Level
Find the equation from which to calculate the resistance of an infinite network of resistances.
Two Cubes
Age 14 to 16
Challenge Level
Two cubes, each with integral side lengths, have a combined volume equal to the total of the lengths of their edges. How big are the cubes? [If you find a result by 'trial and error' you'll need to. . . .
Golden Eggs
Age 16 to 18
Challenge Level
Find a connection between the shape of a special ellipse and an infinite string of nested square roots.
Golden Construction
Age 16 to 18
Challenge Level
Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.
Xtra
Age 14 to 18
Challenge Level
Find the sides of an equilateral triangle ABC where a trapezium BCPQ is drawn with BP=CQ=2 , PQ=1 and AP+AQ=sqrt7 . Note: there are 2 possible interpretations.
Golden Mathematics
Age 16 to 18
A voyage of discovery through a sequence of challenges exploring properties of the Golden Ratio and Fibonacci numbers.
Plus or Minus
Age 16 to 18
Challenge Level
Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.
Interactive Number Patterns
Age 14 to 16
Challenge Level
How good are you at finding the formula for a number pattern ?
Partly Circles
Age 14 to 16
Challenge Level
What is the same and what is different about these circle questions? What connections can you make?
Proof Sorter - Quadratic Equation
Age 14 to 18
Challenge Level
This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.
Golden Fibs
Age 16 to 18
Challenge Level
When is a Fibonacci sequence also a geometric sequence? When the ratio of successive terms is the golden ratio!
Pareq Calc
Age 14 to 16
Challenge Level
Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel. . . .
How Old Am I?
Age 14 to 16
Challenge Level
In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
Square Mean
Age 14 to 16
Challenge Level
Is the mean of the squares of two numbers greater than, or less than, the square of their means?
Power Quady
Age 16 to 18
Challenge Level
Find all real solutions of the equation (x^2-7x+11)^(x^2-11x+30) = 1.
Good Approximations
Age 16 to 18
Challenge Level
Solve quadratic equations and use continued fractions to find rational approximations to irrational numbers.
Kissing
Age 16 to 18
Challenge Level
Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?
Pentakite
Age 14 to 18
Challenge Level
ABCDE is a regular pentagon of side length one unit. BC produced meets ED produced at F. Show that triangle CDF is congruent to triangle EDB. Find the length of BE.
How Many Balls?
Age 16 to 18
Challenge Level
A bag contains red and blue balls. You are told the probabilities of drawing certain combinations of balls. Find how many red and how many blue balls there are in the bag.
Golden Ratio
Age 16 to 18
Challenge Level
Solve an equation involving the Golden Ratio phi where the unknown occurs as a power of phi.
Continued Fractions II
Age 16 to 18
In this article we show that every whole number can be written as a continued fraction of the form k/(1+k/(1+k/...)).
Pent
Age 14 to 18
Challenge Level
The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.
Target Six
Age 16 to 18
Challenge Level
Show that x = 1 is a solution of the equation x^(3/2) - 8x^(-3/2) = 7 and find all other solutions.
A Third of the Area
Age 14 to 16 Short
Challenge Level
The area of the small square is $\frac13$ of the area of the large square. What is $\frac xy$?
Golden Thoughts
Age 14 to 16
Challenge Level
Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.
NRICH is part of the family of activities in the Millennium Mathematics Project.