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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Weekly Challenges

### The Challenges

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### Parabolic Patterns

### Curved Square

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Age 14 to 18

Challenge Level

The NRICH weekly challenges are aimed at Post-16 students to provide an interesting, shorter challenge to try out each week which will fit around any usual course of study. Each challenge is designed to be simple to get into and to cover an important and intriguing area of mathematics.

How many will you solve?

- Weekly Challenge 0: Weekly Challenges are here!

- Weekly Challenge 1: Inner Inequality

- Weekly Challenge 2: Quad Solve

- Weekly Challenge 3: Geometric Trig

- Weekly Challenge 4: Top Marks

- Weekly Challenge 5: Trigger

- Weekly Challenge 6: AP train

- Weekly Challenge 7: Gradient Match

- Weekly Challenge 8: Sixinit

- Weekly Challenge 9: Quick Sum

- Weekly Challenge 10: Solve me!

- Weekly Challenge 11: Unit Interval

- Weekly Challenge 12: Venn Diagram Fun

- Weekly Challenge 13: Comet Catastrophe

- Weekly Challenge 14: Mad Robot

- Weekly Challenge 15: Indexing Problems

- Weekly Challenge 16: Archimedes Numerical Roots

- Weekly Challenge 17: Power Stack

- Weekly Challenge 18: The root of the problem

- Weekly Challenge 19: Prime APs

- Weekly Challenge 20: The Olympic LOGO

- Weekly Challenge 21: Trig Identity

- Weekly Challenge 22: Combinations of Two

- Weekly Challenge 23: Stand up Arcs

- Weekly Challenge 24: Suspicious Integrator

- Weekly Challenge 25: Trig Trig Trig

- Weekly Challenge 26: Max Throw

- Weekly Challenge 27: Cubic roots

- Weekly Challenge 28: The right volume

- Weekly Challenge 29: Integral Equation

- Weekly Challenge 30: Sign of the Times

- Weekly Challenge 31: Common Divisor

- Weekly Challenge 32: Medicine Half life

- Weekly Challenge 33: Crazy Cannons

- Weekly Challenge 34: Googol

- Weekly Challenge 35: Clickety Click and All the Sixes

- Weekly Challenge 36: Seriesly

- Weekly Challenge 37: Magic Bag

- Weekly Challenge 38: Numbered Graph

- Weekly Challenge 39: Symmetrically So

- Weekly Challenge 40: Normal intersection

- Weekly Challenge 41: Happy Birthday

- Weekly Challenge 42: What's my equation

- Weekly Challenge 43: A close match

- Weekly Challenge 44: Prime Counter

- Weekly Challenge 45: Integral arranging

- Weekly Challenge 46: The Jabber-notty

- Weekly Challenge 47: Weird Universes

- Weekly Challenge 48: Quorum-sensing

- Weekly Challenge 49: Get in line

- Weekly Challenge 50: How Old?

We hope that our challenges will stimulate lots of mathematical discussion and activity.

The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.

Can you find the area of the central part of this shape? Can you do it in more than one way?