mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

6 December

\(p(x)\) is a quadratic with real coefficients. For all real numbers \(x\),
$$x^2+4x+14\leq p(x)\leq 2x^2+8x+18$$
\(p(2)=34\). What is \(p(6)\)?

Between quadratics

Source: Luciano Rila (@DrTrapezio)
\(p(x)\) is a quadratic polynomial with real coefficients. For all real numbers \(x\),
$$x^2-2x+2\leq p(x)\leq 2x^2-4x+3$$
\(p(11)=181\). Find \(p(16)\).

Show answer

Parabola

On a graph of \(y=x^2\), two lines are drawn at \(x=a\) and \(x=-b\) (for \(a,b>0\). The points where these lines intersect the parabola are connected.
What is the y-coordinate of the point where this line intersects the y-axis?

Show answer & extension

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2020

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018


List of all puzzles

Tags

dice balancing sum to infinity taxicab geometry speed clocks chalkdust crossnumber chess digital clocks sport logic number coordinates palindromes rectangles factors spheres differentiation planes algebra scales menace hexagons people maths median books dominos quadrilaterals cube numbers multiplication elections prime numbers area regular shapes polygons games complex numbers volume partitions percentages shapes cryptic clues bases probability odd numbers shape cards coins calculus colouring factorials symmetry unit fractions dodecagons crossnumbers indices arrows perfect numbers means wordplay square numbers graphs cryptic crossnumbers quadratics doubling folding tube maps division angles routes surds numbers multiples grids ave combinatorics crossnumber irreducible numbers addition 3d shapes floors geometry chocolate integration advent fractions squares crosswords time dates tiling star numbers christmas triangles digits square roots circles range 2d shapes integers mean gerrymandering proportion sums probabilty products sequences functions the only crossnumber pascal's triangle lines ellipses averages remainders parabolas trigonometry triangle numbers perimeter rugby money

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2021