mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

23 December

I draw the parabola \(y=x^2\) and mark points on the parabola at \(x=17\) and \(x=-6\). I then draw a straight line connecting these two points.
At which value of \(y\) does this line intercept the \(y\)-axis?

Show answer

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 2023

Advent calendar 2022

Advent calendar 2021

Advent calendar 2020


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2024