--- title: "What a 16-year-old learns" description: "30 topics are written for age 16, across 2 subjects." canonical: https://lightmysky.com/learn/age/16 source: https://lightmysky.com/learn/age/16.md retrieved: 2026-09-02 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # What a 16-year-old learns 30 topics are written for age 16, across 2 subjects. Topics are placed by what they need, not by school year, so this is a starting point rather than a syllabus. Page: https://lightmysky.com/learn/age/16 ## Science - [Group 1, Group 7 and Group 0: Trends You Can Predict](https://lightmysky.com/learn/science/group-1-group-7-and-group-0-trends-you-can-predict-mt_cy1OrVAjIo): Use outer-shell electrons to predict how alkali metals, halogens and noble gases behave, including why group 1 gets more reactive down the group while group 7 gets less. - [Ionic Bonding: Electron Transfer and Charged Lattices](https://lightmysky.com/learn/science/ionic-bonding-electron-transfer-and-charged-lattices-mt_sf24C4YLtN): Metal atoms hand their outer electrons to non-metal atoms, and the ions that result pull on each other in a giant lattice. Work out ionic charges and formulas from the group numbers. - [Covalent Bonding: Shared Pairs and Simple Molecules](https://lightmysky.com/learn/science/covalent-bonding-shared-pairs-and-simple-molecules-mt_fn5Dq6qUjP): Two non-metal atoms fill their outer shells by sharing electron pairs. The shared bond is strong, but the pull between separate molecules is weak, which sets the properties of simple molecular substances. - [Giant Covalent Structures: Diamond, Graphite and Graphene](https://lightmysky.com/learn/science/giant-covalent-structures-diamond-graphite-and-graphene-mt_YTEj9srwPG): Some covalent substances never stop bonding. Explain diamond, graphite, graphene and silicon dioxide from how many bonds each atom makes and what is left over. - [Metallic Bonding and Alloys](https://lightmysky.com/learn/science/metallic-bonding-and-alloys-mt_yXOGOwHmZ4): Metal ions sit in a regular lattice inside a sea of delocalised electrons. That one picture explains conduction, malleability, and why an alloy is harder than the pure metal. ## Mathematics - [Rearranging Formulae When the Subject Appears Twice](https://lightmysky.com/learn/mathematics/rearranging-formulae-when-the-subject-appears-twice-mt_Velmpnxfcj): Change the subject of a formula where the new subject shows up more than once: clear any fraction, collect those terms on one side, factorise the subject out, then divide. - [Completing the Square](https://lightmysky.com/learn/mathematics/completing-the-square-mt_rHmCfzB4Fm): Write a quadratic as (x + p)² + q by halving the x coefficient and correcting the constant, then solve it by taking the square root of both sides. - [The Quadratic Formula](https://lightmysky.com/learn/mathematics/the-quadratic-formula-mt_C-4brnRYHY): Solve any quadratic with x = (-b ± √(b² - 4ac))/(2a), including ones that do not factorise, giving answers exactly or to a stated accuracy. - [The Discriminant and the Number of Roots](https://lightmysky.com/learn/mathematics/the-discriminant-and-the-number-of-roots-mt_uj95V0aLVS): Use b² - 4ac to decide whether a quadratic has two roots, one repeated root or none, without solving it, and link that count to the graph crossing the x-axis. - [Sketching Quadratic Graphs from Roots and the Turning Point](https://lightmysky.com/learn/mathematics/sketching-quadratic-graphs-from-roots-and-the-turning-point-mt_RcrJIbbN2x): Sketch a parabola from its roots, y-intercept, line of symmetry and turning point, reading the turning point off the completed square form. - [Simultaneous Equations with One Quadratic](https://lightmysky.com/learn/mathematics/simultaneous-equations-with-one-quadratic-mt_D89ql2sJvc): Solve a linear and a quadratic equation together by substituting the linear one into the quadratic, and read the answers as the points where a line meets a curve. - [Solving Linear Inequalities and Solution Sets](https://lightmysky.com/learn/mathematics/solving-linear-inequalities-and-solution-sets-mt_QkG3Cw5VgM): Solve inequalities in one variable with the balancing steps used for equations, flip the sign when multiplying or dividing by a negative, and show the answer on a number line. - [Solving Quadratic Inequalities](https://lightmysky.com/learn/mathematics/solving-quadratic-inequalities-mt_dukJtB_0i8): Solve inequalities such as x² - x - 6 > 0 by finding the roots, sketching the parabola, and reading off the x values where the curve is on the required side of the axis. - [Quadratic Sequences and Second Differences](https://lightmysky.com/learn/mathematics/quadratic-sequences-and-second-differences-mt_gyZT3Tcw7U): Recognise a quadratic sequence from its constant second difference, and find the nth term rule in the form an² + bn + c. - [Function Notation and Evaluating Functions](https://lightmysky.com/learn/mathematics/function-notation-and-evaluating-functions-mt_YWKWzHK_6Z): Read f(x) as a rule that turns each input into one output, evaluate a function at given values, and solve f(x) = k. - [Composite Functions](https://lightmysky.com/learn/mathematics/composite-functions-mt_jqGJHXgYNw): Apply one function to the output of another, writing fg(x) as f(g(x)), and keep the order of the two rules straight. - [Inverse Functions](https://lightmysky.com/learn/mathematics/inverse-functions-mt_7k7q5ZjMb4): Find the rule that undoes a function by swapping input and output and rearranging, and see the inverse graph as a reflection in the line y = x. - [Transformations of Graphs](https://lightmysky.com/learn/mathematics/transformations-of-graphs-mt_691_c-7Z5M): Describe and apply the effect of f(x) + a, f(x + a), -f(x) and af(x) on a graph, and give the coordinates of a marked point after the change. - [Recognising Cubic, Reciprocal and Exponential Graphs](https://lightmysky.com/learn/mathematics/recognising-cubic-reciprocal-and-exponential-graphs-mt_2IJJ51rmq9): Recognise and sketch the shapes of y = x³, y = 1/x and y = kˣ, and match each shape to the kind of situation it describes. - [Quartiles and the Interquartile Range](https://lightmysky.com/learn/mathematics/quartiles-and-the-interquartile-range-mt_vN10d1I9dA): Find the median, the quartiles and the interquartile range of a data set, and use the interquartile range to compare how spread out two sets are. - [Box Plots and Comparing Distributions](https://lightmysky.com/learn/mathematics/box-plots-and-comparing-distributions-mt_G_SnfEllzQ): Draw a box plot from a five-figure summary, and compare two distributions by their medians and their spread in words about the situation. - [Domain and Range of a Function](https://lightmysky.com/learn/mathematics/domain-and-range-of-a-function-mt_b_4zoHz8Jc): Describe the set of inputs a function accepts and the set of outputs it can return, and say what forces a restriction: a division, a square root, or the situation being modelled. - [Polynomial Division and the Factor Theorem](https://lightmysky.com/learn/mathematics/polynomial-division-and-the-factor-theorem-mt_haL2UkGa5C): Divide a polynomial by a linear expression and read the remainder, then use the fact that a root gives a factor to break a cubic apart. - [Sketching a Curve from Its Factorised Form](https://lightmysky.com/learn/mathematics/sketching-a-curve-from-its-factorised-form-mt_x4tZLdH8fh): Turn a factorised polynomial into a sketch: roots give the crossings, the constant term gives the y-intercept, the highest power decides what the ends do, and a repeated factor touches instead of crossing. - [Forms of the Equation of a Straight Line](https://lightmysky.com/learn/mathematics/forms-of-the-equation-of-a-straight-line-mt_dhIIxdFwcp): Move between y = mx + c, y - y₁ = m(x - x₁) and ax + by + c = 0, and produce the equation of a line from a point and a gradient or from two points. - [Parallel and Perpendicular Lines in Coordinates](https://lightmysky.com/learn/mathematics/parallel-and-perpendicular-lines-in-coordinates-mt_xNEmm139Ka): Use equal gradients for parallel lines and a gradient product of -1 for perpendicular ones, and apply both to find missing lines, midpoints and distances. - [The Equation of a Circle](https://lightmysky.com/learn/mathematics/the-equation-of-a-circle-mt_YARqmi_ioe): Read a circle's centre and radius from (x - a)² + (y - b)² = r², and recover them from an expanded equation by completing the square in both variables. - [Lines Meeting Circles: Tangents and Chords](https://lightmysky.com/learn/mathematics/lines-meeting-circles-tangents-and-chords-mt_ELA4IzIVdv): Find where a line cuts a circle by substitution, use the discriminant to tell a tangent from a chord or a miss, and use the right angle between a tangent and the radius. - [The Gradient of a Curve as a Limit](https://lightmysky.com/learn/mathematics/the-gradient-of-a-curve-as-a-limit-mt_LAlhcwVjln): See that a curve has a different gradient at every point, and that the gradient of a chord settles on a single value as the second point slides in. That limiting value is the gradient of the tangent. - [Differentiation from First Principles](https://lightmysky.com/learn/mathematics/differentiation-from-first-principles-mt_pdfPztEjw_): Write the chord gradient as [f(x + h) - f(x)] / h, simplify it algebraically, and let h approach zero to get the derivative. This is the definition every rule later rests on.