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High School (11–12) · Current Electricity
You will write three functions for the measuring circuits of this course. The idea. A meter bridge balances when (X)/(R) = (l)/(100 - l). A potentiometer compares emfs by their balance lengths. A cell with a resistor…
StemPy LabHigh School (11–12) · Organic Chemistry: Some Basic Principles and Techniques
You will write three functions that count geometrical isomers, stereoisomers of a chain of chiral centres, and meso forms. The idea. Each feature has two settings, so the count starts at 2^n. When the two ends of the…
High School (9–10) · Geometry
You will write functions for the circle inside a triangle: the three tangent lengths, the radius, and a test for a four-sided figure that fits round a circle. Your tasks. In tangent_lengths, return the tuple (from A,…
High School (11–12) · Tissues and Organs
A list gives the width of the annual ring made in each of ten years, taken from a core of a tree. You will find the age of the tree, the year of the widest ring, and the years with a very narrow ring. The idea. One ri…
High School (11–12), High School (9–10), Undergraduate, General · Trigonometry and Waves by Computer
You will fit a sine to 60 noisy readings of a swinging spring, with a first guess from the FFT. The idea. The FFT finds the main frequency to within one bar. curve_fit then refines the amplitude, the frequency and the…
The summary machine Statistics & Data Science
Middle Stage (6–8), High School (9–10), High School (11–12), Undergraduate, General · Averages: Mean, Median and Mode, Spread of Data, Probability and Chance
You will build a function that summarises any list of numbers: how many, the mean, the median, the range and a chance. Then it summarises the month, and the definition of a hot day is yours to choose. The idea. A summ…
High School (11–12) · Current Electricity
You will write three functions that describe a group of cells, and then find the best arrangement. The idea. N identical cells are joined in m rows of k cells, with N = mk. The group has emf kE and internal resistance…
High School (11–12) · Organic Chemistry: Some Basic Principles and Techniques
You will write three small functions: the degree of unsaturation of a formula, the number of carboxylic acids for a number of carbons, and the number of esters. The idea. The table of alkyl groups counts almost everyt…
High School (9–10) · Geometry
You will write functions that decide how a line meets a circle, find the length of a tangent, and count the tangent lines in a list. Your tasks. In common_points, return 2, 1 or 0, the number of points a line at dista…
High School (11–12) · Tissues and Organs
A table gives the xylem cells and the phloem cells that a cambium made in each of six years. You will find the xylem cells for each phloem cell in every year. You will find the share of all the cells that became xylem…
High School (11–12), High School (9–10), Undergraduate, General · Trigonometry and Waves by Computer
You will draw a wave of wavelength 3.0 m and frequency 4.0 Hz at two times, find its first crest each time, and work out its speed. The idea. The crest of y = A(kx - ω t) moves at the speed v = fλ. You find where the…
Graph the month Statistics & Data Science
Middle Stage (6–8), High School (9–10), High School (11–12), Undergraduate, General · Averages: Mean, Median and Mode, Spread of Data, Probability and Chance
The month of 30 days is in two lists: the temperatures and the rainy days. You will split the temperatures into rainy and dry days, and count how many days had each temperature. Then the program draws a line graph wit…
High School (11–12) · Current Electricity
You will write three functions that a designer of resistors might use. The idea. A round wire has R = ρ L/A with A = π d^2/4. A metal has R = R_0[1 + α(T - T_0)]. A carbon resistor shows two digits, a power of ten and…
High School (11–12) · Organic Chemistry: Some Basic Principles and Techniques
You will write functions for the analysis of an organic compound: the per cent of carbon and hydrogen from the masses of carbon dioxide and water, the per cent of nitrogen by the Kjeldahl method, and the empirical for…
High School (9–10) · Geometry
You will test whether points lie on a circle, using the distance from its centre. Your tasks. In on_circle, return True when the point p is at distance r from centre, and False if not. Allow a tiny error: compare with…
High School (11–12) · Tissues and Organs
A student measured the layers of a leaf in a vertical section and counted the stomata on both faces of three leaves. You will total the layers, find the share of mesophyll, name the kind of leaf, and draw a bar chart.…
High School (11–12), High School (9–10), Undergraduate, General · Trigonometry and Waves by Computer
You will write three small functions that check a claimed identity on many angles: one finds the worst miss between the two sides, one says whether the identity holds, and one finds an angle where it fails. The idea.…
Two dice: simulation against exact Statistics & Data Science
Middle Stage (6–8), High School (9–10), High School (11–12), Undergraduate, General · Probability and Chance
You will find the exact probability of each sum of two dice by listing the 36 pairs, then roll two dice 3,600 times and compare. The program draws both side by side. The idea. The exact probability counts equally like…
High School (11–12) · Current Electricity
You will write three small functions about the current in a copper wire. They use I = nAev_d. The idea. One electron has a charge of 1.6 × 10^-19 C. Copper has 8.5 × 10^28 free electrons in each cubic metre. Areas are…
High School (11–12) · Organic Chemistry: Some Basic Principles and Techniques
You will write two small functions for a TLC plate. One finds the R_f of a spot. The other names a spot by matching its R_f with known dyes run on the same plate. The idea. R_f is the distance moved by the spot divide…
High School (9–10) · Geometry
You will write the opposite angle of a cyclic quadrilateral, and a test for whether four angles can belong to one. Your tasks. In opposite, return the angle opposite to a given angle: 180^° minus it. In is_cyclic, ret…
High School (11–12) · Tissues and Organs
Every tissue of the plant body belongs to one of the three tissue systems. You will finish a lookup table, write a function that uses it, and sort a list of tissues from a slide. The idea. A dictionary can hold the lo…
High School (11–12), High School (9–10), Undergraduate, General · Trigonometry and Waves by Computer
You will write three small functions for angles: one that converts degrees to radians without math.radians, one that finds the quadrant of an angle, and one that returns the point of the unit circle at an angle. The i…
The long run of a coin Statistics & Data Science
Middle Stage (6–8), High School (9–10), High School (11–12), Undergraduate, General · Probability and Chance
You will toss a coin 500 times in a program, keep the share of heads after every toss, and draw how that share moves. Then you see how close the last share comes to 0.5. The idea. The share of heads jumps about in a s…
High School (11–12) · Atoms and Atomic Spectra
You will find the energy levels and the spectral lines of any atom or ion that has one electron. The idea. The level n has energy E_n = -(13.6 Z^2)/(n^2) eV. A jump gives a photon with the difference of two levels, an…