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High School (11–12) · Alternating Current
You will write three functions for an LC circuit that has no resistance. The idea. The angular frequency is ω_0 = 1/√(LC). The charge on the capacitor is q = q_0ω_0 t. A capacitor charged to V_0 gives the largest curr…
StemPy LabHigh School (11–12) · Bonding: Valence Bond and Crystal Field Theory
You will write the three steps that fill the d orbitals of an octahedral complex: decide whether the field is strong, split the electrons between the t_2g and e_g sets, and find the CFSE. The idea. If Δ_o > P the comp…
High School (11–12) · Application of Integrals
You will write three small functions that estimate the length of a curve. The program joins points of the curve by straight pieces, adds the lengths, and counts how many pieces give a chosen accuracy. The checker uses…
High School (11–12) · Cell Cycle and Cell Division
A student counts the cells of a root tip and writes the number in each stage in a dictionary. You will find the mitotic index, the minutes that a cell spends in a stage, and the stage that takes the longest. The idea.…
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) · Alternating Current
You will write three small functions about a transformer and a power line. The idea. For an ideal transformer the voltages are in the ratio of the turns. The efficiency is the power out divided by the power in, as a p…
High School (11–12) · Bonding: Valence Bond and Crystal Field Theory
You will write three small functions of valence bond theory. One counts the unpaired electrons of a free ion. One turns a count into the spin-only moment. One names the hybridisation of an octahedral complex. The idea…
High School (11–12) · Application of Integrals
You will write three small functions that find the volume of a solid of revolution by adding up thin discs and thin washers. The checker uses a cone, a sphere and a washer. The idea. A thin disc of radius r and thickn…
High School (11–12) · Cell Cycle and Cell Division
A cell is a dictionary with four numbers. The size is compared with the size needed. The damage is the number of unrepaired breaks in the DNA. The copied number is the share of the DNA copied at G2. The attached numbe…
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) · Alternating Current
You will write three functions for the resonance of a series circuit and for the power it takes. The idea. At resonance ω_0 = 1/√(LC) and Q = ω_0L/R. The average power is P = I_rms^2R, where I_rms = V_rms/Z. All value…
High School (11–12) · Isomerism in Coordination Compounds
You will count the geometrical isomers of an octahedral complex with the trans-pair method. The six corners form three pairs of opposite corners. An isomer is fixed by which ligands sit opposite each other. The idea.…
High School (11–12) · Application of Integrals
You will write three functions that explain why a region must be split where the curves cross. The checker uses the curves y = x^3 and y = 4x, which cross three times. The idea. A signed integral of g - f lets a lobe…
High School (11–12) · Cell Cycle and Cell Division
A cell has a few pairs of homologues. Each gamete gets one chromosome from every pair. You will list all the gametes, and then count the kinds of gamete and of zygote. The idea. With n pairs, each with 2 choices, ther…
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) · Alternating Current
You will write three small functions about a series LCR circuit. They use Z = √(R^2 + (X_L - X_C)^2) and φ = (X_L - X_C)/R. The idea. All the quantities are in ohm. The phase angle is positive when the circuit is indu…
High School (11–12) · Isomerism in Coordination Compounds
You will write functions that describe salts of a chromium complex. One counts the ions outside the bracket. One decides whether two salts are isomers. One says what silver nitrate precipitates. The idea. Isomers have…
High School (11–12) · Application of Integrals
You will write a small program that adds thin strips between two curves, and compare it with the shortcut for a parabola cut by a line. The checker uses a line and a parabola, two parabolas, and the shortcut. The idea…
High School (11–12) · Cell Cycle and Cell Division
A cell with two pairs of chromosomes is a list. Each chromosome is a tuple of three things: its pair ("1" or "2"), its parent ("m" for the mother or "p" for the father), and the number of chromatids it has. You will w…
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) · Alternating Current
You will write four functions that a circuit designer might use for a coil or a capacitor on an AC source. The idea. A coil has X_L = 2π f L and a capacitor has X_C = (1)/(2π f C). The rms current is the rms voltage d…