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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 (9–10), General · Circles
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) · Anatomy of Flowering Plants
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) · 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 (9–10), General · Circles
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) · Anatomy of Flowering Plants
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) · 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 (9–10), General · Circles
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) · Anatomy of Flowering Plants
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) · 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 (9–10), General · Circles
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) · Anatomy of Flowering Plants
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) · 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…