Anallysis Of Existing Methods And Future Nedds (Professor Dylan William)Jorge Borges
Ìý
Comparative analysis of assessment practice and progress in the UK and USA
Theme: Analysis of existing methods and future needs.
Professor Dylan Wiliam, Deputy Director and Professor of Educational Assessment, Institute of Education University of London
The first stage of the bullfight involves picadores weakening the bull's neck muscles. Junior matadors test the bull to study its moves while a senior matador observes. The picadores then probe the bull's neck with lances to weaken it for the matador's confrontation later, while apprentice matadores and clowns distract the bull when needed to protect the horse and picador.
This document discusses finding the values of two angles (α and β) that are in the fourth quadrant, given the sides of a right triangle. It first finds the hypotenuse for one angle, then the other, noting that both sine values will be negative since the angles are in the fourth quadrant. It concludes by substituting the known values into the appropriate trigonometric functions to find the values of α and β.
This document outlines steps to prove an identity involving logarithms and exponents. It involves simplifying expressions by factoring and using Pythagorean identities to show that the base and argument of the logarithm are equal, meaning the logarithm is equal to the exponent. Key steps include multiplying terms to achieve a common denominator, factoring, and applying algebraic manipulations and Pythagorean identities to prove the right hand side is also equal to the exponent.
The document discusses a class that covered integration by parts, a method for solving antiderivatives. It begins by introducing an example where standard substitution techniques do not work and integration by parts is needed instead. It then explains how to apply the integration by parts rule, including deciding which function is f and g', using a mnemonic device. Several examples are worked through to demonstrate the technique. The document notes integration by parts can be used when integrating both composite functions and single functions by taking g'(x) to be 1.
We started class by deriving the difference quotient, which is the average rate of change of y with respect to x over a given interval. Graphically, it represents the slope of the secant line connecting points P and Q. We then worked through an example problem from the textbook involving finding the average rate of change, the secant line equation, and plotting the graph and secant line. Next, we discussed the instantaneous rate of change, which is the limiting value of the average rate of change as the interval size decreases, represented by the tangent line slope. We worked through another example problem finding the slope of the tangent line and its equation at a given point.
The hydrogen atom can only exist at certain quantized energy levels called stationary states. An atom does not emit energy when in one of these stationary states. An atom can change between stationary states by absorbing or emitting a photon with energy equal to the difference between the two states.
A bakery sells different types of breads and bagels in packs of 12 for various prices. A matrix shows the price per pack of plain buns, cheese buns, plain bagels, and cinnamon raisin bagels. Another matrix contains the number of packs sold of each item on Saturday. To calculate total earnings, the price matrix is multiplied by the sales matrix.
The document discusses monthly average temperature data from January to July and how to model it using a sinusoidal function.
It includes a table of the average temperature for each month and instructions to sketch the sinusoidal graph based on the maximum and minimum monthly values.
It then explains how to write two equations to model the temperature pattern - one using sine and one using cosine. It defines the parameters of amplitude, period, phase shift, and vertical shift needed to construct the equations.
Ricky wants to buy a car and has to choose between Car A, valued at $12,000 and depreciating at 4.5% yearly, or Car B, valued at $12,500 and depreciating at 1.35% every six months. To determine which car will have more value after 5 years, the document shows how to use the compound interest formula by plugging in the values for each car to calculate the amount after 5 years, determining that Car B would have more value when sold after 5 years and therefore is the better buy.
The document summarizes how to calculate the magnitude of an earthquake that occurred in Guru Island based on information provided about an earthquake in Pakistan. It states that the earthquake in Pakistan was magnitude 7.6 and the Guru Island earthquake was 8 times stronger. It then shows the steps of setting up and solving an equation using logarithms to determine that the magnitude of the Guru Island earthquake was 8.5 on the Richter scale.
This document contains a step-by-step proof of a trigonometric identity. [1] It begins by working with the right side of the identity, obtaining a common denominator and simplifying the numerator using a Pythagorean identity. [2] It then works through the same steps for the left side of the identity. [3] After bringing the terms from both sides together, it simplifies and verifies the original identity, concluding with "Q.E.D." to indicate the proof is complete.
This document contains a step-by-step proof of a trigonometric identity. [1] It begins by working with the right side of the identity, obtaining a common denominator and simplifying the numerator using a Pythagorean identity. [2] It then works through the same steps for the left side of the identity. [3] After bringing the terms from both sides together, it simplifies and verifies the original identity, concluding with "Q.E.D." to indicate the proof is complete.
This document discusses finding the values of two angles (α and β) that are in the fourth quadrant, given the sides of a right triangle. It first finds the hypotenuse for one angle, then the other, noting that both sine values will be negative since the angles are in the fourth quadrant. It concludes by substituting the known values into the appropriate trigonometric functions to find the values of α and β.
This document outlines steps to prove an identity involving logarithms and exponents. It involves simplifying expressions by factoring and using Pythagorean identities to show that the base and argument of the logarithm are equal, meaning the logarithm is equal to the exponent. Key steps include multiplying terms to achieve a common denominator, factoring, and applying algebraic manipulations and Pythagorean identities to prove the right hand side is also equal to the exponent.
The document discusses a class that covered integration by parts, a method for solving antiderivatives. It begins by introducing an example where standard substitution techniques do not work and integration by parts is needed instead. It then explains how to apply the integration by parts rule, including deciding which function is f and g', using a mnemonic device. Several examples are worked through to demonstrate the technique. The document notes integration by parts can be used when integrating both composite functions and single functions by taking g'(x) to be 1.
We started class by deriving the difference quotient, which is the average rate of change of y with respect to x over a given interval. Graphically, it represents the slope of the secant line connecting points P and Q. We then worked through an example problem from the textbook involving finding the average rate of change, the secant line equation, and plotting the graph and secant line. Next, we discussed the instantaneous rate of change, which is the limiting value of the average rate of change as the interval size decreases, represented by the tangent line slope. We worked through another example problem finding the slope of the tangent line and its equation at a given point.
The hydrogen atom can only exist at certain quantized energy levels called stationary states. An atom does not emit energy when in one of these stationary states. An atom can change between stationary states by absorbing or emitting a photon with energy equal to the difference between the two states.
A bakery sells different types of breads and bagels in packs of 12 for various prices. A matrix shows the price per pack of plain buns, cheese buns, plain bagels, and cinnamon raisin bagels. Another matrix contains the number of packs sold of each item on Saturday. To calculate total earnings, the price matrix is multiplied by the sales matrix.
The document discusses monthly average temperature data from January to July and how to model it using a sinusoidal function.
It includes a table of the average temperature for each month and instructions to sketch the sinusoidal graph based on the maximum and minimum monthly values.
It then explains how to write two equations to model the temperature pattern - one using sine and one using cosine. It defines the parameters of amplitude, period, phase shift, and vertical shift needed to construct the equations.
Ricky wants to buy a car and has to choose between Car A, valued at $12,000 and depreciating at 4.5% yearly, or Car B, valued at $12,500 and depreciating at 1.35% every six months. To determine which car will have more value after 5 years, the document shows how to use the compound interest formula by plugging in the values for each car to calculate the amount after 5 years, determining that Car B would have more value when sold after 5 years and therefore is the better buy.
The document summarizes how to calculate the magnitude of an earthquake that occurred in Guru Island based on information provided about an earthquake in Pakistan. It states that the earthquake in Pakistan was magnitude 7.6 and the Guru Island earthquake was 8 times stronger. It then shows the steps of setting up and solving an equation using logarithms to determine that the magnitude of the Guru Island earthquake was 8.5 on the Richter scale.
This document contains a step-by-step proof of a trigonometric identity. [1] It begins by working with the right side of the identity, obtaining a common denominator and simplifying the numerator using a Pythagorean identity. [2] It then works through the same steps for the left side of the identity. [3] After bringing the terms from both sides together, it simplifies and verifies the original identity, concluding with "Q.E.D." to indicate the proof is complete.
This document contains a step-by-step proof of a trigonometric identity. [1] It begins by working with the right side of the identity, obtaining a common denominator and simplifying the numerator using a Pythagorean identity. [2] It then works through the same steps for the left side of the identity. [3] After bringing the terms from both sides together, it simplifies and verifies the original identity, concluding with "Q.E.D." to indicate the proof is complete.