AS Mathematics runs a 100 mark Pure paper against a 70 mark Applied paper split evenly between mechanics and statistics. Trig equations that lose solutions and dropped second derivative checks are the two most repeated ways marks go missing.
2D Kinematics with Vectors, Displacement-Time Graph Interpretation, Vertical Motion & Connected Bodies (Lifts), Rough Inclined Planes & Limiting Equilibrium, Data Hygiene & Graphical Suitability Critique, Grouped Frequency Mean, Variance & Survey Critique, Venn Diagrams & Statistical Independence, Bivariate Correlation (PMCC) & Linear Regression, Binomial Distribution Modelling & Probability
評級
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計算機規定
A calculator is permitted on both AS papers, but it must not have access to a computer algebra system, no calculator or app that can manipulate algebra symbolically or show algebraic steps is allowed. It must be able to compute summary statistics and access probabilities from standard statistical distributions, which the statistics section of AS 2 draws on directly. As with every CCEA and JCQ subject, no stored or retrievable information, formulae, text or programs, may be held in the calculator, and an exam mode should be activated rather than relying on a manual reset, which does not clear stored memory.
AO1: AO1: use and apply standard techniques (50%)
AO2: AO2: reason, interpret and communicate mathematically (25%)
AO3: AO3: solve problems within mathematics and other contexts (25%)
Statistics mode for grouped mean, variance and PMCC
用途: Get the mean, standard deviation or correlation coefficient of grouped or bivariate data directly, to check your own working.
使用時機: For grouped frequency questions asking for a mean or standard deviation, or for questions giving paired data and asking for the product moment correlation coefficient.
步驟
Enter grouped frequency data or paired bivariate data into the calculator's statistics mode to get the mean, standard deviation or correlation coefficient directly, then use those figures to check your own working rather than relying on the calculator alone.
考試提示: Built-in statistics mode is a standard calculator function, not a stored program. Mark schemes still expect the formula and key intermediate values written down, so quote the calculator result alongside your working, not instead of it.
Binomial distribution function for probability questions
用途: Get a binomial probability or cumulative probability directly once n and p are identified, without expanding the formula by hand.
使用時機: For probability questions that identify a binomial distribution and ask for P(X = r) or a cumulative probability.
步驟
Use the calculator's built-in binomial probability function to find P(X = r) or a cumulative probability directly once n and p are identified from the question, rather than expanding the formula by hand each time.
考試提示: This is a built-in statistical function the specification expects the calculator to have, not a stored program. State the distribution and its parameters in your written answer even when the calculator does the arithmetic.
ANS key through connected mechanics calculations
用途: Carry an unrounded intermediate result, such as an acceleration, forward into the next part of a mechanics question without retyping a rounded figure.
使用時機: For multi-part mechanics questions, such as connected bodies over a pulley, where a later part depends on an earlier calculated value.
步驟
In a multi-part mechanics question, such as connected bodies over a pulley, carry an unrounded intermediate result, an acceleration or a tension, forward with the ANS key into the next part rather than retyping a rounded figure.
考試提示: ANS only carries a value calculated live during that question forward to the next line. No formula, constant or result may be stored in the calculator before the exam begins.
常見錯誤
1high涉及分數: 2Trigonometric equations
Trig equations that reduce to something times sin x equals zero get solved by dividing both sides by sin x rather than factorising, which loses every solution where sin x itself equals zero.
如何避免: Never divide a trig equation by a trig function that could equal zero. Factorise instead, set each factor to zero separately, and solve each one over the full range asked for.
2medium涉及分數: 1Stationary points
A stationary point is labelled a maximum or minimum without showing the second derivative test or a sign table to justify which one it is.
如何避免: Evaluate the second derivative at the stationary point, or check the sign of the first derivative either side of it, and state the conclusion that follows. Do this every time, even when the answer looks obvious.
3medium涉及分數: 2Correlation and regression
The correlation coefficient is described in generic terms, such as a positive correlation, without saying what a value close to zero means for whether the regression line can actually be trusted.
如何避免: State plainly when r is close to zero that the linear relationship is too weak to support a reliable prediction from the regression equation, rather than quoting the equation as if it were valid regardless.
4medium涉及分數: 1Coordinate geometry
The gradient of a line perpendicular to another is found by taking the negative of the original gradient, without also inverting it.
如何避免: For a gradient m, the perpendicular gradient is minus one over m, both the sign changes and the value inverts. Check both parts every time, not just the sign.
5medium涉及分數: 3Forces on inclined planes
On a rough inclined plane, the direction of friction is assumed rather than reasoned from which way the object is on the point of moving, leading to a sign error across the whole equilibrium equation.
如何避免: Decide first which way the object would move if friction were removed, then draw friction acting the opposite way to that impending motion, before resolving any forces.
6medium涉及分數: 1Optimisation and modelling
In geometric optimisation problems, an algebraic root that is physically impossible, for example a negative length or a value that makes another dimension negative, is left in as a valid answer.
如何避免: After solving, substitute each root back into the physical constraints of the problem and reject any that produce a negative length, area or other impossible value, stating clearly why it is rejected.
7medium涉及分數: 1Integration
The constant of integration is left out of an indefinite integral, particularly when the question does not immediately follow with a boundary condition.
如何避免: Write plus c on every indefinite integral as a fixed habit, whether or not the rest of the question goes on to use it, since it is assessed as part of the integration itself.