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You calculate this by adding the x coordinates together and dividing by two to get x = 2, then doing the same with the y coordinates to get y = 1.
Subtract one y coordinate from the other, do the same with the x coordinates, then divide the first result by the second. Voila!
The other plot represents y = 2ˣ.
tan²(x) - tan(x) - 6 = 0cos(x) + tan²(x) - 6 = 06 - tan²(x) = 0
Multiply the whole thing by tan(x) then divide it by cos(x). Simplify using trigonometric identities, and rearrange.
dy/dx = (x² + 10x - 8) / (x² + 5)²dy/dx = (-2x² - 8x + 10) / (x² + 5)²
You need to use the quotient rule for this one. Treat the top and bottom of the fraction as different functions, use the rule, then simplify what you get.
The two stationary points are (1,1) and (-5,-1/5). Solve -2x² - 8x + 10 to find x = 1 and x = -5, then substitute those back into the original curve equation to find y.
v = u + atv² = u² + 2as
You don't have the time, so you have to use the second equation where all you need are the starting velocity (u) the acceleration (a) and the distance (s).
Just substitute in u = 3.5, a = 9.8 and s = 5 to v² = u² + 2as to find v.
There are 20 tree heights in the diagram, so the median height is in between the 10th and 11th values, which are 7.4 and 7.5 respectively.
The IQR = 7.75 - 6.7 = 1.05.
Could You Pass A-Level Maths Right Now?
Let's face it, none of this is relevant to your everyday life, so an F in fake A-level maths is not a big deal.
Not bad! You might just scrape a pass in A-level maths, if you got lucky with the questions.
You passed! Not bad at all. Keep up the good work.
You passed! Amazing work – keep it up and you will go far.
Well done! You passed with a near-perfect score. You really know your A-level maths.
Congratulations! You passed with flying colours. Either you took this quiz as a break from revising actual A-level maths or you're a really, really good guesser.
Questions adapted from OCR past exam papers for all four core modules as well as mechanics and statistics.