A-Level Math Problems.pdf

The difference between the population correlation coefficient and Pearson's Product Moment Correlation Coefficient is that the former describes how correlated two variables are, while the latter is a statistic that estimates the former.
The probability a randomly chosen person likes coffee is not given, likes tea and soda is not given, likes coffee or tea but not both is not given, and likes soda given they like coffee is not given.
The correlation in the scatter plot is described as weak positive correlation.
A convex curve is a curve where any line segment joining two points on the curve stays above the curve.
The differential equation for a savings account subject to compound interest is dM/dt = kM.
The median is a measure of central tendency, the middle value when data is listed in size order.
The advantages and disadvantages of using the median as a statistic are not given.
The CO2 emissions of cars registered in 2016 are generally significantly less than those registered in 2002.
The calculations for the binomial distribution are:
a) P(X = 4) = 0.2186
b) P(X ≤ 11) = 0.9999
c) P(X > 5) = 0.2784
The normal distribution approximation has a mean of np and variance of np(1-p).
The implicitly defined function has a derivative of dy/dx = 4x + 3y / (8 - 3x) = 10 at the point (2,4).
The Newton-Raphson method approximations are x1 = 0.7191445372 and x2 = 0.9013623019.
The Cartesian form of the parametric equation is (x - 2)^2 + (y - 3)^2 = 1.
The equation of the tangent to the circle is 2x + 3y = 25, and it intersects the x-axis at (12.5,0).
The quadratic equation has two real roots.
The area between the curves is 2.
The proof of the trigonometric identity sin(2x) = 2 sin(x)cos(x) is given.
The integral is ∫(2x - 10) / ((x - 1)(x + 3)) dx = 4 ln|x + 3| - 2 ln|x + 1|.
The probability P(54 ≤ X ≤ 72) = 0.9569.
The statements about the normal distribution are:
1) The points of inflection are 1 standard deviation away from the mean.
2) The total area under the curve is 1.
3) ~68% of values lie within 1 standard deviation of the mean.
4) ~99.8% of values lie within 3 standard deviations of the mean.
5) P(X > μ + a) = P(X < μ - a) for any constant a.