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## A Level Warmup – Mock Paper 2

(You’ll need to click on this post to get the download link) a-level-warmup-2016-paper-2 a-level-warmup-paper-2-solutions Solutions may have mistakes. Discuss with me over text if you spot any errors.

## Q16. Hypothesis Testing

Question 16. A marmalade manufacturer produced thousands of jars of marmalade each week. The mass, $x$ grams, of marmalade in a randomly chosen jar has mean $25$g. Following a slight adjustment to the filling machine, a random sample of $50$ Read More …

## Q15. Poisson and related distributions

Question 15. In a certain country, the number of deaths due to old age in the northern and southern parts are recorded separately. It is found that, on average, there are 2 deaths in the northern parts and 1 death Read More …

## Q14. Normal and binomial distributions

Question 14. A fruit grower grows both red and green apples which have masses that are normally distributed. The mass of a randomly chosen red apple has mean $75$ g and standard deviation $12.5$ g. The mass of a randomly chosen Read More …

## Q13. Probability, approximations

Question 13. Ali has 5 different bags and 5 different wallets. They are of 5 colors: black, blue, brown, red and white. He places one wallet into one bag at random. A wallet is said to be in the correct bag Read More …

## Q12. Permuatations

Question 12. (a) 10 friends, including Amy, Betty and Charlie are to line up in a single row for a photograph. Find the number of ways they can be arranged if (i) Amy and Betty are to be together; (ii) Read More …

## Q11. Approximations of distributions

Question 11. A study of the number of male and female children in families of inhabitants on a planet very far away reveals that the probability that a baby girl is born is 0.005. 500 babies are chosen at random. Read More …

## Q10. Maclaurin Series

Question 10. It is given that $\displaystyle y = (\cos x)^\frac{1}{2}$. (a) Show that $\displaystyle 2y \frac{\mathrm{d}^2y}{\mathrm{d}x^2} + 2 \left ( \frac{\mathrm{d}y}{\mathrm{d}x} \right )^2 + y^2 = 0.$ (b) Find the Maclaurin series for $y$ up to and including the Read More …

## Q9. Inequalities

Question 9. Solve, without a calculator, the inequality $$\frac{x^2+5}{x-1} \geq 1.$$ Hints Remember: we cannot cross multiply if we don’t know the whether a term is positive or negative! (After making one side of the equation 0) If we cannot Read More …