Exam Questions Compilation All questions from the assessment (revenue, database, and probability sections). Part A – Revenue Changes (CandyBursts & BerryBonbons) In the table, each numerical value represents the percentage change in the product’s revenue relative to the preceding year. For simplicity, we’ll assume that the percentage changes reported are exact. Table (year-over-year % change): CandyBursts: 2021 +5%, 2022 +4%, 2023 –3% BerryBonbons: 2021 +8%, 2022 –8%, 2023 +6% Question 1: Which of the following sentences are certainly true, given the information currently available? Select all that apply. 1. If we exclude 2022, BerryBonbons have generated more revenue than CandyBursts on average in the given period 2. We don’t have enough information to say whether the total revenues have increased or decreased from 2022 to 2023 3. The percentage change in 2023 revenue from 2020 is exactly the same for CandyBurst and BerryBonbons 4. If the price of a single CandyBurst was $0.20 in 2021 and $0.22 in 2022, then we know that the number of CandyBursts sold in 2022 was lower than the previous year 5. In 2020, BerryBonbons generated less than $3.52 million in revenues 6. The total revenues (of CandyBursts and BerryBonbons combined) increased by no more than 6% in 2023 compared to 2020 7. Total revenues (that is, the revenues of CandyBurst and BerryBonbons combined) increased in 2021 compared to 2020 8. Total revenues decreased in 2022 compared to 2021
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1)A polyhedron ha s12 edges and 6 vertices. How many faces does it have? 2)total surface area of each prism
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Explain why the derivative of x squared is 2x, using a graph.
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Explain how to add and subtract fractions with different denominators, with a worked example."
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Further Maths question (see attached image). 2(i) Using a suitable algorithm and without performing any division, determine whether 13 306 617 is divisible by 9. 2(ii) The group G = {1, 3, 7, 9, 11, 13, 17, 19} has multiplication modulo 20 as its operation. (a) Complete the Cayley table for G. (b) State the inverse of the element 7. (c) Determine the order of the element 13. (d) Write down a subgroup of G of order 4.
A-Level statistics question (see attached image). The graph of the probability density function f(x) of the continuous uniform random variable X is shown. The PDF is constant (height 0.2) from x = -3 to x = 2, and zero elsewhere. (a) Write down P(X = 1). (b) Find E(X). (c) Find Var(X). (d) Sketch the cumulative distribution function of X for -3 <= x <= 2, labelling points where it touches or crosses the axes. (e) Find P(X^2 > 1.96).
A-Level question (see attached image). Let z = sqrt(3) - 3i. (a) Write z in the form r(cos theta + i sin theta) where -pi < theta <= pi. (b) Show and label on a single Argand diagram the point P representing z and the point Q representing iz. (c) Describe the geometrical transformation that maps P onto Q.
Prove that the set of real numbers in the interval [0,1] is uncountable, using Cantor's diagonal argument.
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Explain how gradient descent trains a simple neural network. Describe the loss, the gradient and the weight update rule.
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Find the integral of x e^(2x) with respect to x, using integration by parts. Show full working.
Prove by mathematical induction that 1^3 + 2^3 + ... + n^3 = [n(n+1)/2]^2 for all positive integers n.
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A circle has radius 7 cm. Calculate its area, leaving your answer in terms of pi.
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