Download Computer Science Admissions Test and more Lecture notes Computer Science in PDF only on Docsity! Banner, Bruce Avengers College Computer Science Admissions Test EXAMPLE QUESTIONS. These are meant as practice material and have various degrees of difficulty. Some are inspired from past CSAT papers. Instructions: · The test duration is 100 minutes. Section A has 8 questions. Section B has 12 questions which are more challenging and worth more marks. · All questions attempted are marked. Your best 5 questions from each section are considered. Partial answers are taken into account. You can choose the questions to answer and their order. · Write only on the work-booklet provided and clearly label the question you are solving at the top of each page. Answers without working may not gain full marks. You should show sufficient working to make your solutions clear to the Examiner, but these need not be extremely thorough. · Calculators, phones, watches, smart-glasses or other electronic devices or paper are not permitted. · All paper must be handed in. Do not write on the cover or question sheets. · Do not discuss any test questions with others (e.g. candidates at the same or another College, the Internet, or elsewhere), especially before March. You would disadvantage yourself. It is recommended that you: - take 5 minutes first to read through all questions, - start with Section A and spend no more than 30 minutes on it, - aim for 5 questions in each section; if you finish early then attempt more from Section B. Good luck! 1 of 4 r47.000 Banner, Bruce – Avengers College Section A — aim for 5 questions out of 8, of your choosing 1. You have a card of 10cm by 10cm. What is the largest volume in cm3 of a box (without a lid) that can be obtained by cutting out a square of side x from each corner and then folding the flaps up? 2. Let f(x) mean that function f is applied to x, and fn(x) mean f(f(...f(x))), that is f is applied to x, n times. Let g(x) = x+ 1 and hn(x) = gn(x). What is hmn (0)? 3. Triangle ABC is isosceles with AB = AC. Let the circle having diameter AB and centre O intersect BC at some point P . Find the ratio BP/BC. 4. What is the units digit of the number 1337∑ n=1 (n!)4 ? 5. Using only the functions max and min and arithmetic operations (no if clauses), express the amount of possible overlap between two intervals [a1, a2] and [b1, b2], where a1, a2, b1, b2 are arbitrary real numbers with a1 < a2 and b1 < b2. 6. Which values of k give a maximum at x = −1 for f(x) = (k + 1)x4 − (3k + 2)x2 − 2kx ? 7. The Taylor expansion of ln(1 + x) is defined as ln(1 + x) = x− x2 2 + x3 3 − · · · . Expand ln ( 1−x 1+x2 ) up to and including the 4th power of x. 8. Given a grid of 4× 4 points, how many triangles with their vertices on the grid can be drawn? 2 of 4 r47.000
