GUESS PAPER 9383
Question 1
(a) Graph the function f(x) = 2x²-4x + 1. Label the vertex, symmetry and intercepts. Determine if the function is one-to-one or not. If not restrict the domain to make it invertible and find its inverse.
(b) A factory has a 5% defect rate. Using the binomial distribution, calculate the probability of at most 2 defective items in a batch of 50. Interpret the result for quality control.
Question 2
(a) A smartphone's price increased by 25% in 2022 and decreased by 15% in 2023. Calculate the net percentage change over the two years. If the original price is Rs. 80,000. Find the final price.
(b) The profit function of a company is P(x)=-2x² + 100x800, where x is the units sold. Calculate the maximum profit and the number of units required to break even (profit=0).
Question 3
Calculate the sum of (a) For the geometric sequence 5, 15, 45...., derive the general te term the first 8 terms and interpret the sequence in a real-world context (e.g., viral growth). an
(b) Construct a grouped frequency table (class-intervals:0-10, 11-20, etc.) and a histogram for the dataset: 5. 12. 18. 7. 25, 14. 22, 9, 16, 3
Question 4
(a) A car speed is = modeled by v(t) t -12 + 10 (in m/s). Calculate the average rate of change of speed between = 2 and t = 5. Interpret the result physically.
(b) For the dataset 4,7,9,10,12, compute the mean, variance and stand deviation. Explain why variance is sensitive to outliers.
Question 5
MASTERPIECE
(a) A box contains 6 red, 4 blue and 5 green balls. Two balls are drawn with replacement. Calculate the probability of getting one red and one green ball. Then repeat the calculation without replacement and compare the results.
(b) Using the permutations, determine how many distinct 5-letter codes can be formed from the words 'ALGEBRA' if no letter repeats. Validate your answer using factorial notation.