Get premium membership and access revision papers, questions with answers as well as video lessons.
Sma2160:Mathematics I Question Paper
Sma2160:Mathematics I
Course:Bachelor Of Horticulture
Institution: Meru University Of Science And Technology question papers
Exam Year:2012
QUESTION ONE (30 MARKS)
a) If the roots of equation 2??2 + 3?? - 4 = 0 and ? and ??. Find the equation whose roots are; i. (?2,??2) ii. 1 ? , 1 ?? iii. (? +1,?? + 1) (9 Marks) b) Factorize the given polynomial as far as possible hence obtain the roots of the polynomial ??3 - 7?? - 6 = 0. (4 Marks) c) A customer makes a single deposit of Ksh. 16,000 in an account which pays compound interest at a rate of 6% per annum. i. How much is the investment worth after twelve years? (4 Marks) ii. After how many years will be investment be worth three times its initial value. (3 Marks) d) i) Given ?? = 6 15 4 18 find ??-1. (2 Marks) ii) Two business people John and Abraham deals with farm inputs. One day John bought 6 sprayers and 15 jembes at ksh. 97,500 while Abraham bought 2 sprayers less than John and three jembes more than John and spent ksh. 20,500 less than John. Use this information to find the cost of a sprayer and a jembe. (3 Marks) e) Prove the formula for the sine rule. ?? sin ?? = ?? sin ?? = ?? sin ?? = 2??
Where R is the radius of circumcircle of triangle ABC, considering the case where C is acute or obtuse. (5 Marks)
2
QUESTION TWO (20 MARKS)
a) simplify without using tables or calculator 3cos2 45°cos42° + tan2 60°sin48° - 9cos60°cos42° . (3 Marks) b) solve the following equations i. ??????2(?? + 2 + ??????2 ?? - 2 = 5 ?????? ?? > 0. (3 Marks) ii. ????????2 + 48??????2?? = 14 (3 Marks) iii. 4?? - 15 2?? + 56 = 0. (3 Marks) c) Use exact values for the trigonometric ratios of angles 30°, 45°, 60° to simplify the expression below sin2 315°(1-tan2 210°) 1+cos 120° (1+tan2 330°) (4 Marks) d) Solve the simultaneous equations; ???? = 160 log?? - 3log?? = 1 ?????? ?? > 0,?? > 0 (4 Marks)
QUESTION THREE (20 MARKS)
a) Given the linear equations below; 3?? + 2?? = ?? + 1 3?? + 2?? = 8 - 5?? 3?? - 1 = ?? - 2?? Solve the above system using the method of inverse. (10 Marks) b) An arithmetic progression has 4th term and 8th terms given by 22 and 46 respectively Find; i. The 1st term and the common difference. (3 Marks) ii. The sum of the first twelve terms. (3 Marks) iii. The number n such that the sum of the first n terms is 310. (4 Marks)
QUESTION FOUR (20 MARKS)
a) State the following i. Remainder theorem (3 Marks) ii. Factor theorem (3 Marks) b) Determine the line of symmetry , minimum or maximum value x and y intercept of F(x), hence sketch the curve of the following function ?? ?? = 2??2 + 3?? - 5 . (5 Marks) c) Prove that when a polynomial f(x) is dividend by ???? + ?? where ?? ? 0 the remainder is ?? = -?? ?? . (4 Marks) d) Expand each of the following is ascending powers of x up to and including the term in ??3 stating the range of values of x for which each of the expansion is valid. i. (1 - 4??)-3 (3 Marks) ii. (1 + ??)1 3 (3 Marks)
More Question Papers
Popular Exams
Return to Question Papers