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Sma2160:Mathematics I Question Paper
Sma2160:Mathematics I
Course:Bachelor Of Horticulture
Institution: Meru University Of Science And Technology question papers
Exam Year:2014
QUESTION ONE (30 MARKS)
a) (i) Define the term proportion (1 mark) (ii) If a:b=3:4, b:d=3:4 and d:c=3:1 find a:c (3marks) b) A tea blender buys two grades of tea at sh. 60 and sh. 80 per packet. Find the ratio in which he should mix them so that by selling the mixture at sh. 90, a profit of 25% is realized (4 marks)
c) Given that 35 = 5.9160798 correct to seven decimal places. Evaluate
57 57 ? ?
by
rationalising the denominator. (give your answer to 6 d.p) (4 marks)
d) Solve the equation 4?? - 15 2?? + 56 = 0 (3 marks)
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e) Five books are to be selected from twenty books of which eight are paper back and twelve are hard back. How many selection are possible if at least one paperback book has to be included (4 marks)
f) Solve the equation sin-1 ?? + sin-1 3?? = ?? 2
(4 marks)
g) For two events A and B P ~?? = 3 10 and P ?? = 13 20 P ?? ? ?? = 9 20 find P ?? ? ?? (3 marks)
h) Determine the median and the semi-interquartile range for the date 7.5, 10, 5, 3, 2, 9, 8, 7, 4, 5, 8.5, 9.5 (3 marks)
i) (a) Find the remainder when f(x) =4x5-x3+x2-3 is divided by x+2 (2 marks)
(b) Factorise the expression 6x3-17x2-4x+3 (3 marks)
QUESTION TWO
a) Calculate the variance and the standard deviation of the distribution below using 37 as the assumed mean (7 marks)
Length (cm) Frequency
25-29 5
30-34 12
35-39 25
40-44 11
45-49 7
b) A box holds 8 red and 4 blue beads. Three beads are taken from the box and not replaced. (i) Draw a tree diagram to represent this information (3 marks)
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(ii) What is the probability that; (a) All three are red (2 marks) (b) There are at least two blue beads (3 marks)
c) The masses (in grams) of 50 small fruits are as shown in the following table.
Mass (grams) Number of fruits
50-59 4
60-69 5
70-79 9
80-89 14
90-99 7
100-109 6
110-119 5
Draw a histogram to represent the date and use it to estimate the mode of the distribution (5 marks)
QUESTION THREE
a) The third term of a G.P is 11 4 and the sixth term is5 32 . Determine the first term, the common ratio and the sum of the first six terms of the series. (6 marks)
b) (i) show that x nxn loglog 3 3 1? (3 marks)
(ii) Hence solve the equation 13 logloglog 3 381 ??? xxx (4 marks) c) Evaluate 8 18618 C C ? (4 marks) d) Find the possible values of c if the equation ??2 + ?? + 2 ?? + ??2 has equal roots (3 marks)
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QUESTION FOUR
a) Solve the equation on the domain 0= ?? = 360 6cos2 ?? + cos?? - 1 = 0 (4 marks)
b) (i) Find the inverse of the matrix (3 marks)
? ? ? ? ? ? ?23 11
(ii) Hence solve the pair of simultaneous equation using matrix method. (3 marks)
?? + ?? = 5
3?? - 2?? = 0
c) A surveyor measures the three sides of a triangular field XYZ as XZ=56.7m and ZX=48.9 m. Calculate the area of the field correct to the nearest square metre (4 marks)
d) A track AB is in the shape of an arc of a circle centre O which is 400m long. If the angle AOB is 450, calculate the radius of the arc to the nearest metre. (3 marks)
e) Solve the equation x2-8x+11=0 by completing the square (3 marks)
QUESTION FIVE
a) Two dice, coloured red and green respectively, are thrown in a game. The player has to score a total of 9 or more in order to stay in the game. Find the probability that; (6 marks) (i) The player scores a total of 9 or more
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(ii) The player scores a total of 9 or more given that the score on the green die is 3 (iii) The player scores a total of 9 or more, given that the score on the green die is 6
b) Three people A,B, and C can do a piece of work in 45 hrs and 30 hrs respectively. How long can B take to complete the work when he starts after A and C worked for 13 hours each
(4 marks)
c) Use the reminder theorem to show that ?? + 2 is a factor of ??3 + 6??2 + 12?? + 8, hence solve ??3 + 6??2 + 12?? + 8 = 0 (4 marks)
d) Calculate the remaining side and angles of the triangle ABC in which C=12cm, a=8cm and angle A=300 (3 marks)
DRAWING
e) If a single deposit of sh. 150,000 is invested for four years at compound interest, at what rate will the investment be worth sh. 182, 326 (3 marks)
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