Motithang Higher Secondary School Thimphu Thromde Mid Term Examination 2016 Subject: Mathematics Full Marks: 100

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1 Motithang Highe Seconday School Thimphu Thomde Mid Tem Examination 016 Subject: Mathematics Full Maks: 100 Class: IX Witing Time: 3 Hous Read the following instuctions caefully In this pape, thee ae thee sections: Section A, Section B and Section C. you ae expected to answe ALL the questions in Section A and Section B. Unde Section C, thee ae 7 questions (question numbes 1-1). Each question has two pats, I and II. Attempt eithe I o II fom each question. The intended maks fo a question o its pats ae stated in backets. The use of calculato (fx-8/fx-100) is allowed without memoy. Section A Answe all questions Question 1 i) Which of the following is an example of Powe of Poduct Law? A. C B. 6 3 D ii) Which of these calculations will esult in an iational numbe? A. (0.66 ) C. 0.7 B. 3 (0.33 ) D. (0.99 ) (0. ) iii) What is 144 1? A. 11 C. 1 B. 13 D. 14 iv) What two polynomials ae being multiplied fo the ectangle A. 3( y x) C. (y x) B. (y x) D. (y x) v) What kind of polynomial x x 9x x is it? A. Tinomial C. Monomial B. Tatanomial D. Binomial vi) The equation of a line in slope and y-intecept fom is A. y mx b C. x my b B. Ax By C D. Ax By C vii) The scientific notation of lage numbe is witten in m 10 a fom. The value of m should be A. 1 m 10 C. 1 m 10 B. 1 m 10 D. 1 m 10 MT/Class IX/Mathematics/016 1 of 6

2 viii) What is value of equation x 3 11 A. 1 C. B. 3 D. 0 ix) When (3xy 6y ) (3y), the quotient is A. B. y x y x x) What is coelation of the given gaph C. D. x y x y A. Stong positive coelation C. Stong negative coelation B. Weak positive coelation D. Weak negative coelation Question Calculate (i) (ii) Question 3 n Section B (3 Maks) Answe all questions ( 3 ) Solve fo n whee ( 1) 3 1 Question 4 A 4-yea-old paot has a heat beat ate of about 0 beats pe minute. A 7-yea-old man has a heat beat ate of about 70 beats pe minute. Whose heat has beat moe times in thei life so fa? Question (a). Calculate ( ) [10 3 (.4) [] (b). What numbe multiplied by itself equals 864? Why ae thee two possible answes to this question? [1] Question 6 Ceate a polynomial to fit each desciption. (a). Monomial of degee 3 (b). Coefficient that ae all even (c). Tinomial with all odd coefficients Question 7 Expand and simplify x(x y) 3y( 3x) Question 8 Divide (10x 19x 6) by ( x ) MT/Class IX/Mathematics/016 of 6

3 Question 9 Calculate aea of given shape (x 3) x 4 Question 10 These ae fist two figues in a patten Figue I Figue II Daw next thee figues if the patten wee an exponential elation Question 11 Convet x 3y 1 in slope and y-intecept fom Question 1 Sketch gaph of 1 y x Question 13 Solve a 7 3a 11 Question 14 Detemine elationship between total numbe of cicles and figue numbe Figue No. No. of cicles Section c (48 Maks) Unde this section, thee ae 7 questions (question numbes 1 1). Each question has two pats, I and II. Attempt eithe I o II fom each question. Question 1(I) (a). Wite each way. (i) As a poduct of othe powes of (ii) As a quotient of othe powes of (iii) As a powe of (b). Thee ae seven schools in a dzongkhag with aveage of 48 students pe school. If about % of the students ae male, about how many females attend these schools? 8 MT/Class IX/Mathematics/016 3 of 6

4 Question 1(II) (a). Wite each of the following ways. s s (i) Using the powe law, ( a ) a (ii) 8 10 As a powe of a poduct, (iii) As a powe of a quotient, ( ab) a a ( ) b a b (b). (i) Estimate the numbe of seconds in one week. (ii) Calculate the actual numbe of seconds. How does it compae with you estimate? Question 16(I) (a). Which is geate in the given pai b 4 3 ( 10 ) o 0 billion (b). About people live in China and about people live in Bhutan. The numbe of people living in China is n times the numbe of people living in Bhutan. Find n. Question 16 (II) (a). The aveage gowth ate of a child between bith and age 18 is km/h (i) How fast is that in kilometes pe day? (ii) How fast is that in centimetes pe yea? (b). Assume that a peson blinks his o he eyes evey s. estimate how many times you have blinked you eyes in 6 yeas. Recod you answe in scientific notation Question 17 (I) (a). Model with tiles to add o subtact the given polynomials (y y x) (3y y 4x) (b). Descibe the height of a given shape as a polynomial. The aea and base length ae given 3x x 1) 3x 1 Question 17 (II) (a). Subtact using zeo pinciple ( 3y y 6x) (3y 4y x) 4k 6km (b). Fo k (i) Divide the faction to find the quotient (ii) Evaluate the quotient fo k = and m = 3 (iii) Evaluate the numeato and the denominato fo k = and m = 3 Question 18(I) (a). Multiply ( x 3)( x y) using tiles (b). Find aea of a ectangle whee height is x 1 and the width is 4 units moe than 3 times the height. MT/Class IX/Mathematics/016 4 of 6

5 Question 18(II) (a). A squae pictue with side length of n + is inseted into a squae fame with side length of 3n + 4. Wite an expession that can be used to find the aea of the white space aound the pictue. Show you wok. (b). How many like tems ae thee in poduct afte like tems ae collected? (y 4)(y 4) Question 19 (I) (a). Ceate a table of values to show the elationship between the adius and the cicumfeence of a cicle. Detemine whethe elation is linea, quadatic, o exponential. (b). Fifteen balls ae aanged in a tiangle to fom the base of a pyamid (i) How many moe balls ae needed to build the laye above this? (ii) How many moe balls ae needed in total to complete the pyamid? (iii) How many balls would you need if you wanted to build a laye undeneath the base laye? Daw the gaphs of the elations epesented by y, x y x and y (iv) Detemine whethe the elationship between the total numbe of balls used and the numbe of layes in the pyamid Question 19(II) Daw the gaphs of the elations epesented by y, x y x and x y Question 0(I) (a). This gaph shows the tempeatue of wate in a glass x [6] (i) What does the slope of the gaph epesent? (ii) The slope is negative. What does that tell you about what happened to the wate tempeatue? (iii) What does the y-intecept epesent? (b). A pilot wants to educe he plane s aispeed at a constant ate fom 0 km/h to 100km/h in min. (i) Ceate a table of values. MT/Class IX/Mathematics/016 of 6

6 (ii) Sketch the gaph (iii) Detemine the slope and the y-intecept of the gaph Question 0(II) (a). Lobzang woks at two diffeent jobs. One job pays him Nu. 600 an hou The othe job pays him Nu. 00 an hou He wants to ean a total of Nu. 400 Wite an equation to descibe all the diffeent combinations of pay ates that will ean him Nu Sketch the gaph of this equation (b). Detemine the slope and y-intecept of a given gaph and then wite the equation of a line Question 1(I) (a). A photogaphe chages a sitting fee of Nu. 0 and then chages Nu. 0 fo each photogaph puchased. (i) A custome has Nu 1030 to spend. Wite the equation you could solve to detemine the numbe of photogaphs the custome can buy. (ii) Solve the equation (iii) How many photogaphs can be puchased? (b). A vehicle with an empty fuel tank has a mass of 100 kg. One lite of petol has a mass of 737 g. What is the minimum amount of whole lites of petol that would cause the total mass to exceed 1100 kg? Question 1 (II) (a). A vehicle has a mass of 19 kg and uses petol. Anothe vehicle has a mass of 190 kg and uses diesel fuel. 1L of petol has a mass of 737 g. 1L of diesel has a mass of 80 g. What volume of fuel will esult in the two vehicles having the same mass? (i) Wite an equation to descibe the mass of the petol-poweed vehicle with fuel. (ii) Wite an equation to epesent the mass of the diesel-poweed vehicle with fuel. (iii) You want the vehicles to have the same mass with the same volume of fuel. Solve the system of equations to detemine this mass and fuel volume. (b). A wate tank stats with 400L of wate in it. It is being filled at the ate of 0 L/min and thee ae now less than 1000L of wate in the tank. (i) Wite an inequality to epesent this situation (ii) Solve the inequality to detemine the maximum numbe of minutes the wate could have been flowing into the tank. MT/Class IX/Mathematics/016 6 of 6