Class 9A Past Paper Analysis - PDF

Analysis of Easy/Difficult Questions Class 9A This part of the report shows questions that the children of your class found easy and difficult. This information can be used by you to focus your attention to specific questions an...

Analysis of Easy/Difficult Questions Class 9A This part of the report shows questions that the children of your class found easy and difficult. This information can be used by you to focus your attention to specific questions and skills. You can also use the student performance table to focus on individual students. (Please note that English and Hindi passages are not included here. Log on to www.assetdynamic.com to view the passages). Questions which students of your school found the MOST DIFFICULT compared to the rest of the country: Q Which of these rational numbers is/are less than (-8)? 1 14 A only -7.369 B only -8 19 8 8 14 C only - 7 and -7.369 D only - 7 and -8 19 Skill: Integers and rational numbers, powers and bases Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School B 0% 55% All Schools Q In the following figure, PR ⊥ QS. 2 What is the perimeter of ΔPQR? A 36 cm B 41 cm C 42 cm D 84 cm Skill: Problem solving: advanced or challenging problems Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School C 10% 59% All Schools 6 2408365/M9A/0335/D Q Which of these is 1? 3 ( Note: a 0 = 1, for any non-zero integer a.) A 7 (-4) × 49 -2 B 7 (-4) ÷ 49 2 C 7 (-4) ÷ 49 -2 D 7 (-4) × (-49) -2 Skill: Integers and rational numbers, powers and bases Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School C 0% 48% All Schools Questions which students of your school found the EASIEST compared to the rest of the country: Q Which of these is the same as the Least Common Multiple (LCM) of four numbers 5, 12, 311, 120? 1 A LCM of 5 and 311 B LCM of 311 and 120 C LCM of 5, 12 and 311 D (none of these) Skill: Number sense, related competency and computation skills Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School B 75% 31% All Schools 7 2408365/M9A/0335/D Q Which of these graphs best shows the relation between the speed of the vehicle and its stopping 2 distance? A B C D Skill: Measurement and data interpretation Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School C 67% 36% All Schools Q PQRS is a parallelogram with all FOUR SIDES EQUAL. 3 Which of the following is/are ALWAYS true? I) All its four angles are equal. II) Both its diagonals are of equal length. III) The diagonals are perpendicular to each other. A only I B only II C only III D both II and III 8 2408365/M9A/0335/D Skill: Geometry: concepts and applications Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School C 63% 32% All Schools 9 2408365/M9A/0335/D  Questions With Common Wrong Answer Class 9A From the questions that students across the country have found the most difficult, we have chosen a few to highlight potential misconceptions that students might have. For each question, we have given a break-up (in percentage form) of the number of students choosing a particular option. This has been done both for the section of your school and all student who took ASSET over the world. Compare these to find out how your students have performed. (Please note that English and Hindi passages are not included here. Log on to www.assetdynamic.com to view the passages.) We have highlighted in light grey the correct option and in dark grey the most common wrong answer, and provided an explanation of why students are choosing the most common wrong option. It is recommended that you discuss these questions with the students to uncover students' rationale in choosing the most common wrong option. 4 Q Monica divided a number m by 5. 1 What percentage of m did she get as her answer? A 125% B 120% C 80% D 25% This question tests the understanding of fraction division and conversion of fractions to percentages. Option A is the correct answer since m divided by 4/5 is 5m/4 or 125% of m. Option B shows an error in converting 5/4 to percent. Option C shows an error in fraction division and considering m divided by 4/5 as 4m/5. Option D shows a careless error in converting 5/4 to percent. Performance Option A Option B Option C Option D No. of Students Section 75% 8% 17% 0% 24 Overall 30% 10% 47% 11% 11256 Q Daisy divides a number in the ratio 7 : 4. 2 If x corresponds with one part of the ratio and 20 more than x corresponds with the other part of the ratio, which of the following expressions represents the above situation? ( Note: x is a positive, real number. ) ( 7 A x + 20) / x )} = 4 7 B x /( x + 20))} = 4 ( 7 C x + 20) / x )} = (7 + 4))} 7 D x /( x + 20))} = (7 + 4))} This question tests the skill of forming a linear equation in one variable. Option A is the correct answer as the ratio of the greater part to the lesser part is 7:4, so (x+20)/x = 7/4. Option B shows a confusion in the ratio concept and an inability to form algebraic expressions as it reverses the numerator and the denominator. Option C show an inability to understand ratios as the concept of total ratios is used in this context. Option D not only shows an error in Option C but also an error in framing algebraic expressions. Performance Option A Option B Option C Option D No. of Students Section 79% 13% 4% 4% 24 Overall 41% 44% 6% 8% 9354 10 2408365/M9A/0335/D Q In which of the following pairs are the triangles DEFINITELY congruent? 3 (Note: None of the figures are to scale.) A B C D This question tests studentÔÇÖs understanding of congruence criteria for triangles. Students were expected to use the angle sum property of triangles to find the third angle and thus see that in option D, the triangles are congruent by the angle-side-angle (ASA) or angle-angle-side (AAS) conditions. Many students have chosen option C, not realising that AAA does not prove congruency. Ensure students understand the difference between similarity and congruency and help them understand which conditions are sufficient for congruency and which are not. Show them how we can draw two triangles with the same angles but different side lengths; also, that two right-angled triangles can have the same hypotenuse but the other two sides can be of different lengths. Demonstrate also that in the case of SAS, the congruent angle must be between the two congruent sides, yet this is not so in option A. Performance Option A Option B Option C Option D No. of Students Section 0% 13% 83% 4% 24 Overall 9% 26% 42% 23% 11256 11 2408365/M9A/0335/D  Practice Questions And Explanations Class 9A This section is crafted to aid students in practicing weaker skills. Use these in class discussions, gauge common understanding gaps, and tailor lessons. Answers and explanations are included. Employ a mix of question types to stimulate students' thinking. Here's how we've tailored the practice questions for each subject: For English, if reading comprehension is a challenge, we've provided full passages to work on. In Math, Science, and Social Studies, we've chosen questions based on areas where you've shown room for growth. Hindi practice focuses on non-reading comprehension skills. Computational Thinking covers a variety of skills across the class. Skill: Geometry: concepts and applications (28%) Q What is the measure of angle M of parallelogram MNOP in this figure? (Figure NOT to scale) 1 A 63 o B 91 o C 117 o D 152 o Explanation: C: In a parallelogram, a pair of opposite angles are equal in measure. So we have 10 x - 27 = 7 x. Solving this we get x = 9. So the measure of ∠N = 7 × 9 = 63 o. Now since ON is parallel to MP, ∠N and ∠M are a pair of interior angles on the same side of the transversal MN, they are supplementary. So ∠M = 180 - 63 = 117 o. Note that we are asked the measure of ∠M and not ∠N. Q Leslie and Surekha were standing on opposite sides of a road. Suddenly, they spotted a puppy 2 stranded on the road and both rushed straight to where the puppy was, to pick it up. If Leslie ran at an angle of 35 0 to the edge of the road and Surekha at an angle of 70 0 , at what angle did their paths meet? A 75 0 B 105 0 C 135 0 D 145 0 12 2408365/M9A/0335/D  Explanation: D: Mark the points where Leslie and Surekha are standing as A and B, and the point where the puppy is as C. Draw a line parallel to the sides of the road through C. D is a point on this line. Now ∠DCA = 35 o , as this and the angle marked 35 o , form a pair of alternate interior angles when the side of the road and the line through D are cut by the transversal CA. Now ∠DCB = 180 - 70 = 110 o. Can you reason out why? So the angle marked is of measure 110 + 35 = 145 o. Q In the figure below, lines l and m are parallel but lines p and q are NOT. 3 Which of the following are equal? A angles a and d B angles b and d C angles b and e D angles c and f 13 2408365/M9A/0335/D  Explanation: D: Lines l and m are given to be parallel. Can you see that angles marked c and g in the below figure are a pair of corresponding angles formed when these lines are cut by the transversal q ? Hence they are equal. Now angle marked f is vertically opposite to that marked g and hence are equal. So angles c and f are equal in measure. Angles a and b are a pair of corresponding angles formed when non-parallel lines p and q are cut by a transversal, and hence are not equal. Q Study the following figure: 4 Lines l and m are parallel to each other. What would be the measure of the angle marked z ? A 40 o B 60 o C 80 o D (The given information is not sufficient to answer the question.) 14 2408365/M9A/0335/D  Explanation: C: Lines l and m are parallel, cut by transversal p. The angle marked 120 o in the figure and ∠ABC form a pair of corresponding angles, and hence are equal. So m(∠ABC ) = 120 o. From the figure it can be seen that ∠ABD = 120 o - 40 o = 80 o. Now angle marked z and ∠ABD are vertically opposite angles and hence are equal. So measure of the angle marked z = 80 o. Q Look at the triangles below: 5 Based on these measurements alone, which congruence relation will DEFINITELY be true? A B C D 15 2408365/M9A/0335/D  Explanation: D: In all the 4 triangles given, the three angles are of measure 90 o , 60 o , and 30 o. Can we say that two triangles are congruent, if the three angles on one are equal to the corresponding angles of the other? Look at the two triangles shown below. Are they congruent? Clearly not. So to tell whether two triangles are congruent or not, we need to have some information about the sides too. So we cannot say that ΔLMN is congruent to ΔXYZ, because we do not know anything about the sides of ΔLMN. ∠D, ∠E, and the included side DE of ΔDEF are respectively equal to ∠X, ∠Y, and the included side XY of ΔXYZ. Hence these two triangles are congruent by the ASA congruence rule. Q Mahesh wants to make a quadrilateral by joining two of these triangles. (Triangles should not 6 overlap) Which triangles can he use to form the quadrilateral? A Triangle 1 and Triangle 2 B Triangle 1 and Triangle 3 C Any two of the 3 triangles. D (Two triangles cannot form a quadrilateral.) Explanation: B: In order to be able to join two triangles to form a quadrilateral, should you not have any one side of the first triangle to be equal to one side of the other? If this is not the case, think of how the triangles will fit together. Which of the two triangles given here have a pair of equal sides? Triangle 1 and Triangle 3 both have a side of 8 cm each, so these can be joined along this side to form a quadrilateral. 16 2408365/M9A/0335/D Q The measures of four angles of a quadrilateral are 60°, 72°, 108° and 120°. 7 Which can be said about the quadrilateral? A It has to be a trapezium. B It has to be a rhombus. C It could be any parallelogram. D A quadrilateral with four such angles is not possible. Explanation: A: Can you see that 72 + 108 = 180, and 60 + 120 = 180. So we have two pairs of angles that add up to 180 o. In a parallelogram, in addition to adjacent angles being supplementary, we should also have both pairs of opposite angles equal. That is not so in the given quadrilateral and hence it cannot be a parallelogram. A rhombus is also a parallelogram, and so the given quadrilateral cannot be a rhombus too. In a trapezium, we have a pair of parallel sides and hence two pairs of adjacent angles that are supplementary. Hence the given quadrilateral could be a trapezium. Q Sides QP, PR and RQ of ΔPQR are extended as shown to form angles measuring x, y and z. 8 What is the sum of the measures of the angles marked in the figure? A 180 o B 360 o C 540 o D (We cannot say for sure. It depends on the measures of ∠P, ∠Q, ∠R.) Explanation: B: What ever be the measure of ∠PRQ, measure of ∠PRQ + z = 180 o , as they form a linear pair. Similarly measure of ∠QPR + x = 180 o and measure of ∠PQR + y = 180 o. So we have x + y + z + m(∠PRQ ) + m(∠QPR ) + m(∠PQR ) = 540 o. But by angle sum property of a triangle, m(∠PRQ ) + m(∠QPR ) + m(∠PQR ) = 180 o. substituting this in the above equation, we find that x + y + z = 360 o. 17 2408365/M9A/0335/D  Analysis of Easy/Difficult Questions Class 9B This part of the report shows questions that the children of your class found easy and difficult. This information can be used by you to focus your attention to specific questions and skills. You can also use the student performance table to focus on individual students. (Please note that English and Hindi passages are not included here. Log on to www.assetdynamic.com to view the passages). Questions which students of your school found the MOST DIFFICULT compared to the rest of the country: Q -45, -38, -31, -24......... 1 Which of the following is also a number in the sequence above? A 7 B 4 C 3 D -4 Skill: Number sense, related competency and computation skills Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School B 0% 50% All Schools Q There are 720 boys and 480 girls in a school. 2 What is the difference between the percentage of boys and girls in the school? A 20% B 24% C 33.33% D 50% Skill: Fractions, decimals, ratios and percentages: applications Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School A 25% 70% All Schools Q A teacher gave the following problem to her students: 3 "M is an odd number. Form an odd number using M." The table below shows the number formed by each of her 4 students. Who has/have formed an odd number correctly? A only Vani B only Dadamoni C only Bijoy and Dadamoni D only Vani, Shaivali and Dadamoni 6 2408365/M9B/0338/D  Skill: Algebra: concepts and applications Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School D 25% 64% All Schools Questions which students of your school found the EASIEST compared to the rest of the country: Q Sunita has a grey floor mat with a white circular design as shown here. 1 What is the ratio of the area shaded GREY to the total area of the WHITE CIRCLES? A 10:13 B 12:13 C 13:13 D 25:13 Skill: Applications in daily life: word/visual problems Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School B 63% 44% All Schools Q Daisy divides a number in the ratio 7 : 4. 2 If x corresponds with one part of the ratio and 20 more than x corresponds with the other part of the ratio, which of the following expressions represents the above situation? ( Note: x is a positive, real number. ) ( 7 A x + 20) / x )} = 4 7 B x /( x + 20))} = 4 ( 7 C x + 20) / x )} = (7 + 4))} 7 D x /( x + 20))} = (7 + 4))} Skill: Algebra: concepts and applications Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School A 56% 41% All Schools 7 2408365/M9B/0338/D Q A cubic wooden crate is strengthened by attaching a piece of wood across the diagonal of each 3 face as shown below. The length of the supporting piece of wood is √32 m. What is the volume of the crate? A 43 m3 B 16 3 m 3 C √32 3 m 3 D √64 3 m 3 Skill: Mensuration: area and perimeter; volume and surface area Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School A 50% 39% All Schools 8 2408365/M9B/0338/D  Questions With Common Wrong Answer Class 9B From the questions that students across the country have found the most difficult, we have chosen a few to highlight potential misconceptions that students might have. For each question, we have given a break-up (in percentage form) of the number of students choosing a particular option. This has been done both for the section of your school and all student who took ASSET over the world. Compare these to find out how your students have performed. (Please note that English and Hindi passages are not included here. Log on to www.assetdynamic.com to view the passages.) We have highlighted in light grey the correct option and in dark grey the most common wrong answer, and provided an explanation of why students are choosing the most common wrong option. It is recommended that you discuss these questions with the students to uncover students' rationale in choosing the most common wrong option. 4 Q Monica divided a number m by 5. 1 What percentage of m did she get as her answer? A 125% B 120% C 80% D 25% This question tests the understanding of fraction division and conversion of fractions to percentages. Option A is the correct answer since m divided by 4/5 is 5m/4 or 125% of m. Option B shows an error in converting 5/4 to percent. Option C shows an error in fraction division and considering m divided by 4/5 as 4m/5. Option D shows a careless error in converting 5/4 to percent. Performance Option A Option B Option C Option D No. of Students Section 44% 15% 37% 4% 27 Overall 30% 10% 47% 11% 11256 Q Daisy divides a number in the ratio 7 : 4. 2 If x corresponds with one part of the ratio and 20 more than x corresponds with the other part of the ratio, which of the following expressions represents the above situation? ( Note: x is a positive, real number. ) ( 7 A x + 20) / x )} = 4 7 B x /( x + 20))} = 4 ( 7 C x + 20) / x )} = (7 + 4))} 7 D x /( x + 20))} = (7 + 4))} This question tests the skill of forming a linear equation in one variable. Option A is the correct answer as the ratio of the greater part to the lesser part is 7:4, so (x+20)/x = 7/4. Option B shows a confusion in the ratio concept and an inability to form algebraic expressions as it reverses the numerator and the denominator. Option C show an inability to understand ratios as the concept of total ratios is used in this context. Option D not only shows an error in Option C but also an error in framing algebraic expressions. Performance Option A Option B Option C Option D No. of Students Section 70% 11% 19% 0% 27 Overall 41% 44% 6% 8% 9354 9 2408365/M9B/0338/D Q In which of the following pairs are the triangles DEFINITELY congruent? 3 (Note: None of the figures are to scale.) A B C D This question tests studentÔÇÖs understanding of congruence criteria for triangles. Students were expected to use the angle sum property of triangles to find the third angle and thus see that in option D, the triangles are congruent by the angle-side-angle (ASA) or angle-angle-side (AAS) conditions. Many students have chosen option C, not realising that AAA does not prove congruency. Ensure students understand the difference between similarity and congruency and help them understand which conditions are sufficient for congruency and which are not. Show them how we can draw two triangles with the same angles but different side lengths; also, that two right-angled triangles can have the same hypotenuse but the other two sides can be of different lengths. Demonstrate also that in the case of SAS, the congruent angle must be between the two congruent sides, yet this is not so in option A. Performance Option A Option B Option C Option D No. of Students Section 4% 11% 22% 63% 27 Overall 9% 26% 42% 23% 11256 10 2408365/M9B/0338/D  Practice Questions And Explanations Class 9B This section is crafted to aid students in practicing weaker skills. Use these in class discussions, gauge common understanding gaps, and tailor lessons. Answers and explanations are included. Employ a mix of question types to stimulate students' thinking. Here's how we've tailored the practice questions for each subject: For English, if reading comprehension is a challenge, we've provided full passages to work on. In Math, Science, and Social Studies, we've chosen questions based on areas where you've shown room for growth. Hindi practice focuses on non-reading comprehension skills. Computational Thinking covers a variety of skills across the class. Skill: Fractions, decimals, ratios and percentages: applications (35%) Q A mineral water factory has 6 machines that package 3000 bottles in 1 hour. If 4 more machines 1 of the same type are also put into use, what can be said about the time taken to package the same number of bottles now? A It will be 36 minutes more. B It will be 24 minutes less. C It will be 2 minutes less. D It will be 30 minutes more. Explanation: B: 6 machines package 3000 bottles in 1 hour. Now we put 4 more machines of the same type to use. These 4 machines together would be able to package 23 of the number of bottles as done by 6 machines. That is if we assume that 6 machines do 1 unit of work in 1 hour, 4 machines of the same type would be able to do 23 unit of work in one hour. So when there are 10 machines running, 2 5 1+ 3 = 3 units of work can be done in one hour. So how long would it take to do 1 unit of work? 1 5 3 ÷ 3 = 5 hour = 36 minutes. So what was done in an hour can be done in 36 minutes now, that is we are taking 24 minutes less. Note that with more machines working, it is not possible for us to take more time to complete the work. Q 2 A 3:1:6 B 2:6:1 C 3:1:2 D 1:6:1 11 2408365/M9B/0338/D  Explanation: A: Q If 3 is 25 %, what is ? A 37 1 ⁄ 2 % B 50% C 66 3 ⁄ 2 % D 75% Explanation: 1 A: 25% of something is 4 of it. We are given that 1 is 25%. So can you imagine what the whole would be, if 4 is as given? If the whole is as shown above, what fraction of the whole is 3 3 375 37.5 ? it is 8. Now 8 = 1000 = 1000 = 37.5%. You could also reason out as, " Two parts make 25%. So each part is 12.5% of the whole. So 3 such parts would be 12.5 × 3= 37.5%". Q Rama has a bag with some green and red marbles in the ratio 2:3. She wants to add some more 4 green and red marbles such that their ratio (green marbles: red marbles) remains unchanged. In what ratio should she add the marbles? A 1:1 B 3:2 C 4:6 D (Green and red marbles added in any ratio will change the original ratio of 2:3.) 12 2408365/M9B/0338/D  Explanation: C: For every 2 green marbles in Rama's bag, there are 3 red marbles. So to maintain the ratio, for every 2 green marbles she adds, she should add 3 red marbles as well. That is she should add marbles in the ratio 2:3. Now the ratio 2:3 is the same as 4:6. Q A cake is cut into 3 pieces whose weights are in the ratio 2:1:4 5 If the third piece weighs 360 g more than the second, how much did the whole cake weigh? A 1.44 kg B 1.26 kg C 840 g D 630 g Explanation: 2 C: The weights of the pieces are in the ratio 2:1:4. That is the first piece weights 7 of the whole, 1 4 the second piece 7 of the whole and the third one 7 if the whole. So the excess weight of the third 4 1 3 3 piece over the second piece is 7 - 7 = 7 of the whole. We are given that 7 of the weight of the 7 whole cake is 360 g. So the weight of the cake is 360 × 3 = 840 g. Note that 360 g is NOT the weight of the third piece, but the amount by which it is heavier than the second piece. Q What will be the measure of angle y if 65% of the semi circular region is shaded? 6 A 60 o B 63 o C 65 o D 75 o Explanation: B: If 65% of the semi circular region is shaded, the sector corresponding to angle y would be 100 - 65 = 35% of the semicircular region. The semicircular region corresponds to an angle of 180 o , so the measure of angle y would be 35% of 180 = 63 o. Q On a copying machine you can enlarge or reduce the size of a drawing. Devpal used the machine 7 to make a copy of a drawing and resized it to 60% of the original copy. He was not satisfied with the result so he took the resized copy and increased its size to 140%. What can be said about the size of the final copy? A It is smaller than the original drawing. B It is larger than the original drawing. C It is of the same size as the original drawing. D (Nothing can be said as the dimensions of the drawing are not known.) 13 2408365/M9B/0338/D  Explanation: A: Devpal decreased the size of the drawing to 60% of the original copy. Now when he enlarges it again, he enlarges it to 140% OF THE REDUCED SIZE. That is it becomes 140% of 60% of the original size, that is 84% of the original size. So it is smaller than the original drawing. When dealing with percentages, it is important to ask 60% or 140% OF WHAT. Note that in this question it is 60% of the original drawing and 140% of the reduced drawing. Q Akbar, Ali and Arman are 3 brothers. The ratio of Akbar's age to Arman's age is 1 : 2 and the ratio 8 of Akbar's age to Ali's age is 2 : 5. If the eldest boy is 10 years old, how old is the youngest one? A 1 year B 2 years C 4 years D 5 years Explanation: C: If Akbar's age is x , Arman's age is 2 x. So if Akbar's age is 2 x , Arman's age is 4 x. We are also given that if Akbar's age is 2x, Ali's age is 5 x. So are you able to see that Akbar is the youngest of the 3 boys and Ali is the oldest? Given that Ali is 10 years old. That is 5 x = 10. So x = 2. Now if Ali is 5 x , years old, Akbar is 2 x years old is it not? So Akbar is 4 years old. Note that ratio of ages of Akbar and Ali is 2 : 5. Given that Ali is 10 years old. So we are essentially solving the proportion 2 : 5 = ? : 10. Skill: Integers and rational numbers, powers and bases (40%) Q Which of the following is equal to 1? 1 A 17 -2 + 17 2 B 17 2 - 17 -2 C 17 -2 x 17 2 D 17 2 ÷ 17 -2 Explanation: C: 17 -2 is the same as (17 2 ) -1. Now raising a number to the power -1 is the same as taking its reciprocal. So 17 -2 = 1/17 2. This gives 17 -2 × 17 2 = 1. Look at the expression in option D. When will the quotient of two numbers be equal to 1? When the two numbers are equal, right? Is 17 2 = 17 -2 ? So can the expression in option D be equal to 1? 17 2 ÷ 17 -2 = 17 2 × (1/17 -2 ) = 17 2 × 17 2 = 17 4. Q Given below are the three pairs of numbers. 2 Pair 1: (-10) and (-9) Pair 2: 5.91 and 5.92 2 4 Pair 3: 3 and 5 In which pair(s), can a rational number be found between the given numbers? A only in pair 1 B only in pair 3 C only in pairs 1 and 3 D in all the pairs - pairs 1, 2 and 3 14 2408365/M9B/0338/D  Explanation: D: A rational number is a number that can be written in the form p / q where q is not equal to 0. Is 9.5 a rational number? Yes! It can be written as 95/100. Is -1/2 rational? Yes! It is of form p/q. Now -9.5 is a number between (-10) and (-9) and it is rational as it can be written as -95/100. Can you think of a number that lies between 5.91 and 5.92? 5.911 is a rational number between 5.91 and 5.92. A rational number can be found between any pair of rational numbers, and all the numbers, -10, -9, 5.91, 5.92, 2/3 and 4/5 given here are rational. Q 3 What should come in the empty box to make it a number sentence that is true? A + 125 -1 B + 125 1 C × 125 -1 D × 125 1 Explanation: C: We have a m × a n = a m+n. 125 -2 × 125 -1 = 125 -2 + -1 = 125 -3. Note that a m + a n is not equal to a m+n. Is 2 -2 + 2 -1 = 2 -3 ? In other words is 1/4 + 1/2 = 1/8? No. Similarly 125 -2 + 125 -1 is not equal to 125 -3. Q While solving a numerical in Physics, Archana got the answer as 2.387 x 10 7 instead of 2.367 x 4 10 7 due to a miscalculation. By how much does her answer differ from the correct answer? A 20000000 B 200000 C 2000 D 0.02 Explanation: B: 2.387 × 10 7 = 23870000 and 2.367 × 10 7 = 23670000. So what is the difference between these two numbers? Note that 2.387 × 10 7 - 2.367 × 10 7 = (2.387 - 2.367) × 10 7 and not just (2.387 - 2.367). Q The square root of 27225 lies between 5 ( Note: You need not calculate.) A 50 and 60. B 120 and 130. C 160 and 170. D 500 and 600. Explanation: C: Which are the perfect squares that are somewhere around 27225? 22500 is 150 2 , 25600 is 160 2 , 28900 is 170 2 etc. 27225 lies between 25600 and 28900. So its square root lies between 160 and 170. We cannot say that the square root lies between 500 and 600, because the first two digits of 27225, that is 27 lies between 25 and 36. Note that 500 2 is 250000 and 600 2 is 360000. Q The difference between two temperature readings in an experiment was 9 o. Which of these 6 could be the temperature readings? A 15 o and -6 o B -5 o and 4 o C -1 o and 9 o D -2 o and 11 o 15 2408365/M9B/0338/D  Explanation: B: What does a temperature reading of -6 o tell you? The temperature is 6 o below the zero mark, right? Now what is the difference between readings 15 o and -6 o ? 15 o is above the zero mark and -6 o is below the zero mark, so the difference between them is 21 o , isn't it? What is the difference between -5 o ( 5 o below the zero mark) and 4 o ? ( 4 o above the zero mark) 9 o ! So option B is the correct answer. Find out the differences between the temperatures in options C and D. Q The product of 100 real numbers is -100. AT LEAST how many of these 100 real numbers must be 7 positive? A 99 B 2 C 1 D None Explanation: C: We know that the product of an odd number of negative numbers is negative, and the product of an even number of negative numbers is positive. Since the product of the given 100 real numbers ( an even number of real numbers) is negative, not all of them are negative. We should have some of them positive. How many? We need an odd number of negative integers to make the product negative, and the remaining should be positive. Now 100 is even, and so the difference between 100 and an odd number is also an odd number. So we would have an odd number of positive real numbers as well. What happens if we have just 1 positive real number? The remaining 99 would be negative, and the product would be negative, right? So we should have at least 1 positive number. Q A number is called a perfect square if it is the square of a whole number. If m and n are two 8 perfect squares, which of the following MUST also be a perfect square? A m+n B 2m C 4n D m2 + n2 Explanation: C: Given that n is a perfect square and square root of n is a whole number. Now 4 n = 2 × 2 × n. Can you see that square root of 4 n is twice the square root of n and hence a whole number as well? For problems like these, one approach you may use is to try out with actual numbers, rather than jump into conclusions. Let us take m = 4 and n = 9. m + n = 13, 2 m = 8, 4 n = 36, and m 2 + n 2 = 97. Which of these is a perfect square? Is m 2 + n 2 a perfect square? 16 2408365/M9B/0338/D  Analysis of Easy/Difficult Questions Class 9C This part of the report shows questions that the children of your class found easy and difficult. This information can be used by you to focus your attention to specific questions and skills. You can also use the student performance table to focus on individual students. (Please note that English and Hindi passages are not included here. Log on to www.assetdynamic.com to view the passages). Questions which students of your school found the MOST DIFFICULT compared to the rest of the country: Q Volume of a cylinder is 72π cm 3. The area of its circular base is 9π cm 2. What is the height of 1 the cylinder? A 2 cm B 8 cm C 2π cm D 8π cm Skill: Mensuration: area and perimeter; volume and surface area Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School B 0% 65% All Schools Q A teacher gave the following problem to her students: 2 "M is an odd number. Form an odd number using M." The table below shows the number formed by each of her 4 students. Who has/have formed an odd number correctly? A only Vani B only Dadamoni C only Bijoy and Dadamoni D only Vani, Shaivali and Dadamoni Skill: Algebra: concepts and applications Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School D 13% 64% All Schools 6 2408365/M9C/0341/D Q In the figure below, GI = HI and EF is parallel to GH. 3 I and G are points located on line segments HJ and FI. What is the measure of ∠IJE? A 65 B 60 C 50 D 45 Skill: Geometry: concepts and applications Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School D 0% 44% All Schools Questions which students of your school found the EASIEST compared to the rest of the country: Q Rita cycles to school from home in 12 minutes. 1 If she pedals at the same rate, using wheels with the diameter DOUBLED, how much time will she take to reach school from home? ( Note: If she pedals at the same rate, the number of revolutions the wheels makes in one second remains same ) A 3 min B 6 min C 12 min D 24 min Skill: Applications in daily life: word/visual problems Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School B 83% 54% All Schools 7 2408365/M9C/0341/D Q The sum of the marks obtained by 20 girls of a class in a test is the same as the sum of the marks 2 obtained by 25 boys. The average marks obtained by the girls is __________ that obtained by the boys. A more than B less than C equal to D (We cannot say any of these without knowing their individual marks.) Skill: Measurement and data interpretation Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School A 83% 65% All Schools Q Shown here is trapezium PQRS with PS parallel to QR. 3 What is the area of trapezium PQRS? A 32 cm 2 B 40 cm 2 C 44.62 cm 2 D 64 cm 2 Skill: Mensuration: area and perimeter; volume and surface area Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School A 50% 35% All Schools 8 2408365/M9C/0341/D  Questions With Common Wrong Answer Class 9C From the questions that students across the country have found the most difficult, we have chosen a few to highlight potential misconceptions that students might have. For each question, we have given a break-up (in percentage form) of the number of students choosing a particular option. This has been done both for the section of your school and all student who took ASSET over the world. Compare these to find out how your students have performed. (Please note that English and Hindi passages are not included here. Log on to www.assetdynamic.com to view the passages.) We have highlighted in light grey the correct option and in dark grey the most common wrong answer, and provided an explanation of why students are choosing the most common wrong option. It is recommended that you discuss these questions with the students to uncover students' rationale in choosing the most common wrong option. 4 Q Monica divided a number m by 5. 1 What percentage of m did she get as her answer? A 125% B 120% C 80% D 25% This question tests the understanding of fraction division and conversion of fractions to percentages. Option A is the correct answer since m divided by 4/5 is 5m/4 or 125% of m. Option B shows an error in converting 5/4 to percent. Option C shows an error in fraction division and considering m divided by 4/5 as 4m/5. Option D shows a careless error in converting 5/4 to percent. Performance Option A Option B Option C Option D No. of Students Section 52% 0% 26% 17% 23 Overall 30% 10% 47% 11% 11256 Q Daisy divides a number in the ratio 7 : 4. 2 If x corresponds with one part of the ratio and 20 more than x corresponds with the other part of the ratio, which of the following expressions represents the above situation? ( Note: x is a positive, real number. ) ( 7 A x + 20) / x )} = 4 7 B x /( x + 20))} = 4 ( 7 C x + 20) / x )} = (7 + 4))} 7 D x /( x + 20))} = (7 + 4))} This question tests the skill of forming a linear equation in one variable. Option A is the correct answer as the ratio of the greater part to the lesser part is 7:4, so (x+20)/x = 7/4. Option B shows a confusion in the ratio concept and an inability to form algebraic expressions as it reverses the numerator and the denominator. Option C show an inability to understand ratios as the concept of total ratios is used in this context. Option D not only shows an error in Option C but also an error in framing algebraic expressions. Performance Option A Option B Option C Option D No. of Students Section 61% 13% 13% 4% 23 Overall 41% 44% 6% 8% 9354 9 2408365/M9C/0341/D Q In which of the following pairs are the triangles DEFINITELY congruent? 3 (Note: None of the figures are to scale.) A B C D This question tests studentÔÇÖs understanding of congruence criteria for triangles. Students were expected to use the angle sum property of triangles to find the third angle and thus see that in option D, the triangles are congruent by the angle-side-angle (ASA) or angle-angle-side (AAS) conditions. Many students have chosen option C, not realising that AAA does not prove congruency. Ensure students understand the difference between similarity and congruency and help them understand which conditions are sufficient for congruency and which are not. Show them how we can draw two triangles with the same angles but different side lengths; also, that two right-angled triangles can have the same hypotenuse but the other two sides can be of different lengths. Demonstrate also that in the case of SAS, the congruent angle must be between the two congruent sides, yet this is not so in option A. Performance Option A Option B Option C Option D No. of Students Section 17% 17% 17% 43% 23 Overall 9% 26% 42% 23% 11256 10 2408365/M9C/0341/D  Practice Questions And Explanations Class 9C This section is crafted to aid students in practicing weaker skills. Use these in class discussions, gauge common understanding gaps, and tailor lessons. Answers and explanations are included. Employ a mix of question types to stimulate students' thinking. Here's how we've tailored the practice questions for each subject: For English, if reading comprehension is a challenge, we've provided full passages to work on. In Math, Science, and Social Studies, we've chosen questions based on areas where you've shown room for growth. Hindi practice focuses on non-reading comprehension skills. Computational Thinking covers a variety of skills across the class. Skill: Applications in daily life: word/visual problems (25%) Q A 200 metre long train running at a speed of 10 metre/second starts passing by a 200 metre long 1 platform at exactly 11:00:10. What would be the time when the entire train just finishes crossing the platform? A 11:00:20 B 11:00:30 C 11:00:44 D 11:00:50 Explanation: D: The total distance travelled by the train when the entire train finishes crosses the platform starting from 11:00:10 = (the length of platform) + (the length of the train) = 400 m. The speed of the train is 10 m/s. So the time taken by the train to cross the platform = total distance travelled ÷ speed = 400 ÷10 seconds = 40 seconds. Thus the train crosses the platform at 11:00:50. Q An ant at one corner of an 8 m x 6 m rectangular floor spots a piece of sweet at the opposite 2 corner. What is the MINIMUM distance the ant has to travel to reach the sweet? A 7m B 10 m C 14 m D 28 m 11 2408365/M9C/0341/D  Explanation: B: Is it not that the shortest path from ant's current position to the point where the sweet lies is along the diagonal of the rectangular floor? What is the length of the diagonal of the rectangle with length 8 m and breadth 6 m? By Pythagorean theorem, it is √(8 2 + 6 2 ) m = 10 m. Clearly the path along the length and breadth of the rectangular floor which is 14 m is 4 m longer than that along the diagonal. Hence, B is the answer and not C. Q Amit drives a car daily to his office from his home. The distance is 24 km. On a particular day, he 3 left his home at 8:15 AM, drove for 5 km at a speed of 60 kmph. After that he was stuck in a traffic jam of 1 km during this stretch he could drive only at a speed of 15 kmph. (Figure shown above is upto scale) Which of these is the closest to the MINIMUM speed at which he should drive after the traffic jam to ensure that he reaches the office by 8:45 AM? ( Assuming that he can drive the way he wants to, without any traffic jams. ) A 20 kmph B 30 kmph C 60 kmph D 80 kmph Explanation: 5 C: The time taken to travel first 5 km = distance travelled/speed = 60 hours = 5 minutes. The time 1 taken to travel next 1 km = 15 hours = 4 minutes. Amit wants to reach his office within 30 minutes of the start of the journey. This means he has to travel the next 18 km within 21 minutes. If Amit drives at the speed of 60 kmph, he would reach the office in another 18 minutes, 3 minutes to 8:45 PM. If he drives at the speed of 30 kmph, he would reach in another 36 minutes at 9:00 AM. Thus, C is the answer. 18 (Note: the minimum speed with which Amit should drive = 21 × 60 hours, little more than 51 kmph.) 12 2408365/M9C/0341/D Q Shown here is a cartoon strip of Dilbert. Of the three people that can be seen, the one on the left 4 is Dilbert, on the right is Alice and in the middle is The Boss. If next year, The Boss again gets a 2% raise and Dilbert gets a 3% raise, which of these will NOT change as compared to this year? A ratio of their pays B sum of their pays C amount of raise they got D All of the above will change. Explanation: D: Let x be Dilbert's pay and y be The Boss's pay after the raise. Then Dilbert's pay will be x + 3x 2y 100 and The Boss's pay will be y + 100 in the next year. The ratio 1.03 x : 1.02 y is not the same as x : y. Pays of both Dilbert and The Boss are different and the amount of raise is also different. So the sum of their pays will also be different in each of the two years. Hence, none of A, B and C can be the answer. The ratio, the sum of their pays and the amount of raise they got will change in the next year. Q Jamal's house (J) and Tarang's house (T) are 10 km apart on a straight road. One day, both of them 5 started from their houses at the same moment and met on the road after half an hour. If Jamal walked 2 km/hr faster than Tarang, which diagram correctly shows the position of their meeting point, P? A B C D 13 2408365/M9C/0341/D  Explanation: C: Jamal walked 2 km/hr faster than Tarang. Both of them starts at the same time. In half an hour when they meet each other, is it not that Jamal would have walked 1 km more than Tarang ? Among the given options, only C could be the answer. Had they met each other after walking for an hour, Jamal would have walked 2 km more than Tarang. But they meet each other after half an hour and not an hour. So D cannot be the answer. Q Look at this tube of Glow Face cream being sold under a special offer: 6 How many grams of cream does the tube contain? A 30 B 37.5 C 120 D 150 Explanation: D: Suppose x g of Glow Face cream in a tube is sold without the special offer. Then the amount of cream provided extra under the special offer = x /4)} g = 30 g. So, x = 120 g. The tube contains 120 + 30 (=150) g of cream. Q Baiju's car has a maximum fuel capacity of 50 litres and gives a mileage of 12 km/l. This is what 7 the fuel gauge of his car showed when he started his journey from Ahmedabad to Surat. AT MOST how many kilometres would he have been able to travel after this on the remaining fuel? A 6.25 km B 75 km C 150 km D 600 km Explanation: B: The pointer in the dial will be horizontal pointing to full when the fuel in the tank is 50 litres. It will be vertical when the fuel is 25 litres. So the pointer at the current position points to 25 ÷ 4 (6.25) litres. The mileage of Baiju's car is 12 km/l. So Baiju can go maximum of 12 × 25/4 km, which is 75 km. Hence B is the answer and not A. 14 2408365/M9C/0341/D Q Given here are the advertisement rates (in Rs.) for a 10 second slot during prime time on major TV 8 channels, as published in a magazine. Additional 25% surcharge will be applicable on the rates. Rates for Times Now and Aaj Tak channels are not given. But it is known that the difference between their rates, excluding surcharge, is Rs. 1000. What will be the difference in their rates if 25% surcharge is included? A Rs. 250 B Rs. 1000 C Rs. 1250 D Nothing can be said without knowing the exact rates. Explanation: C: Let the rates of advertisement for Times Now and Aaj Tak excluding surcharge be Rs. x and Rs. 25x 25y y respectively. The rates including surcharge will be x + 100 and y + 100 respectively. The difference in the rates including surcharge is Rs. 1.25 x - 1.25 y = Rs. 1.25( x - y ) = 1.25 × 1000 = Rs. 1250. 15 2408365/M9C/0341/D  Analysis of Easy/Difficult Questions Class 9D This part of the report shows questions that the children of your class found easy and difficult. This information can be used by you to focus your attention to specific questions and skills. You can also use the student performance table to focus on individual students. (Please note that English and Hindi passages are not included here. Log on to www.assetdynamic.com to view the passages). Questions which students of your school found the MOST DIFFICULT compared to the rest of the country: Q x and y are any two numbers such that x : y = 4:5. 1 Which of these is DEFINITELY true? 5 A xy = 20 B x / y )} = 4 C -4 x + 5 y = 0 D 5x-4y=0 Skill: Fractions, decimals, ratios and percentages: applications Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School D 10% 54% All Schools Q Rita cycles to school from home in 12 minutes. 2 If she pedals at the same rate, using wheels with the diameter DOUBLED, how much time will she take to reach school from home? ( Note: If she pedals at the same rate, the number of revolutions the wheels makes in one second remains same ) A 3 min B 6 min C 12 min D 24 min Skill: Applications in daily life: word/visual problems Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School B 13% 54% All Schools 6 2408365/M9D/0344/D Q A class was asked about their favourite pastime. Each student gave one pastime and the data 3 obtained was represented in a pie chart as shown below. The total numbers of students who preferred PC games and reading was 13. How many students preferred cricket? A 1 B 7 C 14 D 28 Skill: Measurement and data interpretation Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School B 25% 65% All Schools Questions which students of your school found the EASIEST compared to the rest of the country: 7 2408365/M9D/0344/D Q The top, front and side views of a solid built with identical cubes are shown below. 1 Which of these could be the solid? A B C D Skill: Geometry: concepts and applications Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School A 70% 45% All Schools Q A rectangular container that measures 2 cm x 11 cm x 20 cm is completely filled with water. The 2 water is then poured into a hollow cylindrical container of base radius 5 cm. What is the height of water in the cylindrical container? 28 184 A 5 cm B 14 cm C 5 cm D 88 cm Skill: Mensuration: area and perimeter; volume and surface area Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School A 50% 35% All Schools -3 Q Which point on the number line shown below is closest to 101 ? 3 8 2408365/M9D/0344/D Skill: Integers and rational numbers, powers and bases Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School D 38% 28% All Schools 9 2408365/M9D/0344/D  Questions With Common Wrong Answer Class 9D From the questions that students across the country have found the most difficult, we have chosen a few to highlight potential misconceptions that students might have. For each question, we have given a break-up (in percentage form) of the number of students choosing a particular option. This has been done both for the section of your school and all student who took ASSET over the world. Compare these to find out how your students have performed. (Please note that English and Hindi passages are not included here. Log on to www.assetdynamic.com to view the passages.) We have highlighted in light grey the correct option and in dark grey the most common wrong answer, and provided an explanation of why students are choosing the most common wrong option. It is recommended that you discuss these questions with the students to uncover students' rationale in choosing the most common wrong option. 4 Q Monica divided a number m by 5. 1 What percentage of m did she get as her answer? A 125% B 120% C 80% D 25% This question tests the understanding of fraction division and conversion of fractions to percentages. Option A is the correct answer since m divided by 4/5 is 5m/4 or 125% of m. Option B shows an error in converting 5/4 to percent. Option C shows an error in fraction division and considering m divided by 4/5 as 4m/5. Option D shows a careless error in converting 5/4 to percent. Performance Option A Option B Option C Option D No. of Students Section 48% 3% 48% 0% 31 Overall 30% 10% 47% 11% 11256 Q Daisy divides a number in the ratio 7 : 4. 2 If x corresponds with one part of the ratio and 20 more than x corresponds with the other part of the ratio, which of the following expressions represents the above situation? ( Note: x is a positive, real number. ) ( 7 A x + 20) / x )} = 4 7 B x /( x + 20))} = 4 ( 7 C x + 20) / x )} = (7 + 4))} 7 D x /( x + 20))} = (7 + 4))} This question tests the skill of forming a linear equation in one variable. Option A is the correct answer as the ratio of the greater part to the lesser part is 7:4, so (x+20)/x = 7/4. Option B shows a confusion in the ratio concept and an inability to form algebraic expressions as it reverses the numerator and the denominator. Option C show an inability to understand ratios as the concept of total ratios is used in this context. Option D not only shows an error in Option C but also an error in framing algebraic expressions. Performance Option A Option B Option C Option D No. of Students Section 48% 39% 10% 3% 31 Overall 41% 44% 6% 8% 9354 10 2408365/M9D/0344/D Q In which of the following pairs are the triangles DEFINITELY congruent? 3 (Note: None of the figures are to scale.) A B C D This question tests studentÔÇÖs understanding of congruence criteria for triangles. Students were expected to use the angle sum property of triangles to find the third angle and thus see that in option D, the triangles are congruent by the angle-side-angle (ASA) or angle-angle-side (AAS) conditions. Many students have chosen option C, not realising that AAA does not prove congruency. Ensure students understand the difference between similarity and congruency and help them understand which conditions are sufficient for congruency and which are not. Show them how we can draw two triangles with the same angles but different side lengths; also, that two right-angled triangles can have the same hypotenuse but the other two sides can be of different lengths. Demonstrate also that in the case of SAS, the congruent angle must be between the two congruent sides, yet this is not so in option A. Performance Option A Option B Option C Option D No. of Students Section 6% 48% 29% 16% 31 Overall 9% 26% 42% 23% 11256 11 2408365/M9D/0344/D  Practice Questions And Explanations Class 9D This section is crafted to aid students in practicing weaker skills. Use these in class discussions, gauge common understanding gaps, and tailor lessons. Answers and explanations are included. Employ a mix of question types to stimulate students' thinking. Here's how we've tailored the practice questions for each subject: For English, if reading comprehension is a challenge, we've provided full passages to work on. In Math, Science, and Social Studies, we've chosen questions based on areas where you've shown room for growth. Hindi practice focuses on non-reading comprehension skills. Computational Thinking covers a variety of skills across the class. Skill: Geometry: concepts and applications (36%) Q What is the measure of angle M of parallelogram MNOP in this figure? (Figure NOT to scale) 1 A 63 o B 91 o C 117 o D 152 o Explanation: C: In a parallelogram, a pair of opposite angles are equal in measure. So we have 10 x - 27 = 7 x. Solving this we get x = 9. So the measure of ∠N = 7 × 9 = 63 o. Now since ON is parallel to MP, ∠N and ∠M are a pair of interior angles on the same side of the transversal MN, they are supplementary. So ∠M = 180 - 63 = 117 o. Note that we are asked the measure of ∠M and not ∠N. Q Leslie and Surekha were standing on opposite sides of a road. Suddenly, they spotted a puppy 2 stranded on the road and both rushed straight to where the puppy was, to pick it up. If Leslie ran at an angle of 35 0 to the edge of the road and Surekha at an angle of 70 0 , at what angle did their paths meet? A 75 0 B 105 0 C 135 0 D 145 0 12 2408365/M9D/0344/D  Explanation: D: Mark the points where Leslie and Surekha are standing as A and B, and the point where the puppy is as C. Draw a line parallel to the sides of the road through C. D is a point on this line. Now ∠DCA = 35 o , as this and the angle marked 35 o , form a pair of alternate interior angles when the side of the road and the line through D are cut by the transversal CA. Now ∠DCB = 180 - 70 = 110 o. Can you reason out why? So the angle marked is of measure 110 + 35 = 145 o. Q In the figure below, lines l and m are parallel but lines p and q are NOT. 3 Which of the following are equal? A angles a and d B angles b and d C angles b and e D angles c and f 13 2408365/M9D/0344/D  Explanation: D: Lines l and m are given to be parallel. Can you see that angles marked c and g in the below figure are a pair of corresponding angles formed when these lines are cut by the transversal q ? Hence they are equal. Now angle marked f is vertically opposite to that marked g and hence are equal. So angles c and f are equal in measure. Angles a and b are a pair of corresponding angles formed when non-parallel lines p and q are cut by a transversal, and hence are not equal. Q Study the following figure: 4 Lines l and m are parallel to each other. What would be the measure of the angle marked z ? A 40 o B 60 o C 80 o D (The given information is not sufficient to answer the question.) 14 2408365/M9D/0344/D  Explanation: C: Lines l and m are parallel, cut by transversal p. The angle marked 120 o in the figure and ∠ABC form a pair of corresponding angles, and hence are equal. So m(∠ABC ) = 120 o. From the figure it can be seen that ∠ABD = 120 o - 40 o = 80 o. Now angle marked z and ∠ABD are vertically opposite angles and hence are equal. So measure of the angle marked z = 80 o. Q Look at the triangles below: 5 Based on these measurements alone, which congruence relation will DEFINITELY be true? A B C D 15 2408365/M9D/0344/D  Explanation: D: In all the 4 triangles given, the three angles are of measure 90 o , 60 o , and 30 o. Can we say that two triangles are congruent, if the three angles on one are equal to the corresponding angles of the other? Look at the two triangles shown below. Are they congruent? Clearly not. So to tell whether two triangles are congruent or not, we need to have some information about the sides too. So we cannot say that ΔLMN is congruent to ΔXYZ, because we do not know anything about the sides of ΔLMN. ∠D, ∠E, and the included side DE of ΔDEF are respectively equal to ∠X, ∠Y, and the included side XY of ΔXYZ. Hence these two triangles are congruent by the ASA congruence rule. Q Mahesh wants to make a quadrilateral by joining two of these triangles. (Triangles should not 6 overlap) Which triangles can he use to form the quadrilateral? A Triangle 1 and Triangle 2 B Triangle 1 and Triangle 3 C Any two of the 3 triangles. D (Two triangles cannot form a quadrilateral.) Explanation: B: In order to be able to join two triangles to form a quadrilateral, should you not have any one side of the first triangle to be equal to one side of the other? If this is not the case, think of how the triangles will fit together. Which of the two triangles given here have a pair of equal sides? Triangle 1 and Triangle 3 both have a side of 8 cm each, so these can be joined along this side to form a quadrilateral. 16 2408365/M9D/0344/D Q The measures of four angles of a quadrilateral are 60°, 72°, 108° and 120°. 7 Which can be said about the quadrilateral? A It has to be a trapezium. B It has to be a rhombus. C It could be any parallelogram. D A quadrilateral with four such angles is not possible. Explanation: A: Can you see that 72 + 108 = 180, and 60 + 120 = 180. So we have two pairs of angles that add up to 180 o. In a parallelogram, in addition to adjacent angles being supplementary, we should also have both pairs of opposite angles equal. That is not so in the given quadrilateral and hence it cannot be a parallelogram. A rhombus is also a parallelogram, and so the given quadrilateral cannot be a rhombus too. In a trapezium, we have a pair of parallel sides and hence two pairs of adjacent angles that are supplementary. Hence the given quadrilateral could be a trapezium. Q Sides QP, PR and RQ of ΔPQR are extended as shown to form angles measuring x, y and z. 8 What is the sum of the measures of the angles marked in the figure? A 180 o B 360 o C 540 o D (We cannot say for sure. It depends on the measures of ∠P, ∠Q, ∠R.) Explanation: B: What ever be the measure of ∠PRQ, measure of ∠PRQ + z = 180 o , as they form a linear pair. Similarly measure of ∠QPR + x = 180 o and measure of ∠PQR + y = 180 o. So we have x + y + z + m(∠PRQ ) + m(∠QPR ) + m(∠PQR ) = 540 o. But by angle sum property of a triangle, m(∠PRQ ) + m(∠QPR ) + m(∠PQR ) = 180 o. substituting this in the above equation, we find that x + y + z = 360 o. 17 2408365/M9D/0344/D  Analysis of Easy/Difficult Questions Class 9E This part of the report shows questions that the children of your class found easy and difficult. This information can be used by you to focus your attention to specific questions and skills. You can also use the student performance table to focus on individual students. (Please note that English and Hindi passages are not included here. Log on to www.assetdynamic.com to view the passages). Questions which students of your school found the MOST DIFFICULT compared to the rest of the country: Q The sheet of paper shown below is folded along the dotted lines to form a cube. 1 Which of these pairs of letters will be on OPPOSITE faces of the cube? A P and U B Q and T C R and T D P and S Skill: Problem solving: advanced or challenging problems Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School B 0% 59% All Schools Q In the following figure, PQRS is a parallelogram. 2 What is the measure of ∠QUT? A 65 o B 95 o C 100 o D 150 o Skill: Geometry: concepts and applications Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School B 13% 70% All Schools 6 2408365/M9E/0347/D Q Zubin has subscribed to a newspaper. On weekdays, the price of the newspaper is Rs 3. On 3 Saturday and Sunday, the price of the newspaper is Rs 5. He goes for a trip for 3 consecutive days in the month of January which had 5 Saturdays and 5 Sundays, due to which the newspaper is not delivered to him on those three days. He receives a bill of Rs 100 for the month. Which of the following could be the three days? A Saturday, Sunday and Monday B Thursday, Friday and Saturday C Wednesday, Thursday and Friday D Monday, Tuesday and Wednesday Skill: Applications in daily life: word/visual problems Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School A 17% 63% All Schools Questions which students of your school found the EASIEST compared to the rest of the country: Q Last year, Ketan sold 40 bags of rice at a price of Rs 800 per bag. 1 This year, he sold some bags of rice at a price 20% less than the last year's price. However, he made the same amount of money he made last year from selling rice. What is the percentage INCREASE in the number of bags he sold this year? A 10% B 20% C 25% D 50% Skill: Applications in daily life: word/visual problems Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School C 57% 31% All Schools 3 Q For a party 120 pieces of cakes were ordered, of which 4 of them were chocolate cakes and the 2 rest pineapple cakes. At the end of the party, 12 of the chocolate cakes and all of the pineapple cakes were left uneaten. What fraction of the UNEATEN cakes are chocolate cakes? 1 3 3 1 A 2 B 5 C 8 D 4 Skill: Applications in daily life: word/visual problems Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School B 50% 28% All Schools 7 2408365/M9E/0347/D Q In the puzzle below, the circles should be filled with numbers 1 to 8 such that the product of the 3 numbers in the circles attached to each quadrant gives the number written inside the quadrant. For example, the product of 6, 8 and the third number in the first quadrant is 240 and the product of 3 numbers in the fourth quadrant is 105 as shown in the figure below. Which number should come in the shaded circle? A 1 B 3 C 5 D 7 Skill: Problem solving: advanced or challenging problems Correct % answered correct % answered correct Graph Answer (your students) (all students) Your School B 67% 48% All Schools 8 2408365/M9E/0347/D  Questions With Common Wrong Answer Class 9E From the questions that students across the country have found the most difficult, we have chosen a few to highlight potential misconceptions that students might have. For each question, we have given a break-up (in percentage form) of the number of students choosing a particular option. This has been done both for the section of your school and all student who took ASSET over the world. Compare these to find out how your students have performed. (Please note that English and Hindi passages are not included here. Log on to www.assetdynamic.com to view the passages.) We have highlighted in light grey the correct option and in dark grey the most common wrong answer, and provided an explanation of why students are choosing the most common wrong option. It is recommended that you discuss these questions with the students to uncover students' rationale in choosing the most common wrong option. 4 Q Monica divided a number m by 5. 1 What percentage of m did she get as her answer? A 125% B 120% C 80% D 25% This question tests the understanding of fraction division and conversion of fractions to percentages. Option A is the correct answer since m divided by 4/5 is 5m/4 or 125% of m. Option B shows an error in converting 5/4 to percent. Option C shows an error in fraction division and considering m divided by 4/5 as 4m/5. Option D shows a careless error in converting 5/4 to percent. Performance Option A Option B Option C Option D No. of Students Section 17% 26% 43% 13% 23 Overall 30% 10% 47% 11% 11256 Q Daisy divides a number in the ratio 7 : 4. 2 If x corresponds with one part of the ratio and 20 more than x corresponds with the other part of the ratio, which of the following expressions represents the above situation? ( Note: x is a positive, real number. ) ( 7 A x + 20) / x )} = 4 7 B x /( x + 20))} = 4 ( 7 C x + 20) / x )} = (7 + 4))} 7 D x /( x + 20))} = (7 + 4))} This question tests the skill of forming a linear equation in one variable. Option A is the correct answer as the ratio of the greater part to the lesser part is 7:4, so (x+20)/x = 7/4. Option B shows a confusion in the ratio concept and an inability to form algebraic expressions as it reverses the numerator and the denominator. Option C show an inability to understand ratios as the concept of total ratios is used in this context. Option D not only shows an error in Option C but also an error in framing algebraic expressions. Performance Option A Option B Option C Option D No. of Students Section 30% 30% 22% 17% 23 Overall 41% 44% 6% 8% 9354 9 2408365/M9E/0347/D Q In which of the following pairs are the triangles DEFINITELY congruent? 3 (Note: None of the figures are to scale.) A B C D This question tests studentÔÇÖs understanding of congruence criteria for triangles. Students were expected to use the angle sum property of triangles to find the third angle and thus see that in option D, the triangles are congruent by the angle-side-angle (ASA) or angle-angle-side (AAS) conditions. Many students have chosen option C, not realising that AAA does not prove congruency. Ensure students understand the difference between similarity and congruency and help them understand which conditions are sufficient for congruency and which are not. Show them how we can draw two triangles with the same angles but different side lengths; also, that two right-angled triangles can have the same hypotenuse but the other two sides can be of different lengths. Demonstrate also that in the case of SAS, the congruent angle must be between the two congruent sides, yet this is not so in option A. Performance Option A Option B Option C Option D No. of Students Section 0% 39% 52% 9% 23 Overall 9% 26% 42% 23% 11256 10 2408365/M9E/0347/D  Practice Questions And Explanations Class 9E This section is crafted to aid students in practicing weaker skills. Use these in class discussions, gauge common understanding gaps, and tailor lessons. Answers and explanations are included. Employ a mix of question types to stimulate students' thinking. Here's how we've tailored the practice questions for each subject: For English, if reading comprehension is a challenge, we've provided full passages to work on. In Math, Science, and Social Studies, we've chosen questions based on areas where you've shown room for growth. Hindi practice focuses on non-reading comprehension skills. Computational Thinking covers a variety of skills across the class. Skill: Geometry: concepts and applications (21%) Q What is the measure of angle M of parallelogram MNOP in this figure? (Figure NOT to scale) 1 A 63 o B 91 o C 117 o D 152 o Explanation: C: In a parallelogram, a pair of opposite angles are equal in measure. So we have 10 x - 27 = 7 x. Solving this we get x = 9. So the measure of ∠N = 7 × 9 = 63 o. Now since ON is parallel to MP, ∠N and ∠M are a pair of interior angles on the same side of the transversal MN, they are supplementary. So ∠M = 180 - 63 = 117 o. Note that we are asked the measure of ∠M and not ∠N. Q Leslie and Surekha were standing on opposite sides of a road. Suddenly, they spotted a puppy 2 stranded on the road and both rushed straight to where the puppy was, to pick it up. If Leslie ran at an angle of 35 0 to the edge of the road and Surekha at an angle of 70 0 , at what angle did their paths meet? A 75 0 B 105 0 C 135 0 D 145 0 11 2408365/M9E/0347/D  Explanation: D: Mark the points where Leslie and Surekha are standing as A and B, and the point where the puppy is as C. Draw a line parallel to the sides of the road through C. D is a point on this line. Now ∠DCA = 35 o , as this and the angle marked 35 o , form a pair of alternate interior angles when the side of the road and the line through D are cut by the transversal CA. Now ∠DCB = 180 - 70 = 110 o. Can you reason out why? So the angle marked is of measure 110 + 35 = 145 o. Q In the figure below, lines l and m are parallel but lines p and q are NOT. 3 Which of the following are equal? A angles a and d B angles b and d C angles b and e D angles c and f 12 2408365/M9E/0347/D  Explanation: D: Lines l and m are given to be parallel. Can you see that angles marked c and g in the below figure are a pair of corresponding angles formed when these lines are cut by the transversal q ? Hence they are equal. Now angle marked f is vertically opposite to that marked g and hence are equal. So angles c and f are equal in measure. Angles a and b are a pair of corresponding angles formed when non-parallel lines p and q are cut by a transversal, and hence are not equal. Q Study the following figure: 4 Lines l and m are parallel to each other. What would be the measure of the angle marked z ? A 40 o B 60 o C 80 o D (The given information is not sufficient to answer the question.) 13 2408365/M9E/0347/D  Explanation: C: Lines l and m are parallel, cut by transversal p. The angle marked 120 o in the figure and ∠ABC form a pair of corresponding angles, and hence are equal. So m(∠ABC ) = 120 o. From the figure it can be seen that ∠ABD = 120 o - 40 o = 80 o. Now angle marked z and ∠ABD are vertically opposite angles and hence are equal. So measure of the angle marked z = 80 o. Q Look at the triangles below: 5 Based on these measurements alone, which congruence relation will DEFINITELY be true? A B C D 14 2408365/M9E/0347/D  Explanation: D: In all the 4 triangles given, the three angles are of measure 90 o , 60 o , and 30 o. Can we say that two triangles are congruent, if the three angles on one are equal to the corresponding angles of the other? Look at the two triangles shown below. Are they congruent? Clearly not. So to tell whether two triangles are congruent or not, we need to have some information about the sides too. So we cannot say that ΔLMN is congruent to ΔXYZ, because we do not know anything about the sides of ΔLMN. ∠D, ∠E, and the included side DE of ΔDEF are respectively equal to ∠X, ∠Y, and the included side XY of ΔXYZ. Hence these two triangles are congruent by the ASA congruence rule. Q Mahesh wants to make a quadrilateral by joining two of these triangles. (Triangles should not 6 overlap) Which triangles can he use to form the quadrilateral? A Triangle 1 and Triangle 2 B Triangle 1 and Triangle 3 C Any two of the 3 triangles. D (Two triangles cannot form a quadrilateral.) Explanation: B: In order to be able to join two triangles to form a quadrilateral, should you not have any one side of the first triangle to be equal to one side of the other? If this is not the case, think of how the triangles will fit together. Which of the two triangles given here have a pair of equal sides? Triangle 1 and Triangle 3 both have a side of 8 cm each, so these can be joined along this side to form a quadrilateral. 15 2408365/M9E/0347/D Q The measures of four angles of a quadrilateral are 60°, 72°, 108° and 120°. 7 Which can be said about the quadrilateral? A It h