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CHAPTER – 1 INTEGER CBSE Class 7th
1. At Srinagar temperature was – 5°C on Monday and then it dropped by 2°C on Tuesday. What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by 4°C. What was the temperature on this day? 2. A plane is flying at the height of 5000 m above the sea level. At a particular point, it is exactly above a submarine floating 1200 m below the sea level. What is the vertical distance between them? 3. Mohan deposits Rs 2,000 in his bank account and withdraws Rs 1,642 from it, the next day. If withdrawal of amount from the account is represented by a negative integer, then how will you represent the amount deposited? Find the balance in Mohan’s account after the withdrawal. 4. Rita goes 20 km towards east from a point A to the point B. From B, she moves 30 km towards west along the same road. If the distance towards east is represented by a positive integer then, how will you represent the distance travelled towards west? By which integer will you represent her final position from A? 5. Write a pair of integers whose sum gives (a) a negative integer (b) zero (c) an integer smaller than both the integers. (d) an integer smaller than only one of the integers. (e) an integer greater than both the integers. 6. Write a pair of integers whose difference gives (a) a negative integer. (b) zero. (c) an integer smaller than both the integers. (d) an integer greater than only one of the integers. (e) an integer greater than both the integers. 7. Write down a pair of integers whose (a) sum is –3 (b) difference is –5 (c) Difference is 2 (d) sum is 0 8. Write down a pair of integers whose: (a) sum is –7 (b) difference is –10 (c) sum is 0 9. Write a pair of negative integers whose difference gives 8. 10. Write a negative integer and a positive integer whose sum is –5. 11. Write a negative integer and a positive integer whose difference is –3. 12. Find: 4 × (– 8), 8 × (–2), 3 × (–7), 10 × (–1) using number line. 13. Verify (–30) × [13 + (–3)] = [(–30) × 13] + [(–30) × (–3)] 14. In a class test containing 15 questions, 4 marks are given for every correct answer and (–2) marks are given for every incorrect answer. (i) Gurpreet attempts all questions but only 9 of her What will be her score? 15. An elevator descends into a mine shaft at the rate of 5 metre per minute. What will be its position after one hour? If it begins to descend from 15 m above the ground, what will be its position after 45minutes? 16. A certain freezing process requires that room temperature be lowered from 40°C at the rate of 5°C every hour. What will be the room temperature 10 hours after the process begins? 17. In a test (+5) marks are given for every correct answer and (–2) marks are given for every incorrect answer. (i) Radhika answered all the questions and scored 30 marks though she got 10 correct answers. (ii) Jay also answered all the questions and scored (–12) marks though he got 4 correct answers. How many incorrect answers had they attempted? 18. A shopkeeper earns a profit of Re 1 by selling one pen and incurs a loss of 40 paise per pencil while selling pencils of her old stock. (i) In a particular month she incurs a loss of Rs 5. In this period, she sold 45 pens. How many pencils did she sell in this period? (ii) In the next month she earns neither profit nor loss. If she sold 70 pens, how many pencils did she sell? 19. The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2°C per hour until midnight, at what time would the temperature be 8°C below zero? What would be the temperature at mid-night? 20. An elevator descends into a mine shaft at the rate of 6 m/min. If the descent starts from 10 m above the ground level, how long will it take to reach – 350 m. 21. Evaluate each of the following: (a) (–30) ÷ 10 (b) 50 ÷ (–5) (c) (–36) ÷ (–9) (d) (– 49) ÷ (49) (e) 13 ÷ [(–2) + 1] (f ) 0 ÷ (–12) (g) (–31) ÷ [(–30) + (–1)] (h) [(–36) ÷ 12] ÷ 3 (i) [(– 6) + 5)] ÷ [(–2) + 1] 22. Find the product, using suitable properties: (a) 26 × (– 48) + (– 48) × (–36) (b) 8 × 53 × (–125) (c) 15 × (–25) × (– 4) × (–10) (d) (– 41) × 102 (e) 625 × (–35) + (– 625) × 65 (f) 7 × (50 – 2) (g) (–17) × (–29) (h) (–57) × (–19) + 57 23. Verify the following: (a) 18 × [7 + (–3)] = [18 × 7] + [18 × (–3)] (b) (–21) × [(– 4) + (– 6)] = [(–21) × (– 4)] + [(–21) × (– 6)] 24. A cement company earns a profit of Rs 8 per bag of white cement sold and a loss of Rs 5 per bag of grey cement sold. (a) The company sells 3,000 bags of white cement and 5,000 bags of grey cement in a month. What is its profit or loss? (b) What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey bags sold is 6,400 bags. 25. Find each of the following products: (i) (–18) × (–10) × 9 (ii) (–20) × (–2) × (–5) × 7 (iii) (–1) × (–5) × (– 4) × (– 6) MCQ’S 1. In addition and subtraction of two integers , sign of the answer depends upon (a) Smaller number (b) Their difference (c) Their sum (d) Greater numerical value 2. Sum of two negative number is always (a) Positive (b) Negative (c) 0 (d) 1 3. Sum of two Positive number is always (a) Negative (b) Positive (c) 1 (d) 0 4. Identify the property used in the following: 2 x 13 + 8 x 13 = ( 2+8 ) x 13 (a) Commutative (b) Closure (c) Associative (d) Distributive 5. Which number is multiplicative identity for the whole numbers (a) 0 (b) 1 ( c) 2 (d) 3 6. Which property is reflected in the following? 7 x 5 = 5 x 7 (a) Closure (b) Commutative (c) Associative (d) Distributive 7. Which of the following statement is true (a) 7 ÷ 0 = 7 (b) 7 ÷ 0 = 0 (c) 7 ÷ 0 = 0 ÷ 7 (d) 0 ÷ 7 = 0 8. Product of two negative integers is always (a) Always negative (b) Always positive (c) Either positive or negative (d) 0 9. The integer whose product with – 1 is – 40 is (a) 20 (b) – 20 (c) – 40 (d) 40 10. Absolute value of – 11 is (a) – 10 (b) 10 (c) 11 (d) 0 Heat and Temperature 7th CBSE Physics
Check point-01 [Formative Assessments] 1. Fill in the blanks a. Substances which produce large amount of heat on burning are called Fuel. b. Very low temperature reduce the rate of the growth of bacteria c. Degree of hotness of a body is called its temperature. d. Hotness and coldness are comparative term, not absolute. e. Change of the state is caused by heating or cooling a substance. f. First stem engine invented by James watt based on the principal of Transformation of energy. 2. What type of energy change takes place in: a. Thermal power Station: heat energy ®Electrical Energy b. Nuclear power station: Nuclear energy ® Heat energy ® Electrical Energy Check point-02 [Formative Assessments] Fill in the blanks a. Sir Thomas Clifford Albutt in 1866 invented Clinical thermometer. b. Thermometer is used to measure temperature. c. The most commonly use scale to measure temperature is the Celsius scale d. In the Celsius scale freezing point of water is 00 C and boiling point is 1000C e. Lab thermometer can measure temperature safely from 00 C to 1000C. f. The average body temperature is 370C or (98.40C) g. The highest reading on clinical thermometer is 420C. h. An object expands on heating and contracts on cooling. i. The heat can cause change of state in object. State True and False: a. A clinical temperature measure temperature up to 1200C [F] b. A laboratory thermometer has kink in its capillary [F] c. The degree of hotness cannot be estimated by touching and feeling [T] d. Disposing of broken thermometer is common trash is harmful to environment [T] Practice: Answer these Questions: 1. Q. Does every human being have exactly the same body temperature? Answer: No. every human being have little variation in body temperature 2. Q. What is the range of clinical thermometer? Answer: 350C to 420C 3. Q. Why does not a clinical thermometer contain marking above 420C? Answer: This is because no human can survive above 420C. 4. Q. Can a clinical thermometer used to measure temperature of boiling milk? Give reason? Answer: No, because boiling point of milk is more than 1000C which is above highest marking of clinical thermometer. 5. Q. Why is the stem of thermometer made up of glass? Answer: The stem of thermometer made up of glass so that reading became easy 6. Q. Paper and dry cloth catch fire easily. Why are they not used as a fuel? Answer: Paper and dry cloth catch fire easily but cannot produce large amount of heat so they are not used as a fuel. 7. Q. Why a laboratory thermometer cannot be used to measure body temperature? Answer: Ans: There is no ‘kink’ in laboratory thermometer. Therefore the temperature will fall as soon as we remove the thermometer from the mouth and we will not be able to measure the correct temperature of the body. 8. Q. Why kink is provided in the capillary of clinical thermometer? Answer: kink is provided in the capillary of clinical thermometer to prevent level of mercury from falling back. 9. Q. Why drinking water recommended to boil and filtered before using? Answer: Drinking water contain gem that is fatal for body so we recommended to boil and filtered before using water to kill bacteria. 10. Q. What are the differences between clinical and lab Thermometer? Answer: (a) A clinical thermometer reads temperature from 35OC to 42OC, while a laboratory thermometer ranges between –10OC to 110OC. (b) Clinical thermometer has a kink near the bulb while there is no kink in laboratory thermometer. 11. Q. How does digital thermometer measure temperature? Answer: Digital thermometers provide an easy-to-read, LCD display. The heat sensor within the digital thermometer reads the temperature of body and displays it. 12. Q. Why liquid mercury used in thermometer? Answer: Mercury is used in thermometer because of following reasons: i) It does not stick to the walls of capillary tube. ii) Its silvery shine helps us to see temperature accurately. iii) Its expansion is uniform. iv) It does not vaporize easily. 13. Q. Why by touching and feeling the hotness of a body is not sufficient to measure temperature? Answer: Sometime touching and feeling the hotness of a body give us wrong result so touching and feeling the hotness of a body is not sufficient to measure temperature. 14. Q. State two phenomenons involve the transformation of heat energy? Answer: 15. Q. How is life of bacteria affected by heat? Answer: Bacteria cannot grow and multiply at high temperature. 16. Q. State precautions taken while using clinical thermometer? Answer: We should take following precautions while while using clinical thermometer:- i)It should be washed before and after using with an antiseptic solution. ii) We should check or ensures that the mercury level should be 35 degree Celsius before using it. iii)The reading should be taken while keeping the level of mercury along the line of sight. iv)W e should not hold the thermometer by its bulb while reading it. v) We should handle the thermometer with care, as it is breakable. 17. Q. State precautions taken while using Laboratory thermometer? Answer: precautions taken while using Laboratory thermometer are a. Bulb of Laboratory thermometer must be in contact of object properly. b. Reading should be taken without removing from its position. c. Eyes should be at the vertical level d. Do not used to measure temperature below - 100C and above 1100C. 18. Q. Why are bottle containing liquid left with some space at the top? Answer: Bottle containing liquid is left with some space at the top to provide space for expansion of liquid on heating. 19. Q. Why are huge bridge provided with flexible joint? Answer: flexible joint in huge bridge allow expansion in summer and protect from bending. 20. Define Heat and Energy and temperature. Answer: According to Rumford and James Prescott, Heat is a form of energy that is known as Thermal Energy. Energy in a substance is due to movement of its molecules. Energy is capacity to do work. Energy is neither created nor destroyed it can only transformed [changed] one form to another. Temperature is a measure of the degree of hotness and coldness of an object. S.I unit of Temperature is Kelvin. Other Units are degree Celsius and degree Fahrenheit Q. (iv) Why digital thermometers are used these days Ans.: Mercury is a poisonous metal if a thermometer breaks in mouth. . To overcome this, digital thermometers are used these days.  1. AB is a line segment and line l is its perpendicular bisector. If a point P lies on l, show that P is equidistant from A and B.
2. In DABC , ∠Q > ∠R, PA is the bisector of ∠QPR and PM ^QR. Prove that <∠APM = 1/2(∠< Q – ∠<R). 3. D ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. Show that ∠BCD is a right angle. 4. In a right angled triangle, one acute angle is double the other. Prove that the hypotenuse is double the smallest side. 6. Example 5. If the bisector of the vertical angle of a triangle bisects the base, prove that the triangle is isosceles. 7. A triangle ABC is right angled at A. L is a point on BC such that AL ^ BC. Prove that ∠ < BAL = ∠ < ACB 8. Q is a point on the side SR of a Δ PSR such that PQ = PR. Prove that PS > PQ. 9. S is any point on side QR of a Δ PQR. Show that: PQ + QR + RP > 2 PS. 10. D is any point on side AC of a Δ ABC with AB = AC. Show that CD < BD. 11. l || m and M is the mid-point of a line segment AB. Show that M is also the mid-point of any line segment CD, having its end points on l and m, respectively. 12. Bisectors of the angles B and C of an isosceles triangle with AB = AC intersect each other at O. BO is produced to a point M. Prove that ∠MOC =∠ABC. 13. Bisectors of the angles B and C of an isosceles triangle ABC with AB = AC intersect each other at O. Show that external angle adjacent to ∠ABC is equal to ∠BOC. 14. S is any point in the interior of Δ PQR. Show that SQ + SR < PQ + PR. {Produce QS to intersect PR at T} 15. Prove that in a right triangle, hypotenuse is the longest (or largest) side. Related posts: PDF Download CLICK HERE CBSE Sample Questions Papers Maths Ch: Triangle IX Mathematics Congruence of Triangle CBSE Examination Question 2012-13 CBSE Test sample paper- IX Mathematics (Congruent triangle) CBSE TEST PAPER CLASS - IX Mathematics (Congruent triangle) |