ABC is a traingle .AD⊥ BC and BD =3 CD =. prove that 2(AB)2 =2(AC)2 + BC 2
Answers
Answer:
Worksheet - Mathematics
Chapter-1 Integers
Topic-1 Addition and Subtraction Of Integers :
1) Sum of two negative number is always ______________. (1)
2) What will be the additive inverse of -5 ?−5 (1)
3) Sum of two positive number is always ______________. (1)
Find The sum of the following : i) ( 4) -7)+ 8 =_____.
ii) (-24) +30=____
(2)
Subt Subtract the following : i) ( 5) -63) -(-3)=_______.
ii) (-42) -21 =_______ .
(2)
6) Use the number line to add the following integers : (-4)+(6) (2)
7) Use the number line to subtract the following : (-3) -(-4) (2)
8) In one of the places in the Arctic , the average temperature in winters is -24°c. In summers ,
the average temperature is 8°C.What is the difference between these temperatures?
(2)
9) On a winter morning in Shimla , the temperature was 2°C below zero . By noon , the
temperature rose by 17 °C . By 4 p.m. in the evening , the temperature came down by 4°C.
What was the temperature at 4 p.m. ?
(3)
Topic-2 Properties of Integers
10) Write down pair of integers whose i)sum is -11. ii) difference gives 8 (2)
11) Which property us reflected in the following : 17×15= 15×17. (1)
12) Fill in the blanks
i) (-14)+(-17) = (-17)+(____). ii) 0-(___)= 6
iii) [24+(-12)]+(____)= (-12)+[24+(-7) iv) ___+36=0
(3)
13) Which property used in the following : i) [-15+7] +(-18) = -15 +[7+(-18)]
ii) 40+(-37)= -37+40
iii) 15- 103 is an integer .
(3)
14) _______________is equals to its additive inverse (1)
Topic-3Multiplication of integers
15) What is multiplicative identity of integers ? (1)
16) Is 10 ×[(6+(-2)]=10×6 +10×(-2)?State Yes or No, also mention the property used (2)
17) Fill in the blanks i) 18×(-4) + 18 ×(-6) = 18 [___+___] =_______ ii) -10× ___=100 (2)
18) Using distributive property find : 105×-32? (3)
19) 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 above the ground , what will be its
position after 45 minutes?
(4)
Topic-3 Division of Integers
20) Find the value of 125 ÷(-25)=? (1)
21) In a test (+5) marks are given for every correct answer and (-2)marks are given for every
incorrect answer . i) Ishika answered all the questions and scored 30 marks though she got
10 correct answers. ii) Ram also answered all the questions and scored (-12) marks though
he got 4 correct answers. How many incorrhad they attempted ?
(4)
22) 0÷10 gives= ? (1)
23) Verify that ÷ ( + ) ≠ ( ÷ ) + ( ÷ )for each of the following values of : a=24, b=-6 ,
c= 4 .
(3)
Step-by-step explanation:
Worksheet - Mathematics
Chapter-1 Integers
Topic-1 Addition and Subtraction Of Integers :
1) Sum of two negative number is always ______________. (1)
2) What will be the additive inverse of -5 ?−5 (1)
3) Sum of two positive number is always ______________. (1)
Find The sum of the following : i) ( 4) -7)+ 8 =_____.
ii) (-24) +30=____
(2)
Subt Subtract the following : i) ( 5) -63) -(-3)=_______.
ii) (-42) -21 =_______ .
(2)
6) Use the number line to add the following integers : (-4)+(6) (2)
7) Use the number line to subtract the following : (-3) -(-4) (2)
8) In one of the places in the Arctic , the average temperature in winters is -24°c. In summers ,
the average temperature is 8°C.What is the difference between these temperatures?
(2)
9) On a winter morning in Shimla , the temperature was 2°C below zero . By noon , the
temperature rose by 17 °C . By 4 p.m. in the evening , the temperature came down by 4°C.
What was the temperature at 4 p.m. ?
(3)
Topic-2 Properties of Integers
10) Write down pair of integers whose i)sum is -11. ii) difference gives 8 (2)
11) Which property us reflected in the following : 17×15= 15×17. (1)
12) Fill in the blanks
i) (-14)+(-17) = (-17)+(____). ii) 0-(___)= 6
iii) [24+(-12)]+(____)= (-12)+[24+(-7) iv) ___+36=0
(3)
13) Which property used in the following : i) [-15+7] +(-18) = -15 +[7+(-18)]
ii) 40+(-37)= -37+40
iii) 15- 103 is an integer .
(3)
14) _______________is equals to its additive inverse (1)
Topic-3Multiplication of integers
15) What is multiplicative identity of integers ? (1)
16) Is 10 ×[(6+(-2)]=10×6 +10×(-2)?State Yes or No, also mention the property used (2)
17) Fill in the blanks i) 18×(-4) + 18 ×(-6) = 18 [___+___] =_______ ii) -10× ___=100 (2)
18) Using distributive property find : 105×-32? (3)
19) 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 above the ground , what will be its
position after 45 minutes?
(4)
Topic-3 Division of Integers
20) Find the value of 125 ÷(-25)=? (1)
21) In a test (+5) marks are given for every correct answer and (-2)marks are given for every
incorrect answer . i) Ishika answered all the questions and scored 30 marks though she got
10 correct answers. ii) Ram also answered all the questions and scored (-12) marks though
he got 4 correct answers. How many incorrect answers had they attempted ?
(4)