Moderate Level Questions

1.      Taking today as zero on the number line, if the day before yesterday is 17 January, what is the date 3 days after tomorrow?

2.      Solve them as per the instructions:

• (a) Write a positive integer and a negative integer whose sum is a negative integer.
• (b) Write a positive integer and a negative integer whose sum is a positive integer.
• (c) Write a positive integer and a negative integer whose difference is a negative integer.
• (d) Write a positive integer and a negative integer whose difference is a positive integer.
• (e) Write two integers which are smaller than – 5 but their difference is – 5.
• (f) Write two integers which are greater than – 10 but their sum is smaller than – 10.
• (g) Write two integers which are greater than – 4 but their difference is smaller than – 4.
• (h) Write two integers which are smaller than – 6 but their difference is greater than – 6.
• (i) Write two negative integers whose difference is 7.
• (j) Write two integers such that one is smaller than –11, and other is greater than –11 but their difference is –11.
• (k) Write two integers whose product is smaller than both the integers.
• (l) Write two integers whose product is greater than both the integers.
• (m) Write a pair of integers whose product is –12 and there lies seven integers between them (excluding the given integers).
• (n) Write a pair of integers whose product is – 36 and whose difference is 15.
• (o) Write two integers which are smaller than –3, but their difference is greater than –3.
• (p) Write a pair of integers whose product is –15 and whose difference is 8.

3.      What’s the Error? Reetu evaluated the expression –7 – (–3) and came up with the answer –10. What did Reetu do wrong?

4.      What’s the Error? Ramu evaluated –4 + d for d = –6 and gave an answer of 2. What might Ramu have done wrong?

5.      Height of a place A is 1800 m above sea level. Another place B is 700 m below sea level. What is the difference between the levels of these two places?

6.      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?

7.      A green grocer had a profit of ₹47 on Monday, a loss of ₹12 on Tuesday and loss of ₹8 on Wednesday. Find his net profit or loss in 3 days.

8.      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?

9.      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.

10.    In a quiz, positive marks are given for correct answers and negative marks are given for incorrect answers. If Jack’s scores in five successive rounds were 25, – 5, – 10, 15 and 10, what was his total at the end?

11.    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?

12.    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?

13.    Madhre is standing in the middle of a bridge which is 20 m above the water level of a river. If a 35 m deep river is flowing under the bridge, then find the vertical distance between the foot of Madhre and bottom level of the river.

14.    Mohan deposits ₹2,000 in his bank account and withdraws ₹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.

15.    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?

16.    You are at an elevation 380 m above sea level as you start a motor ride. During the ride, your elevation changes by the following metres: 540 m, –268 m, 116 m, –152 m, 490 m, –844 m, 94 m. What is your elevation relative to the sea level at the end of the ride?

17.    In a test, +3 marks are given for every correct answer and –1 mark are given for every incorrect answer. Sona attempted all the questions and scored +20 marks though she got 10 correct answers.

• (i) How many incorrect answers has she attempted?
• (ii) How many questions were given in the test?

18.    In a true-false test containing 50 questions, a student is to be awarded 2 marks for every correct answer and –2 for every incorrect answer and 0 for not supplying any answer. If Yash secured 94 marks in a test, what are the possibilities of his marking correct or wrong answer?

19.    In an objective type test containing 25 questions. A student is to be awarded +5 marks for every correct answer, –5 for every incorrect answer and zero for not writing any answer. Mention the ways of scoring 110 marks by a student.

20.    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 answers are correct. What is her total score?
• (ii) One of her friends gets only 5 answers correct. What will be her score?

21.    In a class test containing 10 questions, 5 marks are awarded for every correct answer and (–2) marks are awarded for every incorrect answer and 0 for questions not attempted.

• (i) Mohan gets four correct and six incorrect answers. What is his score?
• (ii) Reshma gets five correct answers and five incorrect answers, what is her score?
• (iii) Heena gets two correct and five incorrect answers out of seven questions she attempts. What is her score?

22.    In a class test (+ 3) marks are given for every correct answer and (–2) marks are given for every incorrect answer and no marks for not attempting any question.

• (i) Radhika scored 20 marks. If she has got 12 correct answers, how many questions has she attempted incorrectly?
• (ii) Mohini scores –5 marks in this test, though she has got 7 correct answers. How many questions has she attempted incorrectly?

23.    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?

24.    A multi-storey building has 25 floors above the ground level each of height 5 m. It also has 3 floors in the basement each of height 5 m. A lift in building moves at a rate of 1m/s. If a man starts from 50 m above the ground, how long will it take him to reach at 2nd floor of basement?

25.    Sana and Fatima participated in an apple race. The race was conducted in 6 parts. In the first part, Sana won by 10 seconds. In the second part she lost by 1 minute, then won by 20 seconds in the third part and lost by 25 seconds in the fourth part, she lost by 37 seconds in the fifth part and won by 12 seconds in the last part. Who won the race finally?

26.    The highest point measured above sea level is the summit of Mt. Everest which is 8,848m above sea level and the lowest point is challenger Deep at the bottom of Mariana Trench which is 10911m below sea level. What is the vertical distance between these two points?

27.    If ∆ is an operation such that for integers a and b we have a∆b = a × a + b × b – a × b, then find (–3)∆2 .

28.    If ○ is an operation such that for integers a and b we have a○b = a × b + (a × a + b × b), then find

• (i) ( –3)○(–5)
• (ii) (–6)○2

29.    If ∆ is an operation such that for integers a and b we have a∆b = a × b – 2 × a × b + b × b (–a) × b + b × b then find

• (i) 4∆(–3)
• (ii) (–7)∆(–1)

Also show that 4∆(–3) ≠ (– 3)∆4 and (–7)∆(–1) ≠ (–1)∆(–7).

30.    Below u, v, w and x represent different integers, where u = –4 and x ≠ 1. By using following equations, find each of the values:

u × v = u     x × w = w    u + x = w

• (a) v
• (b) w
• (c) x

Explain your reasoning using the properties of integers.

31.    Water level in a well was 20 m below ground level. During rainy season, rain water collected in different water tanks was drained into the well and the water level rises 5 m above the previous level. The wall of the well is 1 m 20 cm high and a pulley is fixed at a height of 80 cm. Raghu wants to draw water from the well. The minimum length of the rope that he can use is

32.    Suppose we represent the distance above the ground by a positive integer and that below the ground by a negative integer, then answer the following:

• (i) An elevator descends into a mine shaft at the rate of 5 metre per minute. What will be its position after one hour?
• (ii) If it begins to descend from 15 m above the ground, what will be its position after 45 minutes?

33.    A cement company earns a profit of ₹8 per bag of white cement sold and a loss of ₹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.

34.    A shopkeeper earns a profit of ₹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 ₹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?

35.    An application from Science:

An atom consists of charged particles called electrons and protons. Each proton has a charge of +1 and each electron has a charge of –1. Remember number of electrons is equal to number of protons, while answering these questions:

• (a) What is the charge on an atom?
• (b) What will be the charge on an atom if it loses an electron?
• (c) What will be the charge on an atom if it gains an electron?

36.    An application from Social Studies:

Remembering that 1AD came immediately after 1BC, while solving these problems take 1BC as –1 and 1AD as +1.

• (a) The Greeco-Roman era, when Greece and Rome ruled Egypt started in the year 330 BC and ended in the year 395 AD. How long did this era last?
• (b) Bhaskaracharya was born in the year 1114 AD and died in the year 1185 AD. What was his age when he died?
• (c) Turks ruled Egypt in the year 1517 AD and Queen Nefertis ruled Egypt about 2900 years before the Turks ruled. In what year did she rule?
• (d) Greek mathematician Archimedes lived between 287 BC and 212 BC and Aristotle lived between 380 BC and 322 BC. Who lived during an earlier period?