BLE Assignment 1 - Summit to sir Coming Sunday | Assignment 1: BLE Mathematics Preparation

FOCUS EDGE EDUCATION NETWORK (FEEN)

Grade 08 BLE Assignment: Mathematics

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NOTICE TO BLE STUDENTS: Everyone must bring their practice copy and show this assignment to Sabal Sir. Strict action will be taken if not completed!

SECTION 1: SET (समूह)

1. If the Universal set U = { x : x is a whole number less than 15 }, A = { prime numbers } and B = { odd numbers }, represent the relationship between sets A and B in a Venn diagram. Are they overlapping or disjoint sets?

यदि सर्वव्यापक समूह U = { x : x, 15 भन्दा साना पूर्ण संख्याहरू हुन् }, A = { रूढ संख्याहरू } र B = { विजोड संख्याहरू } छन् भने, समूह A र B बीचको सम्बन्धलाई भेन चित्रमा देखाउनुहोस्। यी समूहहरू खप्टिएका हुन् वा अलगिएका हुन्?

Hint: First list elements of A and B. If they have common elements like {3, 5, 7, 11, 13}, they are overlapping.

2. Let P = { factors of 12 } and Q = { factors of 18 }. Find P intersection Q and represent it in a Venn diagram.

यदि P = { 12 का गुणनखण्डहरू } र Q = { 18 का गुणनखण्डहरू } भए, P प्रतिच्छेदन Q पत्ता लगाउनुहोस् र यसलाई भेन चित्रमा प्रस्तुत गर्नुहोस्।

Hint: List factors of 12 (1, 2, 3, 4, 6, 12) and 18 (1, 2, 3, 6, 9, 18). Find common numbers.

3. Write all possible subsets of the set M = { a, b, c }. Also, identify the proper and improper subsets.

समूह M = { a, b, c } का सबै सम्भावित उपसमूहहरू लेख्नुहोस्। साथै, उचित र अनुचित उपसमूहहरू पहिचान गर्नुहोस्।

Hint: Total subsets = 2^3 = 8. The set itself is the only improper subset.

4. In a class of 40 students, 25 like Mathematics and 20 like Science. If 10 students like both subjects, find the number of students who like neither of the subjects using a Venn diagram.

40 जना विद्यार्थी भएको एउटा कक्षामा, 25 जनाले गणित र 20 जनाले विज्ञान मन पराउँछन्। यदि 10 जनाले दुवै विषय मन पराउँछन् भने, भेन चित्र प्रयोग गरी कुनै पनि विषय मन नपराउने विद्यार्थीको संख्या पत्ता लगाउनुहोस्।

Hint: Use the formula n(U) = n(M) + n(S) - n(M intersection S) + n(M union S) complement.

5. If n(A) = 45, n(B) = 35 and n(A union B) = 60, find the value of n(A intersection B) and represent it in a Venn diagram.

यदि n(A) = 45, n(B) = 35 र n(A union B) = 60 भए, n(A प्रतिच्छेदन B) को मान पत्ता लगाउनुहोस् र यसलाई भेन चित्रमा देखाउनुहोस्।

Hint: Use the relation: n(A union B) = n(A) + n(B) - n(A intersection B).

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SECTION 2: PROFIT AND LOSS (नाफा र नोक्सान)

1. A shopkeeper bought a mobile phone for Rs 15,000 and marked its price 20% above the cost price. If he then sold it with a 10% discount, find his profit or loss percentage.

एक पसलेले एउटा मोबाइल फोन रु 15,000 मा किनेर त्यसको अंकित मूल्य क्रय मूल्यभन्दा 20% बढी राखे। यदि उनले 10% छुट दिएर सो मोबाइल बेचे भने, उनको नाफा वा नोक्सान प्रतिशत पत्ता लगाउनुहोस्।

Hint: MP = CP + 20% of CP. Then find SP = MP - 10% of MP. Finally, find Profit% = [(SP-CP)/CP] * 100.

2. The marked price of a calculator is Rs 1,200. If it is sold for Rs 1,020 after allowing a certain percentage of discount, find the discount percentage.

एउटा क्याल्कुलेटरको अंकित मूल्य रु 1,200 छ। यदि केही प्रतिशत छुट दिएपछि यसलाई रु 1,020 मा बेचियो भने, छुट प्रतिशत पत्ता लगाउनुहोस्।

Hint: Discount Amount = MP - SP. Then, Discount% = (Discount Amount / MP) * 100.

3. A watch is sold for Rs 2,260 after a 13% VAT was added to its price after a 10% discount. Find the marked price of the watch.

एउटा घडीमा 10% छुट दिएर 13% भ्याट जोड्दा त्यसको बिक्री मूल्य रु 2,260 हुन्छ भने, सो घडीको अंकित मूल्य पत्ता लगाउनुहोस्।

Hint: Let MP be x. Price after discount = 0.9x. Then, 1.13 * (0.9x) = 2260. Solve for x.

4. If the cost price of 10 articles is equal to the selling price of 8 articles, find the profit or loss percentage.

यदि 10 वटा सामानको क्रय मूल्य 8 वटा सामानको बिक्री मूल्यसँग बराबर छ भने, नाफा वा नोक्सान प्रतिशत पत्ता लगाउनुहोस्।

Hint: Let CP of 1 article be Rs 1. CP of 8 articles = Rs 8. SP of 8 articles = Rs 10. Profit = Rs 2.

5. A shopkeeper marks his goods at such a price that after allowing a 12.5% discount, he still makes a profit of 20%. If the cost price of an item is Rs 1,400, find its marked price.

एक पसलेले आफ्नो सामानको मूल्य यसरी निर्धारण गर्छन् कि 12.5% छुट दिँदा पनि उनलाई 20% नाफा हुन्छ। यदि एउटा सामानको क्रय मूल्य रु 1,400 छ भने, त्यसको अंकित मूल्य पत्ता लगाउनुहोस्।

Hint: Find SP from CP and Profit first. Then use that SP to find MP using the discount percentage.

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SECTION 3: SIMPLE INTEREST (साधारण ब्याज)

1. Ganga deposited Rs 3,500 in a bank at a 7% per annum simple interest rate. How much interest will she receive at the end of 4 years?

गंगाले एउटा बैंकमा प्रतिवर्ष 7% साधारण ब्याजदरमा रु 3,500 जम्मा गरिन्। 4 वर्षको अन्त्यमा उनले कति ब्याज पाउनेछिन्?

Hint: Use the direct formula: Interest (I) = (P * T * R) / 100.

2. At what rate of simple interest per annum will Rs 7,600 yield Rs 1,254 as interest in 3 years?

कुन वार्षिक साधारण ब्याजदरमा रु 7,600 को 3 वर्षमा रु 1,254 ब्याज हुन्छ?

Hint: Use the formula for Rate (R) = (I * 100) / (P * T).

3. In how many years will the interest on Rs 5,000 at 10% per annum be equal to the interest on Rs 8,000 at 5% per annum for 5 years?

कति वर्षमा रु 5,000 को 10% वार्षिक दरले हुने ब्याज, रु 8,000 को 5% वार्षिक दरले 5 वर्षमा हुने ब्याजसँग बराबर हुन्छ?

Hint: First calculate the interest for the second case (Rs 8000). Then use that interest to find Time (T) for the first case.

4. A sum of money amounts to Rs 6,600 in 2 years and Rs 7,800 in 4 years at simple interest. Find the principal and the rate of interest.

साधारण ब्याजमा कुनै रकम 2 वर्षमा रु 6,600 र 4 वर्षमा रु 7,800 हुन्छ। सावाँ र ब्याजदर पत्ता लगाउनुहोस्।

Hint: Interest for 2 years = Rs 7,800 - Rs 6,600. Subtract this interest from the 2-year amount to find the Principal (P).

5. If the simple interest on a certain sum of money for 3 years at 8% per annum is Rs 1,200 less than the simple interest on the same sum for 5 years at the same rate, find the sum.

यदि कुनै निश्चित सावाँको 8% वार्षिक दरले 3 वर्षको साधारण ब्याज, सोही सावाँको सोही दरले 5 वर्षको ब्याजभन्दा रु 1,200 कम छ भने, सावाँ पत्ता लगाउनुहोस्।

Hint: Let the Principal be P. Form the equation: [ (P * 5 * 8) / 100 ] - [ (P * 3 * 8) / 100 ] = 1200.

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SECTION 4: INDICES (घातांक)

1. Simplify using the laws of indices: (x^a / x^b)^(a + b) * (x^b / x^c)^(b + c) * (x^c / x^a)^(c + a)

घातांकको नियम प्रयोग गरी सरल गर्नुहोस्: (x^a / x^b)^(a + b) * (x^b / x^c)^(b + c) * (x^c / x^a)^(c + a)

Hint: Use (x^a / x^b) = x^(a-b). Then apply the power rule: (x^(a-b))^(a+b) = x^(a^2 - b^2).

2. Evaluate the value of: (27 / 8)^(-2/3) * (81 / 16)^(3/4)

मान पत्ता लगाउनुहोस्: (27 / 8)^(-2/3) * (81 / 16)^(3/4)

Hint: Write 27 as 3^3, 8 as 2^3, 81 as 3^4, and 16 as 2^4. Then apply the power of a quotient rule.

3. If a = 2 and b = 3, find the value of (a^b + b^a)^(-1).

यदि a = 2 र b = 3 भए, (a^b + b^a)^(-1) को मान पत्ता लगाउनुहोस्।

Hint: First calculate 2^3 and 3^2, add them, and then take the reciprocal.

4. Simplify: [ (x^(m+n) * x^(n+p) * x^(p+m)) / (x^m * x^n * x^p)^2 ]

सरल गर्नुहोस्: [ (x^(m+n) * x^(n+p) * x^(p+m)) / (x^m * x^n * x^p)^2 ]

Hint: Add the exponents in the numerator and multiply the exponents in the denominator by 2. Then subtract.

5. Solve for x: 2^(x + 3) * 4^(x - 1) = 16

x को मान पत्ता लगाउनुहोस्: 2^(x + 3) * 4^(x - 1) = 16

Hint: Convert all bases to 2. 4^(x-1) becomes 2^(2x-2) and 16 becomes 2^4. Equate the total power of 2.

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SECTION 5: ALGEBRAIC EXPRESSION (बीजगणितीय अभिव्यञ्जक)

1. Factorize the given expression: ax + bx + ay + by

दिइएको अभिव्यञ्जकलाई खण्डीकरण गर्नुहोस्: ax + bx + ay + by

Hint: Group the terms in pairs: (ax + bx) + (ay + by). Take 'x' common from the first part and 'y' common from the second.

2. Factorize using the formula a^2 - b^2: 169 - 196z^2

a^2 - b^2 को सूत्र प्रयोग गरी खण्डीकरण गर्नुहोस्: 169 - 196z^2

Hint: Write the expression as (13)^2 - (14z)^2 and then use the formula (a - b)(a + b).

3. Factorize the following trinomial: x^2 + 10x + 24

दिइएको त्रिपदीय अभिव्यञ्जकलाई खण्डीकरण गर्नुहोस्: x^2 + 10x + 24

Hint: Find two numbers whose sum is 10 and product is 24. Split the middle term 10x into 6x + 4x.

4. Factorize: a^3 + 125

खण्डीकरण गर्नुहोस्: a^3 + 125

Hint: Express it as a^3 + 5^3 and use the formula: a^3 + b^3 = (a + b)(a^2 - ab + b^2).

5. Simplify: (x^2 - 9) / (x^2 + 5x + 6)

सरल गर्नुहोस्: (x^2 - 9) / (x^2 + 5x + 6)

Hint: Factorize both the numerator and denominator first, then cancel the common terms.

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