...-------------------------------------------------
Primenumber
A primenumber (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a primenumber is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2 and 3 in addition to 1 and 6. The fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 can be expressed as a product of primes that is unique up to ordering. This theoremrequires excluding 1 as a prime.
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Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of theintegers. Number theorists study primenumbers (which, when multiplied, give all the integers) as well as the properties of objects made out of integers (such as rational numbers) or defined as generalizations of the integers (such as, for example, algebraic integers).
Integers can be considered either in themselves or as solutions to equations (diophantine geometry). Questions in number...

...3)(x2 + 3x + 9) A) x3 - 6x2 - 6x - 27 B) x3 + 27 C) x3 - 27 D) x3 + 6x2 + 6x - 27
Factor the trinomial, or state that the trinomial is prime. 6) 20x2 + 23x + 6 A) (20x + 3)(x + 2) B) (4x - 3)(5x - 2) C) (4x + 3)(5x + 2) D) Prime
Factor completely, or state that the polynomial is prime. 7) 28x2 y - 28y - 28x2 + 28 A) (2y - 7)(7x - 2)(7x + 2) C) (7y - 7)(2x - 2)(2x + 2) Solve the system by the addition method. 8) 3x + 7y = 40 3x + 2y = 50 A) {(-2, 18)} Solve and check the linear equation. 9) 2x - 4 + 5(x + 1) = -2x - 3 A) {- 2} B) {4 } 3 C) {4 } 9 D) {- 6} B) {(-18, 3)} C) {(-18, 7)} D) {(18, -2)} B) (28y - 28)x2 + 4(-7y + 7) D) (28x2 - 28)y + 7(4 - 4x2 )
1
Solve the equation. x x 10) 27 - = 2 7 A) { 243 } 14 B) {42} C) {3} D) { 243 } 2
First, write the value(s) that make the denominator(s) zero. Then solve the equation. x-1 x+9 11) +3 = 4x x A) x ≠ 0; {34 } 3 5 B) No restrictions; { } 6 C) x ≠ 0, 4; { 37 } 9 D) x ≠ 0; { 37 } 9
Determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 12) 3(2x - 36) = 6x - 108 A) Identity Solve the problem. 13) You inherit $70,000 from a very wealthy grandparent, with the stipulation that for the first year, the money must be invested in two stocks paying 4% and 10% annual interest, respectively. How much should be invested at each rate if the total interest earned for the year is to be $4000? A) $30,000 invested at 4%;...

...COMPARATIVE ANALYSIS OF DATA 1 (RULES) AND DATA 2 (ITEMS)
John Paul Llenos (Organizer)
Patricia Lorica (Secretary)
CED 02 – 601P
Language and Literature Assessment
Rules
Items
Error
Correct
Error
Correct
11 – 47
29 – 45
25 – 44
1 – 37
9 – 36
23 – 35
5 – 30
17 – 30
27 – 30
3 – 29
15 – 28
21 – 27
13 – 27
7 – 19
19 – 17
22 – 46
8 – 35
12 – 35
26 – 31
20 – 30
24 – 29
30 – 26
16 – 25
4 – 21
18 – 20
2 – 17
10 – 17
14 – 12
28 – 10
6 – 1
This paper aims to compare the data’s 1 and 2 through comparative analysis. It can be seen above the top items that obtained the most number of mistakes.
In rules data, there were 47 and 45 students who got items number 11 and 29 wrong. In the same manner with the items data, wherein 46 students got it wrong in item number 22. Items 11 and 29 hold Dangling Modifier as the correct answer. Therefore, error data articulates that Dangling Modifier is one of the grammar and style that needs special attention to the students subjected in this analysis.
In conclusion, though there is only a little difference between the two items. There’s much difference in the overall items between RULES data and ITEMS data. In rules data, most of the students got errors in most of the items compared to the items dat. We noticed that the items in rules data seem more difficult than the items in items data.
70. Dora Williams
WHEN Reuben Pantier ran away and...

...GRADE 5)
CHAPTER 1 (LARGE NUMBERS) ONE MARK QUESTIONS
1. 7000 lakh = _______________________ crore. a) 7 b) 70 c) 700 d) 7000
TWO MARK QUESTIONS
1. Write 700083460 in numerals and their number names in both the systems of numeration. 2. Write the smallest and the greatest numbers using each of the digits 4, 8, 0, 1, 7, 6, 5 only once.
CHAPTER 2 (ROUNDING NUMBERS AND ESTIMATION) ONE MARK QUESTIONS
1. The municipal corporation spent Rs. 25, 37, 981 on repairing the roads (round it to the nearest ten thousand). a) 25,40,000 b) 25,30,000 c) 26,00,000 d) 25,37,000 2. Which of the following numbers could be rounded to 9700? a) 9585 b) 9755 c) 9655 d) 9645
TWO MARK QUESTIONS
1. Round off the greatest 9 – digit number to the nearest ten – lakh. 2. Estimate: 63809 – 5523.
CHAPTER 3 (OPERATIONS ON LARGE NUMBERS) ONE MARK QUESTIONS
1. If 3900 kg of onions are put into sacks and each sack holds 30 kg, how many sacks are required? a) 30 b) 130 c) 117000 d) 3900
TWO MARK QUESTIONS
1. Find the product of the successor of the greatest 3 digit number and 999.
THREE MARK QUESTIONS
1. Raj won 35 tournaments. The prize money totalled up to Rs. 6, 47,500. If he received the same amount for every tournament, how much had he earned per tournament?
CHAPTER 4 (FACTORS AND MULTIPLES) ONE MARK QUESTIONS
1. The prime factorization of 27 is...

... 27. nothing up Stone down
28. Queen down Stone and King up
29. nothing up Stone down
30. Prince down Stone up
31. nothing up Stone down
32. King down Prince up
33. Stone up Prince down
34. One of 9 otherwise identical balls is overweight. How can it be identified after 2 weighings with an old balance?
Ans: Weigh 3 against 3, then you'll know which group of 3 contains the heavy ball. Pick 2 balls from that group and weigh one against the other.
35. One of 27 otherwise identical balls is overweight. How can it be identified after 3 weighings with an old balance?
Ans: Weigh 9 against 9, then 3 against 3.
36. How many ways can you put 10 sweets into 3 bags so that each bag contains an odd number of sweets?
Ans 15 solutions. The first trick is to realise that if you put one bag inside another, then sweets in the inner bag are also in the outer bag. The only workable configuration is to put one bag inside another and leave the third alone. The answers can be obtained using the following octave script, where bag b is inside bag a
37. for a=0:10
38. for b=0:(10-a)
39. c=10-a-b;
40. if (rem((a+b),2)==1 && rem(b,2)==1 && rem(c,2)==1)
41. fprintf('a=%d b=%d c=%d\n',a,b,c)
42. end
43. end
44. end
1. A man has to take a hen, a fox, and some corn across a river. He can only take one thing across at a time. Unless the man is present the fox will eat the hen...

...10th Real Numbers test paper
2011
1.
Express 140 as a product of its prime factors
2.
Find the LCM and HCF of 12, 15 and 21 by the prime factorization method.
3.
Find the LCM and HCF of 6 and 20 by the prime factorization method.
4.
State whether13/3125 will have a terminating decimal expansion or a non-terminating repeating
decimal.
5.
State whether 17/8 will have a terminating decimal expansion or a non-terminating repeating
decimal.
6.
Find the LCM and HCF of 26 and 91 and verify that LCM × HCF = product of the two numbers.
7.
Use Euclid’s division algorithm to find the HCF of 135 and 225
8.
Use Euclid’s division lemma to show that the square of any positive integer is either of the form
3m or 3m + 1 for some integer m
9.
Prove that √3 is irrational.
10. Show that 5 – √3 is irrational
11. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some
integer.
12. An army contingent of 616 members is to march behind an army band of 32 members in a parade.
The two groups are to march in the same number of columns. What is the maximum number of
columns in which they can march?
13. Express 156 as a product of its prime factors.
14. Find the LCM and HCF of 17, 23 and 29 by the prime factorization method.
15. Find the HCF and LCM of 12, 36 and 160,...

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