Q1) From the choices given below mark the co-prime numbers
a) 2,3 (b) 2,4 (c) 2,5 (d) 2,107

Q2) Given a rational number -5/9. This rational number can also be known as a) A natural number (b) a rational number
(c) a whole number (d) a real number

Q3) The square root of which number is rational
a) 7 (b) 1.96 (c) 0.04 (d) 13

Q4) 2 - √7 is
a) A rational number (b) an irrational number
(c) a real number (d) a natural number

Q5) To rationalize the denominator of the expression 1 , we multiply and divide by √7 - √6 a) √7 + √6 (b) √6 (c) √7 × √6 (d) √7

Q6) (125)-1/3 can be written as
a) 5 (b) -5 (c) 1/5 (d) none of these

Q7) Every point on the number line
a) can be associated with a rational number
b) can be associated with an irrational number
c) can be associated with a natural number
d) can be associated with a real number

Q8) If z2 = 0.04, then z represents a ____________ number.

Q9) The number of irrational numbers between 15 and 18 is infinite. True or False

Q10) Multiply 5√2 by 17

Q11) Give an example each of two irrational numbers, whose Sum, Difference, Product and Quotient is rational and irrational number.

Q12) Find two rational and irrational numbers between 0.5 and 0.55.

Q13) Represent -12/5 on the number line

Q14) Express 0.047 in the form p/q where p and q are integers and q≠0.

LEVEL II
Q1) Examine whether the following numbers are rational or irrational: i) (2-√3)2 ii) (√2+√3)2 iii) √3-1 √3+1 Q2) Express each of the following as...

...RATIONALNUMBERS
In mathematics, a rationalnumber is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. Since q may be equal to 1, every integer is a rationalnumber. The set of all rationalnumbers is usually denoted by a boldface Q it was thus named in 1895 byPeano after quoziente, Italian for "quotient".
The decimal expansion of a rationalnumber always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rationalnumber. These statements hold true not just for base 10, but also for binary, hexadecimal, or any other integer base.
A real number that is not rational is called irrational. Irrational numbers include √2, π, and e. The decimal expansion of an irrational number continues forever without repeating. Since the set of rationalnumbers is countable, and the set of real numbers is uncountable, almost all real numbers are irrational.
The rationalnumbers can be formally defined as the equivalence classes of the quotient set is the set...

...A rationalnumber is a number that can be written as a ratio of two integers. The decimal of a rationalnumber will either repeat or terminate. There is a way to tell in advance whether a rational number’s decimal representation will repeat or terminate. When trying to find a pattern in the relationship between rationalnumbers and their decimals, it is best to start with a list. A random list of rationalnumbers and their decimal values was made in order to find a pattern. The list included ½, 5/6, 44/10, 3/7, 23/36, 89/53, 3/50, and 4/31. These ratios were 0.5, 0.8333…, 4.4, 0.42857…, 0.63888…, 1.67924…, 0.06, and 0.12903… in decimal form. When analyzing these rationalnumbers, they were placed into categories of repeating and terminating decimals. In the terminating decimal category, the numbers ½, 44/10, and 3/50 had something in common. It was determined that each of the denominators were multiples of two. To solidly identify a pattern, more examples were used. Rationalnumbers such as 2/25, 6/8, and 9/64 helped to identify a definite pattern. What all the denominators of terminating decimals shared was the fact that their prime factors included only 2’s and 5’s. When 2, 10, 50, 25, 8, and 64 were prime factorized the only prime factors were 2’s and 5’s. When...

...Polynomial
The graph of a polynomial function of degree 3
In mathematics, polynomials are the simplest class of mathematical expressions (apart from the numbers and expressions representing numbers). A polynomial is an expression constructed from variables (also called indeterminates) and constants (usually numbers, but not always), using only the operations of addition, subtraction, multiplication, and non-negative integer exponents (which are abbreviations for several multiplications by the same value). However, the division by a constant is allowed, because the multiplicative inverse of a non-zero constant is also a constant. For example, x2 − x/4 + 7 is a polynomial, but x2 − 4/x + 7x3/2 is an algebraic expression that is not a polynomial, because its second term involves a division by the variable x (the term 4/x), and also because its third term contains an exponent that is not a non-negative integer (3/2).
A polynomial function is a function which is defined by a polynomial. Sometimes, the term polynomial is reserved for the polynomials that are explicitly written as a sum (or difference) of terms involving only multiplications and exponentiation by non negative integer exponents. In this context, the other polynomials are called polynomial expressions. For example, is a polynomial expression that represents the same thing as the polynomial The term "polynomial", as an adjective, can also be used for quantities that can...

...
TUTORIAL: NUMBER SYSTEM
1. Determine whether each statement is true or false
a) Every counting number is an integer
b) Zero is a counting number
c) Negative six is greater than negative three
d) Some of the integers is natural numbers
2. List the number describe and graph them on the number line
a) The counting number smaller than 6
b) The integer between -3 and 3
3. Given S = {-3, 0,[pic], [pic], e, , 4, 8…}, identify the set of
(a) natural numbers (b) whole numbers (c) integers
(d) rationalnumbers (e) irrational numbers (f) real numbers
4. Express each of the numbers as a quotient [pic]
(a) 0.7777…… (b) 2.7181818….
5. Write each of the following inequalities in interval notation and show them on the real number line.
(a) 2 < x < 6 (b) (5 < x < (1
(c) (3 ( x ( 7 (d) (2 < x ( 0
(e) x < 3 (f) x ( (1
(g) x ( (2 (h) (3 ( x < 2
6. Show each of the following intervals on the real number line.
(a) [(2, 3] (b) ((4, 4)
(c) (((, 5] (d) [(1, ()
(e) ((3, 6] (f) [(2, 3)
(g) ((2, 0) ( (3, 6) (h) [(6, 2) ( [(3, 7)
2 Evaluate
(a) [pic] (b) 27[pic] (c) [pic] (d) [pic]
(e) (0.36)[pic] (f) (2.56)[pic] (g) [pic] (h) [pic]
7. Simplify the...

...the capsize screening value. To do so, I need to replace d, the displacement value in pounds, with 23,245; and, also replace b, the beam’s width in feet, with 13.5. I do not need to convert the inches to feet using a decimal value because that was already done. By following the order of operations I first need to solve for the exponent before multiplying across. The radical exponent of -1/3 means that I have to apply the reciprocal of the cubed root of d and use that value within my multiplication.
C=4d^(-1/3) b Capsize formula
C=4(23245)^(-1/3) (13.5) Replace variables with given values
C=4(1/〖23245〗^(1/3) )(13.5) Convert the reciprocal of the negative radical exponent
C=4(1/28.539)(13.5) Factor the radical exponent, then the rationalnumber (computed with a calculator and then rounded to thousandths place)
C=4(0.035)(13.5) Multiply all terms
C=1.89 Capsize screening value is less than 2; this boat is safe to sail.
b) The second part of the problem asks that I solve the formula for d, the displacement value in pounds. Since I will use the same capsize formula, I will not replace any of the variables. I just need to convert the formula to solve for d.
...

...In mathematics, a real number is a value that represents a quantity along a continuous line. The real numbers include all the rationalnumbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers such as √2 (1.41421356... the square root of two, an irrational algebraic number) and π (3.14159265..., a transcendental number). Real numbers can be thought of as points on an infinitely long line called the number line or real line, where the points corresponding to integers are equally spaced. Any real number can be determined by a possibly infinite decimal representation such as that of 8.632, where each consecutive digit is measured in units one tenth the size of the previous one. The real line can be thought of as a part of the complex plane, and correspondingly, complex numbers include real numbers as a special case.
These descriptions of the real numbers are not sufficiently rigorous by the modern standards of pure mathematics. The discovery of a suitably rigorous definition of the real numbers — indeed, the realization that a better definition was needed — was one of the most important developments of 19th century mathematics. The currently standard axiomatic definition is that real numbers form the unique complete totally ordered field...

...Real number
In mathematics, a real number is a value that represents a quantity along a continuum, such as 5 (an integer), 3/4 (a rationalnumber that is not an integer), 8.6 (a rationalnumber expressed in decimal representation), and π (3.1415926535..., an irrational number). As a subset of the real numbers, the integers, such as 5, express discrete rather than continuous quantities. Complex numbers include real numbers as a special case. Real numbers can be divided into rationalnumbers, such as 42 and −23/129, and irrational numbers, such as pi and the square root of two. A real number can be given by an infinite decimal representation, such as 2.4871773339..., where the digits continue indefinitely. The real numbers are sometimes thought of as points on an infinitely long line called the number line or real line.
History
Vulgar fractions had been used by the Egyptians around 1000 BC; the Vedic "Sulba Sutras" ("The rules of chords") in, ca. 600 BC, include what may be the first 'use' of irrational numbers. The concept of irrationality was implicitly accepted by early Indian mathematicians since Manava (c. 750–690 BC), who were aware that the square roots of certain numbers such as 2 and 61 could not be...

...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, using the prime factorization method.
16. State whether 6/15 will have...