IX Maths-I Exam Prep
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Simplify (i). $\frac{4}{7}\sqrt{147} + \frac{3}{8}\sqrt{192} - \frac{1}{5}\sqrt{75}$
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Resulting simplified expression
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Out of 100 persons in a group, 72 persons speak English and 43 persons speak French. Each one out of 100 persons speak at least one language. Then how many speak only English? How many of them speak English and French both?
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29 speak only English, 43 speak both
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(i). Find the reduced form of the ratio of the first quantity to second quantity. (a). 3 years 4 months, 5 years 8 months
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1 : 2
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(ii). Using the property $\frac{a}{b} = \frac{ak}{bk}$, fill in the blanks by substituting proper numbers in the following. $\frac{9}{14} = \frac{...}{4.5} = \frac{...}{42} = \frac{3.5}{...}$
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Fill in with appropriate values
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If $x - 2$ and $x - \frac{1}{2}$ both are the factors of the polynomial $nx^2 - 5x + m$, then show that $m = n = 2$.
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Show m = n = 2
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Which polynomial is to be added to $6m + 3n + 10p$ to get the polynomial $6m + 2n + 3$?
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-n - 10p + 3
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The ratio of two numbers is 5:7. If 40 is added in each number, then the ratio becomes 25:31. Find the numbers.
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50 and 70
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Simplify. $(8m^2 + 3m - 6) - (9m - 7) + (3m^2 - 2m + 4)$
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5m^2 - 8m + 5
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If $(x - 2)$ is a factor of $x^3 - mx^2 + 10x - 20$, then find the value of m.
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m = 4
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Write the following number in its decimal form. $\sqrt{5}$
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Approximately 2.236
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Three persons can build a small house in 8 days. To build the same house in 6 days, how many persons are required?
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4 persons
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If $\frac{15a^2 + 4b^2}{15a^2 - 4b^2} = \frac{47}{7}$, then find the value of the following ratios: (i) $\frac{7a - 3b}{7a + 3b}$ (ii) $\frac{b^2 - 2a^2}{b^2 + 2a^2}$
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Calculate the ratios
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Divide the following polynomials by synthetic division method. Write the quotient and the remainder. $(3x^3 - 8x^2 + x + 7) \div (x - 3)$
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Quotient and remainder
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(i) Multiply the following polynomials. $(m^2 - 2m + 3) (m^4 - 2m^2 + 3m + 2)$
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Resulting polynomial
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(ii) The ratio of present ages of Albert and Salim is 5:9. Five years hence ratio of their ages will be 3 : 5. Find their present ages.
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Present ages of Albert and Salim
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Solve the following equations. (i) $\frac{10x^2 + 15x + 63}{5x^2 - 25x + 12} = \frac{2x + 3}{x - 5}$
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Solution for x
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(ii) $(3x - 4)^2 + (x + 1)^2 = 61$
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Solution for x
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(iii) $(x - 3)(x - 4)^2 (x - 5) - 6$
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Solution for x
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(i) Factorize the following polynomials. $5x^2 - 25x + 12$ $10x^2 + 15x + 63$
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Factors of both polynomials
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(ii) Find the factors of the polynomial given below: $12x^2 + 61x + 77$
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Factors of the polynomial
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Write the following polynomial in coefficient form: $x^4 + 16$
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[1, 0, 0, 0, 16]
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Convert the following ratio into percentage. $\frac{144}{1200}$
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12%
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Find the following ratio. The ratio of diagonal of a square to its side, if the length of side is 7 cm.
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1 : $\sqrt{2}$
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Write any three rational numbers between the two numbers given below. $-4.5$ and $-4.6$
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-4.51, -4.52, -4.53
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Represent the union of two sets by Venn diagram of the following. $A = \{3, 4, 5, 7\}$, $B = \{1, 4, 8\}$
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Venn diagram showing A and B with intersection at 4
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Decide whether set A and B are equal sets. Give reason for your answer. A = Even prime numbers, B = $\{x | 7x - 1 = 13\}$
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A = {2}, B = {2}, hence A = B.
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$P = \{x | x \text{ is an odd natural number, } 1 < x \leq 5\}$. How to write this set in roster form?
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\{3, 5\}
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What is $\sqrt{n}$, if n is not a perfect square number?
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Irrational number
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If $p(x) = x^2 - x + 3$, then $p(7\sqrt{7})$ = ?
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$42\sqrt{7}+3$
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If $P \subseteq M$, then which of the following set represent $P \cap (P \cup M)$?
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P
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The ages of Amit, Nitin and Sumit are 16, 24 and 36 years respectively. What is the ratio of Nitin's age to Sumit's age?
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2 : 3
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