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Algebra Math - Junior आधुनिक विद्या निकेतन ट्यूशन सेंटर Visit: avnlearn.com

Mr. Guddu Kumar

Algebraic Expression

  1. Write the following using literals, numbers and signs of basic operations.
    1. x increased by 12
    2. y decreased by 7
    3. The difference of a and b. when a > b
    4. 5 times x added to 7 times y
    5. Sum of x and the quotient of y by 5
    6. x taken away from 4
    7. 2 less than the quotient of x by y
    8. x multiplied by itself
    9. Twice x increased by y
    10. Thrice x added to y squared
    11. x cubed less than y cubed
  2. Write the following in the exponential form:
    1. b × b × b × …15 times
    2. y × y × y × …20 times
    3. 14 × a × a × a × a × b × b × b
    4. 6 × x × x × y × y
    5. 3 × z × z × z × y × y × x
  3. Write down the following in the product form:
    1. x2y4
    2. 6y5
    3. 9xy2z
    4. 10a3b3c3
  4. If a = 2 and b = 3. find the value of
    1. a + b
    2. a2 + ab
    3. ab − a2
    4. 2a − 3b
    5. 5a2 − 2ab
    6. a3 − b3
  5. If x = 1, y = 2 and z = 5, find the value of
    1. 3x − 2y + 4z
    2. x2 + y2 + z2
    3. 2x2 − 3y2 + z2
    4. xy + yz − zx
    5. 2x2y − 5yz + xy2
    6. x3 − y3 − z3
  6. If p = −2, q = −1 and r = 3, find the value of
    1. p2 + q2 − r2
    2. 2p2 − q2 + 3r
    3. p − q − r
    4. p3 + q3 + r3 + 3pqr
    5. p4 +q4 - r4
    6. 3p2q + 5pq2 + 2pqr
  7. Write the coefficient of
    1. x in 13x
    2. y in −5y
    3. y2 in 8xy2z
    4. z in −7xz
    5. p in −2pqr
    6. a in 6ab
    7. x3 in x3
    8. x2 in −x2
  8. Write die numerical coefficient of
    1. ab
    2. −6bc
    3. 7xyz
    4. −2x3y2z
  9. Write the constant term of
    1. 3x2 + 5x + 8
    2. 2x2 − 9
    3. 4y2 − 5y + \(\frac{3}{5}\)
    4. z3 - 2z2 + z − \(\frac{8}{3}\)
  10. Identify the monomials, binomials and trinomials in the following:
    1. −2xyz
    2. 5 + 7x3y3z3
    3. −5x3
    4. a + b − 2c
    5. xy + yz - zx
    6. x5
    7. 2x + 1
    8. −14
    9. ax3 + bx3 + cx + d
  11. Write all the terms of the algebraic expressions:
    1. 4x5 − 6y4 + 7x2y − 9
    2. 9x3 − 5z4 + 7x3y − xyz
  12. Identify the like terms in the following:
    1. a2, b2, −2a2, c2 , 4a
    2. 3x, 4xy, −yz, −zy, \(\frac{1}{2}\)zy
    3. −2xy2, x2y, 5y2x, x2z
    4. abc, ab2c, acb2, c2ab, b2ac, a2bc, cab2
Add:
    1. 3x, 7x
    2. 7y, −9y
    3. 2xy 5xy, −xy
    4. 3x, 2y
    5. 2x2, 3x2, 7x2
    6. 6a3, −4a3, 10a3, − 8a3
    7. 7xyz, −5xyz, 9xyz, − 8xyz
    8. x2 −a2, − 5x2 + 2a2, − 4x2 + 4a2
    1. x − 3y − 2z, 5x + 7y − z and −7x − 2y + 4z
    2. m2 − 4m + 5, −2m2 + 6m − 6 and −m2 − 2m − 7
    3. 2x2 − 3xy + y2, −7x2 − 5xy − 2y2 and 4x2 + xy − 6y2
    4. 4xy − 5yz − 7zx, −5xy + 2yz + zx and −2xy − 3yz + 3zx
    1. 3a − 2b + 5c, 2a + 5b − 7c, − a − b + c
    2. 8a − 6ab + 5b, 6a − ab − 8b, − 4a + 2ab + 3b
    3. 2x3 − 3x2 + 7x − 8, − 5x3 + 2x2 − 4x + 1, 3 − 6x + 5x2 − x3
    4. 2x2 − 8xy + 7y2 − 8xy2, 2xy2 + 6xy − y2 + 3x2, 4y2 − xy − x2 + xy2
    5. x3 + y3 − Z3 + 3xyz, − x3 + y3 + z3 − 6xyz, x3 − y3 − z
    6. 2 + x − x2 + 6x3, − 6 − 2x + 4x2 − 3x3, 2 + x2, 3 − x3 + 4x − 2x
Subtract:
    1. 5x from 2x
    2. −xy from 6xy
    3. 3a from 5b
    4. −7x from 9y
    5. 10x2 from −7x2
    6. a2 − b2 from b2 − a2
    1. 5a + 7b − 2c from 3a − 7b + 4c
    2. a − 2b − 3c from −2a + 5b − 4c
    3. 5x2 − 3xy + y2 from 7x2 − 2xy − 4y2
    4. 6x3 − 7x2 + 5x − 3 from 4 − 5x + 6x2 − 8x3
    5. x3 + 2x2y + 6xy2 − y3 from y3 − 3xy2
    6. −11x2y2 + 7xy − 6 from 9x2y2 − 6xy + 9
    7. −2a + b + 6d from 5a − 2b − 3c
Simplify:
    1. 2p3 − 3p2 + 4p5 − 6p3 + 2p2 − 8p − 2 + 6p + 8
    2. 2x2 − xy + 6x − 4y + 5xy − 4x + 6x + 3y
    3. x4 − 6x3 + 2x − 7 + 7x3 − x + 5x2 + 2 − x4
    1. a − (b − 2a)
    2. 4x − (3y − x + 2z)
    1. (a2 + b2 + 2ab) − (a2 + b2 − 2ab)
    2. −3(a + b) + 4(2a − 3b) − (2a − b)
    3. −4x2 + {(2x2 − 3) − (4 − 3x2)}
    4. −2(x2 − y2 + xy) − 3(x2 + y2 − xy)
    5. a − [2b − {3a − (2b − 3c)}]
    6. − x + [5y − {x − (5y − 2x)}]
    7. 86 − [15x − 7(6x − 9) − 2{10x − 5(2 − 3x)}]
    8. 12x − [3x2 + 5x2 − {7x2 − (4 − 3x − x3) + 6x3} − 3x]
    9. 5a − [a2 − {2a(1 − a + 4a2)− 3a(a2 − 5a3)}] − 8a
    10. 3 − [x − {2y −(5x + y − 3) + 2x2} −(x2 − 3y)]
    11. xy − [yz − zx − {yx −(3y − xz)−(xy − zy)}]
    12. 2a − 3b − [3a − 2b − {a − c − (a − 2b)}]
    13. −a − [a + {a + b − 2a − (a − 2b)} − b]

Simple Equations

  1. Write each of the following statements as an equation:
    1. 5 times a number equals 40.
    2. A number Increased by 8 equals 15.
    3. 25 exceeds a number by 7.
    4. 5 subtracted from thrice a number is 16.
  2. Write a statement for each of the equations, given below:
    1. x − 7 = 14
    2. 2y = 18
    3. 11 + 3x = 17
    4. 2x − 3 = 13
    5. 12y − 30 = 6
    6. \(\frac{2z}{3}\) = 8
  3. Verify by substitution that
    1. the root of 3x − 5 = 7 is x = 4
    2. the root of 3 + 2x = 9 is x = 3
  4. Solve each of the following equations by the trial-and-error method:
    1. y + 9 = 13
    2. x − 7 = 10
    3. 4x = 28
    4. 3y = 36
    5. 11 + x = 19
    6. \(\frac{x}{3}\) = 4
    7. 2x − 3 = 9
    8. \(\frac{1}{2}\)x + 7 = 11
    9. 2y + 4 = 3y
Solve each, of the following equations and. verify the answer in each case:
    1. x – 1 = 0
    2. x + 1 = 0
    3. x – 1 = 5
    4. x + 6 = 2
    5. y – 4 = –7
    6. y – 4 = 4
    7. y + 4 = 4
    8. y + 4 = –4
    9. x + 5 = 12
    1. 3l = 42
    2. \(\frac{b}{2}\) = 6
    3. \(\frac{p}{7}\) = 4
    4. 4x = 25
    5. 8y = 36
    6. \(\frac{z}{3}\) = \(\frac{5}{4}\)
    7. \(\frac{a}{5}\) = \(\frac{7}{15}\)
    8. 20t = –10
    1. 3n – 2 = 46
    2. 5m + 7 = 17
    3. \(\frac{20p}{3}\) = 40
    4. \(\frac{3p}{10}\) = 6
    5. 10p + 10 = 100
    1. 10p = 100
    2. \(\frac{\text{p}}{4} = 5\)
    3. \(\frac{\text{–P}}{3} = 5\)
    4. \(\frac{3p}{4} = 6\)
    5. 3s = –9
    6. 3s + 12 = 0
    7. 3s = 0
    8. 2q = 6
    9. 2q – 6 = 0
    10. 2q + 6 = 0
    11. 2q + 6 = 12
    1. 2y + \(\frac{5}{2}\) = \(\frac{37}{2}\)
    2. 5t + 28 = 10
    3. \(\frac{a}{5}\) + 3 = 2
    4. \(\frac{q}{4}\) + 7 = 5
    5. \(\frac{5}{2}\)x = 10
    6. \(\frac{5}{2}\)x = \(\frac{52}{4}\)
    7. 7m + \(\frac{19}{2}\) = 13
    8. 6z + 10 = –2
    9. \(\frac{3l}{2}\) = \(\frac{2}{3}\)
    10. \(\frac{2b}{3}\) – 5 = 3
    1. 2(x + 4) = 12
    2. 3(n – 5) = 21
    3. 3(n – 5) = – 21
    4. – 4(2 + x) = 8
    5. 4(2 – x) = 8
    1. 4 = 5(p – 2)
    2. – 4 = 5(p – 2)
    3. 16 = 4 + 3(t + 2)
    4. 4 + 5(p – 1) = 34
    5. 0 = 16 + 4(m – 6)

Exponents and Powers

  1. Find the value of:
    1. 26
    2. 93
    3. 112
    4. 54
  2. Express the following in exponential form:
    1. 6 × 6 × 6 × 6
    2. t × t
    3. b × b × b × b
    4. 5 × 5 × 7 × 7 × 7
    5. 2 × 2 × a × a
    6. a × a × a × c × c × c × c × d
  3. Express each of the following numbers using exponential notation:
    1. 512
    2. 343
    3. 729
    4. 3125
  4. Identify the greater number, wherever possible, in each of the following?
    1. 43 या 34
    2. 53 या 35
    3. 28 या 82
    4. 23 या 22
  5. Express each of the following as product of powers of their prime factors:
    1. 648
    2. 405
    3. 540
    4. 3600
Simplify:
    1. 2 × 103
    2. 72 × 22
    3. 23 × 5
    4. 3 × 44
    5. 0 × 102
    6. 52 × 33
    7. 24 × 32
    8. 32 × 104
    1. (– 4)3
    2. (–3) × (–2)3
    3. (–3)2 × (–5)2
Using laws of exponents, simplify and write the answer in exponential form:
    1. 25 × 23
    2. p3 × p2
    3. 43 × 42
    4. a3 × a2 × a7
    5. 53 × 57 × 512
    6. (–4)10 × (–4)20
    1. 29 ÷ 23
    2. 108 ÷ 104
    3. 2015 ÷ 2013
    4. 911 ÷ 97
    5. 713 ÷ 710
    6. 116 ÷ 112
    1. (62)4
    2. (22)100
    3. (750)2
    4. (53)7
    1. 43 × 23
    2. 25 × b5
    3. a2 × t2
    4. 56 × (–2)6
    5. (–2)4 × (–3)4
    6. am × bm
    1. 45 ÷ 35
    2. 25 ÷ b5
    3. (–2)5 ÷ b3
    4. 56 ÷ (–2)6
    1. 80
    2. (−3)0
    3. 40 + 50
    4. 6^0 × 70
    1. (4)−1
    2. (−6)−1
    3. \(\Big(\frac{1}{3}\Big)^{-1}\)
    4. \(\Big(\frac{-2}{3}\Big)^{-1}\)
    1. 32 × 34 × 38
    2. 615 ÷ 610
    3. a3 × a2
    4. 7x × 72
    5. (52)3 ÷ 53
    6. 25 × 55
    7. a4 × b4
    8. (34)3
    9. 8t ÷ 82
  9. Express each of the following as a product of prime factors only in exponential form:
    1. 108 × 192
    2. 270
    3. 729 × 64
    4. 768
  10. Write the following numbers in the expanded forms:
    • 279404,
    • 3006194,
    • 2806196,
    • 120719,
    • 20068
  11. Find the number from each of the following expanded forms:
    1. 8 × 104 + 6 × 103 + 0 × 102 + 4 × 101 + 5 × 100
    2. 4 × 105 + 5 × 103 + 3 × 102 + 2 × 100
    3. 3 × 104 + 7 × 102 + 5 × 100
    4. 9 × 105 + 2 × 102 + 3 × 101
  12. Express the following numbers in standard form:
    1. 5,00,00,000
    2. 70,00,000
    3. 3,18,65,00,000
    4. 3,90,878
    5. 39087.8
    6. 3908.78
  13. Expregs each of the following numbers in standard form:
    1. Diameter of Earth = 12756000 m.
    2. Distance between Earth and Moon = 384000000 m.
    3. Population of India in March 2001 = 1027000000.
    4. Number of stars in a galaxy = 100000000000.
    5. The present age of universe = 12000000000 years.

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Data Handling Math - Junior

Data Handling Math - Junior

Data Handling The sale of shoes of various sizes at a shop on a particular day is given below: 6, 9, 8, 5, 5, 4, 9, 8, 5, 6, 9, 9, 7, 8, 9, 7, 6, 9, 8, 6, 7, 5, 8, 9, 4, 5, 8, 7. Represent the above data in the form of a frequency distribution table. The number of two wheelers owned individually by each of 50 families are listed below. Make a table using tally marks: 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 0, 1, 1, 2, 3, 1, 2, 1, 1, 2, 1, 2, 3, 1, 0, 2, 1, 0, 2, 1, 2, 1, 2, 1, 1, 4, 1, 3, 1, 1, 2, 1, 1, 1, 1, 2, 3, 2, 1, 1 The lengths in centimetres (to the nearest centimetre) of 30 carrots are given as follows: 15, 20,22, 22,21, 21, 20, 22, 15, 20, 15, 21, 21, 18, 18, 21, 20, 18, 20, 15, 20, 18, 20, 15, 21, 18, 20, 18, 22 Arrange the data given above in a table using tally marks and answer the following questions. What...
By Mr. Guddu Kumar