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Algebra Test - 12

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Algebra Test - 12
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  • Question 1
    1 / -0
    Directions: Find the equation for the given statement.

    th of a number, when added to 9 is 15.
    Solution
    Let p be the number.
    So, according to the question
    p + 9 = 15
  • Question 2
    1 / -0
    The product of a calculation is 230. This calculation is made by multiplying a certain number with 15 and then adding 5 to the product. Find the number.
    Solution
    Let the number be x.
    According to the question,
    15x + 5 = 230
    15x = 230 - 5
    15x = 225
    x =
    So, x = 15
  • Question 3
    1 / -0
    Directions: Find the equation which suits the given statement.

    Half of length l and twice of breadth b is equal to 432
    Solution
    According to the question, half of length l and twice of breadth b is equal to 432.
    So, + 2b = 432.
    Hence, option (3) is the right answer.
  • Question 4
    1 / -0
    Find the number, if 7 times a number gives you 5 less than 430.
    Solution
    Let the number be X.
    According to the question,
    7X = 430 - 5
    7X = 425
    X = = 60.71
  • Question 5
    1 / -0
    How to write the algebraic expression '2x - 3y' as a statement?
    Solution
    '2x - 3y' - Twice of x is less than thrice of y.
  • Question 6
    1 / -0
    Area of a square is double its side. Which of the following equations justifies the statement, if L is the side?
    Solution
    Area of a square = Side x Side
    Where side = L
    Area of a square is double its side = (2L)2
    So,Area of a square is double its side = 4L2
  • Question 7
    1 / -0
    Directions: Find the number from the given statement.

    8 more than 4 times a number is 126.
    Solution
    Let the number be X.
    4X + 8 = 126
    4X = 126 - 8
    4X = 118
    X = = 29.5
    So, X = 29.5
  • Question 8
    1 / -0
    Directions: Find the value of x in the given equation.


    Solution






    2x - 6 = 114
    2x = 114 + 6
    2x = 120
    x = 60
  • Question 9
    1 / -0
    Directions: Find the value of x in the given equation.


    Solution




    16 + 7x = 12 × 28
    16 + 7x = 336
    7x = 320
    x = 320 ÷ 7 = 45.71
  • Question 10
    1 / -0
    Directions: Find the value of x in the given equation.

    + =
    Solution
    + =
    According to the equation,









    6x = 3

    x = =
  • Question 11
    1 / -0
    Which of the following types of numbers are a and b in linear equation ax + by = c?
    Solution
    A linear equation in two variables is a first-degree equation that can be written in the form ax + by = c and a and b both are not zero, where a, b and c are real numbers.
  • Question 12
    1 / -0
    If the side of a square is thrice the smallest even number, then the perimeter of the square is
    Solution
    P = 4a (where P is the perimeter, a is the side of square)
    The smallest even number is 2.
    So, thrice of 2 is 3 × 2 = 6 = a (side of square)
    Now, P = 4 × 6
    P = 24 units
  • Question 13
    1 / -0
    If the number of female employees in a company is rd the number of male employees, then how many male employees are there in the company, if there are total 32 employees in a company?
    Solution
    Let x be number of male employees.
    Total number of employees = 32
    According to the question,
    x + x = 32
    3x + x = 96
    4x = 96
    x = 24
    So, Number of male employees = 24

  • Question 14
    1 / -0
    Which of the following correctly represents the algebraic expression for linear equation for straight line?
    Solution
    y = mx + c
    Where,
    y = How far up
    x = How far along
    m = How steep the line is (slope or gradient)
    The slope of a line can be understood with the help of the following diagram.

  • Question 15
    1 / -0
    Directions: Find the algebraic expression for the given statement.

    Half of y added to x gives double the sum of x and y in the equation.
    Solution
    According to question we have,
     + x = 2(x + y)

    = 2(x + y)

    y + 2x = 4x + 4y
    2x - 4x = 4y - y
    -2x = 3y
    2x + 3y = 0
  • Question 16
    1 / -0
    If a = b, then a × b × a is equal to
    Solution
    If a = b, then a × b × a = a × a × a = a3
  • Question 17
    1 / -0
    Which of the following equations has the solution x = 4?
    Solution
    (1) 3x + 6 = 8
    3x = 2
    x =

    (2) x + 5 = 6
    x = 1

    (3) x + 2 = 0
    x = -2

    (4) 4x + 2 = 18
    4x = 18 - 2
    4x = 16
    x = 4

    So, option (4) is the right answer.
  • Question 18
    1 / -0
    Which of the following equations has the same solution as 3x - 8 = 1?
    Solution
    Given:
    3x - 8 = 1
    3x = 8 + 1
    3x = 9
    x = 3

    Option 1:
    5x + 7 = 2
    5x = 2 - 7 = -5
    x = = -1

    Option 2:
    4x + 6 = 5
    4x = 5 - 6 = - 1
    x =

    Option 3:
    2x - 2 = 4
    2x = 4 + 2
    2x = 6
    x = 3
    So, it has the same solution x = 3

    Option 4:
    x + 2 = 2
    x = 2 - 2 = 0

    Hence, option 3 is correct.

  • Question 19
    1 / -0
    Directions: Find the value of x in the given equation.

    x + 3 = 17
    Solution
    x + 3 = 17
    x = 17 - 3
    x = 14
    x = 14 ×
    x = 35
  • Question 20
    1 / -0
    Which of the following methods is used to find the factors or roots of any polynomial of degree more than two?
    Solution
    This method is used to find the factors or roots of any polynomial of degree more than two. In this method, we generally try to put some different values in the given polynomial, until the polynomial satisfies to zero of that polynomial.
    For example,
    x2 + 2 = 6
    x2 = 4
    So,
    22 = 4
    So, answer is 2.
  • Question 21
    1 / -0
    Raj earns Rs. 630 a day, lends to Amit, spends on food and is left with at the end of the day. How much money does he spend on food?
    Solution
    Raj earns Rs. 630 a day, lends to Amit, spends on food and is left with .
    So,

    = 630


    = 630

    = 630


    x =

    x = 900

    So,

    Amount of money spent on food = = 300
  • Question 22
    1 / -0
    If a traveller travels x km in total and travels 3y km by car, 7z km on foot and the rest by bus, then which of the following represents the distance covered by bus?
    Solution
    According to the question:
    The traveler travels x km in total, and travels 3y km by car, 7z km on foot and the rest by bus.
    So, distance covered by bus =Total - Traveled by car - Traveled on foot
    = x - 3y - 7z
  • Question 23
    1 / -0
    A student scores 75 marks in his monthly Mathematics test, in which each answer is of 2 marks. He later finds out that x of his correct answers had not been checked. What is his new corrected score in the exam?
    Solution
    The student scores 75 marks in his monthly Mathematics test.
    Each question is of 2 marks.
    So, x questions will be of 2x marks.
    So, increased marks = 75 + 2x
  • Question 24
    1 / -0
    There are 12 tennis balls in every packet and 5 balls have been found to be defective in total. If y = The number of packets, then which of the following expressions shows the number of non-defective balls?
    Solution
    There are 12 tennis balls in every packet and y = Number of packets
    So, number of balls = 12 × y = 12y
    Defective balls = 5
    So, non-defective balls = 12y - 5
  • Question 25
    1 / -0
    The number of bananas in basket A is 18 less than two fifth the number of mangoes in basket B. If the number of bananas in basket A is y, then find the number of mangoes.
    Solution
    Let the number of mangoes be x.
    According to question, the number of bananas in basket A is 18 less than two fifth the number of mangoes in basket B.
    So, y = x - 18
    So, y + 18 = x
    (y + 18) = x
  • Question 26
    1 / -0
    There are 57 pages in a child's book. The pages are in three different colours, with y red pages, 7 more blue pages than red pages and 4 green pages less than blue pages. Which of the following equations can be used to find the number of pages of each colour?
    Solution
    Number of pages = 57
    Number of red pages = y
    7 more blue pages than red pages.
    So, blue pages = y + 7
    4 less green pages than blue pages.
    So, green pages = y + 7 - 4 = y + 3
    So,
    y + (y + 7) + (y + 3) = 57
  • Question 27
    1 / -0
    Directions: Fill in the blanks.

    (a) An expression with a variable that has a power as one and the sign of equality is P.
    (b) Adding 2 to a number x, followed by doubling the whole is Q.
    (c) The value that does not change in an equation is R.
    Solution
    (a) An expression with a variable that has a power as one and the sign of equality is called a linear equation.
    (b) Adding 2 to a number x = x + 2,
    doubling the whole = 2(2 + x) = 4 + 2x.
    (c) The value that does not change in an equation is called the constant.
  • Question 28
    1 / -0
    Which of the following equations has a solution as a positive even number?
    Solution
    (1) x + 2 = 3
    x = -1

    (2) 2x + 6 = 4
    2x = -2
    x = -1

    (3) 3x + 4 = 2
    3x = -2
    x =

    (4) 3x - 2 = 4
    3x = 4 + 2
    3x = 6
    x = 2

    So, solution x = 2 is a positive real number.
  • Question 29
    1 / -0
    Directions: State T for true and F for false.

    P. The solution of equation 3x + 4 = 16 is x = 4.
    Q. A linear algebraic equation always has an integer solution.
    R. If x is 4 more than thrice of y, then it can be expressed as x = 3y + 4
    Solution
    For P,
    Solution of 3x + 4 = 16
    3x = 12
    x = 4 (True)

    For Q,
    (False)
    For example

    x - = 0

    x =

    For R,
    According to statement, x is 4 more than thrice of y.
    So, x = 3y + 4 (True)
  • Question 30
    1 / -0
    Directions: Match the following.


    Solution
    For 1,
    Cost of 3 books = Rs. 12
    Cost of two is x each.
    Cost of third = 12 - 2x

    For 2,
    y marbles in one packet
    So, 4 packets = 4y

    For 3,
    He had x, gave 5 and received 3
    So, now he has
    x - 5 + 3
    x - 2
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