Pre-algebra begins actually from knowledge of integers and their operations. Once we are comfortable with these operations, we we learn about the translation of statement into algebraic form. Then we learn about algebraic expressions, their operations, solving linear equations, quadratic  equations etc. In this section let us see some of the practice questions  

Pre Algebra Practice Questions 


1.   Express the following into positive or negative integers:
      a. Deposit of $\$$ 500 in the bank.
      b. Withdrawal of $\$$ 1,000 from the bank.
      c. Going towards east by 5 km
      d. Going towards west by 6 km
      e. Gain of weight by 3 kg
      f. Loss of weight by 3 kg

2. Identify the integers shown by the points K, S, M and N.
Number Line
               
3. Draw a number line marking the points from - 10 to + 10 and mark the following points on the number line.
    a.  A ( - 7 )
    b.  B ( 8 )
    c.  S ( - 3 )
    c.  Y ( 0 )
    d.  X ( 1)
4. Use the symbol < , >, $\leq$, $\geq$  or  =.
   a.   - 5          ......     4
   b. -2 + 7       ......    -9
   c.  4 ( - 6)      .....     3 ( -12 )
   d.  -125 $\div$ 5 .......   50 $\div$ ( -2 )

5. Simplify the following integers using the operation mentioned.
    a.    5 +  6 - 10 + 12 - 34
    b.    ( - 5 ) x ( - 7 ) x ( 2 )
    c.   ( - 125 ) $\div$ ( - 5 )
    d.   ( -12 ) x 10 $\div$ 5

6. Use the appropriate rule and simplify the following.
    a.    ( -2 ) x ( - 5 ) + 10 $\div$ 5
    b.    ( - 147 ) + 81 + ( - 253 ) + ( - 37 ) + 69

7. A shop keeper bought a pen for $\$$ 45, a book for $\$$ 127 and a pencil box for $\$$ 12. He sold the pen for $\$$ 36, book for $\$$ 130 and the pencil
    box for $\$$ 18. What was his gain or loss? Express the final answer in integer form.

8. solve the following equations:
    a. | x - 2 | = 10
    b. | 3x | = 6
    c. | 4x - 5 | = 20
    d. 5x - 17 = 18
    e. 3 ( 5 - x ) = 18

9. Find the sum of 2x + 9c - 5b,  4a - 5b + 8 c and a + b + c.

10. Subtract 3x + 4y - 6z from x - 5 y

11. Multiply ( 5 x y ) by ( 3 y z )

12. Divide ( 15 x3 y2 z ) by ( 5 y z )

13   Find the product.
      a.   2a ( 3 - 5 b )
      b.   5 ( x + y - 2 z )
      c.  ( 2m + 3n ) ( 3m + 2n )
14. An elevator descends into a mine shaft at the rate of 5 meters/min. If the descend starts from 14 m above the ground level, how long will it take to reach
      115 meters.
15. A plane is flying  at the height of 4500 m above sea level. At a particular point, it is exactly above a submarine floating 1350 m below the sea level.
     What is the vertical distance between them.?

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