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2013 1st Year Orals – Solution

Here are the solutions to 2013 division finals-oral category for first year. Have fun while learning.

1. When I opened my Math book, the sum of the page number facing me was 17. What was the page number on the left side?

Solution:

Think of two consecutive numbers whose sum is 17. That is 8 and 9. 9 on the right and 8 on the left. Thus, 8 is the answer.

2. Express the product of 400 x 100 in terms of scientific notation.
Solution: We factor 400 as 4*100 and copy another 100.
$4\times 100\times 100 = 4\times 10^4$ Since every 100 has 2 zeroes.

3. By how much does 1/2 of 100 exceed 1/4 of 40?
Solution:
$\displaystyle\frac{1}{2}\cdot 100-\displaystyle\frac{1}{4}\cdot 40=50-10=40$

4. For what values of x is x+4<1?
Solution:

$x+4<1$
$x<1-4$
$x<-3$

5. Expand the expression $(x+2)^2$
Solution: The quickest way to solve the problem is to take note that $(a+b)^2=a^2+2ab+b^2$

$(x+2)^2=x^2+2(x)(2)+2^2$
$(x+2)^2=x^2+4x+4$

6. What is the sum of the first two prime numbers?
Solution: A prime number is a number who has no divisors other than 1 and itself. Like 11, 13, etc.
The first two prime number however is 2 and 3. Giving a sum of 5.

7. Ana has a piece of paper 5 cm by 3 cm. What is the area of the square that can be cut from it?
Solution: The largest square that can be cut from the rectagular paper is a 3 by 3 square. hence, the area is 3*3=9 sq. cm.

8. When 2 is multiplied to the sum of 2 and a number, the result is 10. What is the number?
Solution: Form an equation relating the given.
Let x be the number,

$2(x+2)=10$
$(x+2)=10/2$
$x+2=5$
$x=5-2$
$x=3$

9. How many 2-digit multiples of 5 are there?
Solution:
95/5 = 19. In 19 multiples, 1 of them is 5. The rest multiples ranging from 10 to 95. Thus, the answer is 18.

10. A map of a small town is scaled 1 cm: 100 m. If two actual locations are 200 m apart, how many centimeters apart are these locations on the map?
Solution: use ration and proportion.
In every hundred, the distance on the map on the paper is 1 cm. Since there were 2 hundreds, there were a total of 2 cm distance.

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Proceed to page 2 for 30-second questions.