ISEE Upper Level Quantitative Reasoning › Variables and Exponents
Simplify:
Break the fraction up and apply the quotient of powers rule:
Simplify:
The cube of a sum pattern can be applied here:
Simplify:
Break the fraction up and apply the quotient of powers rule:
Factor completely:
A trinomial whose leading term has a coefficent other than 1 can be factored using the -method. We split the middle term using two numbers whose product is
and whose sum is
. These numbers are
, so:
Fill in the box to form a perfect square trinomial:
To obtain the constant term of a perfect square trinomial, divide the linear coefficient, which here is , by 2, and square the quotient. The result is
Fill in the box to form a perfect square trinomial:
To obtain the constant term of a perfect square trinomial, divide the linear coefficient, which here is , by 2, and square the quotient. The result is
Factor completely:
A trinomial whose leading term has a coefficent other than 1 can be factored using the -method. We split the middle term using two numbers whose product is
and whose sum is
. These numbers are
, so:
Simplify:
The cube of a sum pattern can be applied here:
Half of one hundred divided by five and multiplied by one-tenth is __________.
1
5
2
10
Let's take this step by step. "Half of one hundred" is 100/2 = 50. Then "half of one hundred divided by five" is 50/5 = 10. "Multiplied by one-tenth" really is the same as dividing by ten, so the last step gives us 10/10 = 1.
Half of one hundred divided by five and multiplied by one-tenth is __________.
1
5
2
10
Let's take this step by step. "Half of one hundred" is 100/2 = 50. Then "half of one hundred divided by five" is 50/5 = 10. "Multiplied by one-tenth" really is the same as dividing by ten, so the last step gives us 10/10 = 1.