All HSPT Math Resources
Example Questions
Example Question #82 : Use Parentheses, Brackets, Or Braces In Numerical Expressions And Evaluate These Expressions: Ccss.Math.Content.5.Oa.A.1
Solve:
When solving this problem, remember order of operations PEMDAS. The parentheses come first followed by the division.
Example Question #541 : Numbers And Operations
Solve:
When solving this problem, remember order of operations PEMDAS. The parentheses come first, followed by the multiplication, and then addition.
Example Question #1 : Word Problems
Mark is three times as old as his son Brian. In ten years, Mark will be years old. In how many years will Mark be twice as old as Brian?
In ten years, Mark will be years old, so Mark is
years old now, and Brian is one-third of this, or
years old.
Let be the number of years in which Mark will be twice Brian's age. Then Brian will be
, and Mark will be
. Since Mark will be twice Brian's age, we can set up and solve the equation:
Mark will be twice Brian's age in years.
Example Question #92 : Algebra
Gary is twice as old as his niece Candy. How old will Candy will be in five years when Gary is years old?
Not enough information is given to determine the answer.
Since Gary will be 37 in five years, he is years old now. He is twice as old as Cathy, so she is
years old, and in five years, she will be
years old.
Example Question #93 : Algebra
A parking garage charges a minimum fee of to park in the garage. It also charges an additional fee of
for every hour, or portion of an hour, in which a person parks in the garage. Cliff wants to pay a maximum of
to park there. If he pulls into the garage at exactly
, when must he leave at latest?
Let be the number of hours that Cliff parks his car in the garage. Since he pays a flat fee of
plus
per hour or portion thereof, he pays
dollars. Since he does not want to spend more than
,
Since a portion of an hour counts as much as an hour, must be a whole number.
implies that
.
Cliff can park in the garage for a maximum of 6 hours, and since he entered the garage at , he must exit
hours later:
,
or .
Example Question #61 : Common Core Math: Grade 5
Solve the following:
When solving this problem, remember order of operations PEMDAS. The parentheses come first followed by the multiplication.
Example Question #24 : Use Parentheses, Brackets, Or Braces In Numerical Expressions And Evaluate These Expressions: Ccss.Math.Content.5.Oa.A.1
Solve:
When solving this problem, remember order of operations PEMDAS. The parentheses come first followed by the multiplication.
Example Question #1 : How To Simplify Expressions
You are given that are whole numbers.
Which of the following is true of if
and
are both odd?
None of the other statements are true.
is always odd.
is always odd if
is even, and always even if
is odd.
is always even.
is always odd if
is odd, and always even if
is even.
is always odd if
is even, and always even if
is odd.
If is odd, then
is odd, since the product of two odd whole numbers must be odd. When the odd number
is added, the result,
, is even, since the sum of two odd numbers must be even.
If is even, then
is even, since the product of an odd number and an even number must be even. When the odd number
is added, the result,
, is odd, since the sum of an odd number and an even number must be odd.
Example Question #2 : How To Simplify Expressions
Simplify the expression:
Combine all the like terms.
The terms can be combined together, which gives you
.
When you combine the terms together, you get
.
There is only one term so it doesn't get combined with anything. Put them all together and you get
.
Example Question #3 : How To Simplify Expressions
Simplify the following expression:
First distribute the 2:
Combine the like terms:
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