HiSET Practice Test Math
A triangle with one right angle and two acute angles.
A right triangle is a type of triangle that has one angle measuring exactly 90 degrees, which is known as a right angle. The other two angles in a right triangle are acute angles, meaning they are both less than 90 degrees.
Factor: 4y(3x + 2) − 2(3x + 2)
Correct answer: (4y − 2)(3x + 2)
Any part of an expression that is shared by all of its terms can be factored out. (3x + 2) is a common term in this case and can be factored out of both parts of the expression:
4y(3x + 2) − 2(3x + 2) = (3x + 2)[4y − 2]
See that distributing (3x + 2) through [4y − 2] yields the original expression, which validates the answer.
Jennie wants to paint a room's walls. She is aware that each can of paint holds one gallon. A half gallon of paint will completely cover a 55 square foot wall. The room's four walls are each 10 feet tall. Two of the walls are 10 feet wide, while the other two are 15 feet wide. How many 1-gallon buckets of paint does Jennie need to paint the entire room?
Correct answer: 5
The total number of buckets required will be determined by dividing the total area of the walls by the total area covered by each bucket. First, determine the size of the walls Jennie intends to paint. Two of the walls are 10 × 10 and the other two are 10 × 15:
2 (10 × 10) = 200 sq. ft.
2 (10 × 15) = 300 sq. ft.
As a result, the total area of the walls is 500 square feet.
If a half gallon of paint covers 55 square feet, each gallon covers 2 × 55 = 110 square feet. Four gallons can only cover 440 square feet. Five gallons will cover 550 square feet, which is enough to cover the entire wall area.
An angle produced by connecting lines that has two opposite congruent angles.
Vertical angles are a pair of non-adjacent angles formed by intersecting lines. When two lines intersect, they create four angles, and the two opposite angles among them are called vertical angles. These vertical angles are congruent, meaning they have the same measure.
What was Jelly's tip percentage if she left a $10.16 tip on a breakfast that cost $86.89?
Correct answer: 12%
To find out what percentage A is of B, divide A by B and multiply the result by 100 percent:
10.16 ÷ 86.89 = 0.1169 × 100% = 11.69%
This is approximately 12%.
A dot-based graphical representation of data.
A dot plot is a graphical representation of data that uses dots to display individual data points along a number line or a specific axis. Each dot in the plot represents a single data point, and the dots are stacked above each other if multiple data points have the same value.
A box contains four yellow marbles and eight blue marbles. What is the probability that Emma will choose a yellow marble at random from the box?
Correct answer: 1/3
The probability of a successful event is defined as the ratio of successful events to total events. A successful event in this case is selecting a yellow marble from the box. The number of events equals the number of marbles in the box:
P(Yellow) = Yellow Marbles/Total Marbles
P(Yellow) = 4/12
P(Yellow) = 1/3
Finding which prime numbers multiply together to make the original number.
less than 90 degrees
An acute angle is an angle that measures less than 90 degrees. Acute angles are characterized by their openness and sharpness, as they are narrower than a right angle (90 degrees) and do not reach the measure of a straight angle (180 degrees). In an acute triangle, all three angles are acute, and in a right triangle, one angle is a right angle (90 degrees) while the other two angles are acute.
Angel was three times Brian's age five years ago. How old is Angel now that Brian is 10 years old?
Correct answer: 20
To keep things organized, create a table that compares the situation five years ago to the situation today.
Five years ago Today
Brian 10 - 5 = 5 10
Angel 3 x 5 = 15 15 + 5 = 20
Brian is now 10 years old, so he was 5 years old five years ago.
Angel was 3 times Brian's age five years ago, so Angel must have been 15 at the time.
To calculate Angel's current age, add 5 years to her age five years ago. Angel is now 15 + 5 = 20 years old.
If a truck travels 360 kilometers in 5 hours, how far will it travel in 9 hours if the same speed is maintained?
Correct answer: 648
First, determine distance the car travels in one hour:
360 km ÷ 5 hours = 72 km per hour
Then multiply this number by the total number of hours traveled:
9 hours × 72 km per hour = 648 km
It is important to note that the final calculation produces the correct units; this helps to confirm that the calculation is correct.
A circular form with no beginning or end.
A circle is a two-dimensional geometric shape that consists of all points in a plane that are equidistant from a fixed center point. It has no beginning or end, and it is continuous, making it an infinite shape. The distance from the center of the circle to any point on its boundary is called the radius, and the distance across the center through any two points on the boundary is called the diameter, which is twice the length of the radius. Circles have many interesting properties and are fundamental in mathematics and geometry.
How many outfit combinations are possible with six shirts, three slacks, and five ties?
Correct answer: 90
Multiply the number of options for each factor to determine the number of possible outfit combinations:
6×3×5=90
The side of a right triangle opposite the right angle.
A prime factor is a prime number that exactly divides the given composite number without leaving a remainder. Prime factors are the building blocks of composite numbers because any composite number can be expressed as a product of prime factors.
Robert makes $8.10 per hour and works 40 hours per week. John's hourly wage is $10.80. How many hours would John have to work to earn the same as Robert over 40 hours?
Correct answer: 30
To begin, compute Robert's total earnings after 40 hours: 40 hours × $8.10 per hour = $324
Then, divide this total by John's hourly rate to determine how many hours John would need to work:
$324 ÷ $10.80 per hour = 30 hours
What is equivalent to 3x(2 + 5y)?
Correct answer: 6x + 15xy
Begin by taking note of the format in which the answer options are written. As there is no parenthetical expression in any of the answer choices, begin by distributing the 3x through the parentheses. Multiply each of the term inside the parentheses three times and combine any similar terms:
3x(2 + 5y)
= 3x(2) + 3x(5y)
= 6x + 15xy