Free Full Length HiSET Mathematics Practice Test

The correct answer is \(- \ 62\)
Use PEMDAS (order of operation):
\([4 \ × \ (– \ 18)\ + \ 6] \ – \ (– \ 2)\ + \ [4 \ × \ 4] \ ÷ \ 8 = [– \ 72 \ + \ 6] \ – \ (– \ 2) \ + \ [16] \ ÷ \ 8 = [– \ 72 \ + \ 6] \ – \ (– \ 2)\ + \ 2 =
[– \ 66] \ – \ (– \ 2)\ + \ 2 = [– \ 66] \ + \ 2 \ + \ 2 = – \ 62\)

The correct answer is \(89.6\)
average (mean) \(= \frac{sum \ of \ terms}{number \ of \ terms}⇒ 90 = \frac{sum \ of \ terms}{40}⇒ sum = 90 \ × \ 40 = 3600\)
The difference of \(84\) and \(68\) is \(16\).
Therefore, \(16\) should be subtracted from the sum.
\(3600 \ – \ 16 = 3584\)
mean \(= \frac{sum \ of \ terms }{number \ of \ terms}⇒\) mean \(= \frac{3584}{40}= 89.6\)

The correct answer is \(231\)
To solve absolute values equations, write two equations.
\(x \ - \ 16\) could be positive \(5\), or negative \(5\). Therefore,
\(x \ - \ 16=5⇒x=21\)
\(x \ - \ 16=- \ 5⇒x=11\)
Find the product of solutions: \(11 \ × \ 21 = 231\)

The correct answer is \(67\)
Plug in the value of \(x\) and \(y\). \(x=5\) and \(y=- \ 3\)
\(6(x \ - \ 3 \ y) \ + \ (4 \ - \ x)^2=6 \ (5 \ - \ 3 \ (- \ 3)) \ + \ (4 \ - \ 5)^2=6(5 \ + \ 6) \ + \ (- \ 1)^2 = 66 \ + \ 1=67\)

The correct answer is \(16\)
\(4 \ ÷ \frac{1}{4} =16 \)

The correct answer is \(27\)
The red box is \(30\%\) greater than the blue box.
Let \(x\) be the capacity of the blue box. Then:
\(x \ + \ 30\%\) of \(= 50 →1.8 \ x=50 → x=\frac{50}{1.8}=27\)

The correct answer is\(-\frac{1}{2}\)
The equation of a line in slope intercept form is: \(y=m \ x \ + \ b\)
Solve for \(y\) .\(6 \ x \ - \ 3 \ y=24 ⇒- \ 3 \ y=24 \ - \ 6 \ x⇒y =(24 \ - \ 6 \ x) \ ÷ \ (- \ 3)⇒
y=2 \ x \ - \ 8\)
The slope is \(2\).
The slope of the line perpendicular to this line is:
\(m_1 \ × \ m_2= - \ 1 ⇒ 2 \ × \ m_2= - \ 1⇒ m_2= -\frac{1}{2}\)

The correct answer is \(90\)
To find the number of possible outfit combinations, multiply number of options for each factor:
\(5 \ × \ 3 \ × \ 6 =90\)

The correct answer is \(15 \ x^2 \ - \ 17 \ x \ y \ - \ 4 \ y ^2\)
Use FOIL method.\((3 \ x \ - \ 4 \ y) \ (5 \ x \ + \ y) = 15 \ x^2 \ + \ 3 \ x \ y \ - \ 20 \ x \ y \ - \ 4 \ y^2=15 \ x^2 \ - \ 17 \ x \ y \ - \ 4 \ y^2\)

The correct answer is \(8\) feet
Use formula of rectangle prism volume.
V = (length) (width) (height) ⇒ \((3600) = (30) \ (15) \ (height) ⇒ height = 3600 \ ÷ \ 450= 8\)

The correct answer is \(72\)
The diagonal of the square is \(12\). Let \(x\) be the side.
Use Pythagorean Theorem: \(a^2 \ + \ b^2 = c^2\)
\(x^2 \ + \ x^2 = 12^2⇒2 \ x^2= 12^2⇒2 \ x^2= 144⇒x^2= 72 ⇒x= \sqrt{72}\)
The area of the square is:
\(\sqrt{72} \ × \sqrt {72} = 72\)

The correct answer is \(9\)
Th ratio of boy to girls is \(5:8\).
Therefore, there are \(5\) boys out of \(13\) students.
To find the answer, first divide the total number of students by \(13\), then multiply the result by \(5\).
\(39 \ ÷ \ 13 = 3 ⇒ 3 \ × \ 5 = 15\)
There are \(15\) boys and \(24\) \( (39 \ – \ 15)\) girls.
So, \(9\) more boys should be enrolled to make the ratio \(1:1\)

The correct answer is \(140 \ x \ + \ 10,000 \ ≤18,000\)
Let  be the number of shoes the team can purchase.
Therefore, the team can purchase \(140 \ x\).
The team had \($\ 18,000\) and spent \($\ 10000\).
Now the team can spend on new shoes \($\ 8000\) at most. Now, write the inequality:
\(140 \ x \ + \ 10,000 \ ≤18,000\)

The correct answer is \(\frac{- \ 3}{4}\)
Solving Systems of Equations by Elimination
Multiply the first equation by \((– \ 2)\), then add it to the second equation
\(- \ 2  (4 \ x \ + \ 3 \ y =15)\)
\(8 \ x \ - \ 3 \ y =- \ 6\)
\(- \ 8 \ x \ - \ 6 \ y =- \ 30\)
\(8 \ x \ - \ 3 \ y = - \ 6\)
\(- \ 9 \ y =- \ 36\)
\(y=4\)
Plug in the value of\(y\) into one of the equations and solve for \(x\)
\(4 \ x \ + \ 3 \ (4)= 15⇒4 \ x \ + \ 12 = 15⇒4 \ x= - \ 3⇒x=\frac{- \ 3}{4}\).

The correct answer is \(\frac{1}{25}\)
\(3,000\)out of \(75,000\) equals to \(\frac{30000}{75000} = \frac{30}{750} = \frac{1}{25}\)

The correct answer is \(30\)
Jacob needs an \(60\%\) average to pass for five tests. Therefore, the sum of \(5\) tests must be at least \(5 \ × \ 60 = 300\)
The sum of\(4\) tests is: \(45 \  + \ 65 \ + \ 75 \ + 85 =270 \).
The minimum score Jacob can earn on his fifth and final test to pass is:\(300 \ – \ 270 =30\)

The correct answer is \(38\)
Solve for the sum of five numbers.
average \(= \frac{sum \ of \ terms}{number \ of \ terms}⇒ 36= \frac{sum \ of \ 5 \ numbers}{5}⇒\)sum of \(5\) numbers \(= 36 \ × \ 5 = 180\)
The sum of \(5\) numbers is \(180\).
If a sixth number \(50\) is added, then the sum of \(6\) numbers is
\(180 \ + \ 50 = 230\)
average\( =\frac{sum \ of \ terms}{number \ of \ terms} = \frac{230}{6} = 38\)

The correct answer is \(\frac{3}{8}\)
Isolate and solve for \(x\).
\(\frac{4}{9}x \ + \frac{2}{3}=\frac{5}{6}⇒\frac{4}{9} \ x=\frac{5}{6} \ - \frac{2}{3} = \frac{1}{6}⇒\frac{4}{9} \ x= \frac{1}{6}\)
Multiply both sides by the reciprocal of the coefficient of \(x\).
\((\frac{9}{4})\frac{4}{9} \ x= \frac{1}{6}(\frac{9}{4})⇒x= \frac{9}{24}=\frac{3}{8}\)

The correct answer is \($\ 800\)
Use simple interest formula: (I = interest, p = principal, r = rate, t = time)
\(I=(16000)(\ 0.025)\ (2)=800\)

The correct answer is \(72000\)
Three times of \(32,000\) is \(96,000\). One fourth of them cancelled their tickets.
One fourth of \(96,000\) equals\(24,000\) \(\frac{1}{4}\ × \ 96000 = 24000\).
\(72,000\) \((96000 \ – \ 24000 =72000)\) fans are attending this week

The correct answer is \(135 \ x^8 \ y^7\)
Simplify. \(5 \ x^2 \ y^4 \ (3 \ x^2 \ y)^3= 5 \ x^2 \ y^4 \ (27 \ x^6 \ y^3 ) =135 \ x^8 \ y^7\)

The correct answer is \(- \ 2 \ , \ - \ 4\)
Frist, factor the function:\(x \ (x \ + \ 2) \ (x \ + \ 4)\)
To find the zeros, \(f(x)\) should be zero.
\(f(x)=x \ (x \ + \ 2) \ (x \ + \ 4)=0\)
Therefore, the zeros are:\(x=0\)
\((x \ + \ 2)=0 ⇒x= - \ 2 \)        
\((x \ + \ 4)=0 ⇒x= - \ 4\)

The correct answer is \(\frac{216}{343}\)
The square of a number is \(\frac{36}{49}\),
then the number is the square root of \(\frac{36}{49}\)
\(\sqrt\frac{36}{49}= \frac{6}{7}\)
The cube of the number is:\((\frac{6}{7})^3 =\frac{216}{343}\)

The correct answer is \(112 \ π\ in^2\)
Surface Area of a cylinder \(= 2 \ π \ r \ (r \ + \ h)\),
The radius of the cylinder is \(4\)       \((8 \ ÷ \ 2)\) inches and its height is \(10\) inches.
Therefore,
Surface Area of a cylinder \(= 2 \ π \ (4) \ (4 \ + \ 10) = 112 \ π\)

The correct answer is \(- \ 8\)
\(g(x)= \ - \ 2\), then:
\(f(g(x))= f(- \ 2)=3 \ (- \ 2)^3 \ + \ 6(- \ 2)^2 \ + \ 4(- \ 2) =\)
\( - \ 24\ + \ 24 \ - \ 8 = - \ 8\)

The correct answer is \(28\) inches
The area of the square is \(49\) inches.
Therefore, the side of the square is square root of the area.
\(\sqrt{49}=7\) inches,
Four times the side of the square is the perimeter : \(4 \ × \ 7 = 28\) inches

The correct answer is \(3 \ x^3 \ 5 \ x^2 \ 2 \ x\)
Combine like terms:
\((x^3 \ + \ 4 \ x^2 \ - \ 5 \ x) \ + \ (2 \ x^3 \ + \ x^2 \ + \ 7 \ x)=(x^3 \ + 2 \ x^3) \ + \ (4 \ x^2 \ +x^2 ) \ + \ (- \ 5 \ x \ + \ 7 \ x)=\)
\(3 \ x^3 \ + \ 5 \ x^2 \ + \ 2 \ x\)

The correct answer is \(134\) miles
Use the information provided in the question to draw the shape.
Use Pythagorean Theorem: \(a^2 \ + \ b^2 = c^2\)
\(60^2 \ + \ 120^2 = c2⇒ 3600 \ + \ 14400 = c2 ⇒ 18000 = c2 ⇒ c =134\)

The correct answer is \(( - \ 5 \ , \ - \ 8)\)
Since the ordered pair is reflected over the \(x-\)axis,
then, the value of \(x\) of the point doesn’t change and the sign of \(y\) changes.
\((– \ 5 \ , \ 8) ⇒ (– \ 5 \ , \ – \ 8)\)

The correct answer is \(30\)
Write the numbers in order: \(3 \ , \ 15 \ , \ 26 \ , \ 30 \ , \ 37 \ , \ 45 \ , \ 54\)
Median is the number in the middle. So, the median is \(30\).

The correct answer is \(31\)
Find the difference of each pairs of numbers:\(3 \ , \ 4 \ , \ 6\ , \ 9 \ , \ 13 \ , \ 18 \ , \ 24 \ , ...., \ 39\)
The difference of \(3\) and \(4\) is \(1\), \(4\) and \(6\) is \(2\) , \(6\) and \(9\) is \(3\) , \(9\) and \(13\) is \(4\) , \(13\) and \(18\) is \(5\), \(18\) and \(24\) is \(6\) , \(24\) and next number should be \(7\).
The number is \(24 \  + \ 7 = 31\)

The correct answer is \(72\)
Plug in \(120\) for F and then solve for C.         C\(= \frac{6}{8}(F \ ­– \ 24) ⇒ C = \frac{6}{8} (120 \  ­– \ 24) ⇒ C = \frac{6}{8} \ (96) =72\)

The correct answer is \(34\)
\(average = \frac{sum \ of \ terms}{number \ of \ terms}\)⇒ (average of \(8\) numbers)\(16\)\( = \frac{sum \ of \ numbers}{8}\)⇒sum of \(8\) numbers is
\(16 \ × \ 8 = 128\)
(average of \(6\) numbers) \(10\) \(=\frac{sum \ of \ numbers}{6}\)⇒sum of \(6\) numbers is \(10 \ × \ 6 = 60\)
sum of \(8\) numbers \(–\) sum of \(6\) numbers = sum of \(2\) numbers
\(128 \ – \ 60 = 68\) average of \(2\) numbers = \(\frac{68}{2} = 34\)

The correct answer is \(\frac{1}{4}\)
Probability\(= \frac{number \ of \ desired \ outcomes}{number \ of \ total \ outcomes} =\frac {15}{10 \ + \ 14 \ + \ 15 \ + \ 22}= \frac{15}{61} =\frac {1}{4}\)

The correct answer is \(336\) cm\(^3\)
Volume of a box = length × width × height \(= 6 \ × \ 7 \ × \ 8 =336\)

The correct answer is \(50\%\)
the population is increased by \(20\%\) and \(25\%\). \(20\%\) increase changes the population to \(120\%\) of original population.
For the second increase, multiply the result by \(125\%\).
\((1.20) \ × \ (1.25) = 1.50 = 150\%\)
\(50\) percent of the population is increased after two years.

The correct answer is \(44\)
First, find the number.Let \(x\) be the number.
Write the equation and solve for \(x\).
\(180\%\) of a number is \(80\),
then:\(1.8 \ × \ x= 80⇒ x=80 \ ÷ \ 1.8=44\)
\(85\%\) of \(44\) is:\(0.85 \ × \ 44 = 37\)

The correct answer is \(- \ 10 \ x^4 \ + \ 11\ x^3 \ - \ x^2\)
Simplify and combine like terms.
\((8 \ x^3 \ + \ 4 \ x^2 \ - \ 4 \ x^4 ) \ - \ (5 \ x^2 \ + \ 6 \ x^4 \ - \ 3 \ x^3 )⇒(8 \ x^3 \ +4 \ x^2 \ - \ 4 \ x^4 ) \ - \ 5 \ x^2 \ - \ 6 \ x^4 \ + \ 3 \ x^3⇒
- \ 10 \ x^4 \ + \ 11\ x^3 \ - \ x^2\)

The correct answer is \(6\) meters
The width of the rectangle is twice its length.
Let \(x\) be the length. Then, width\(=2 \ x\)
Perimeter of the rectangle is \(2\) (width + length) \(= 2 \ (2 \ x \ + \ x)=36 ⇒ 6 = 36 ⇒x=6\)
Length of the rectangle is \(6\) meters.

The correct answer is \(4\)
Solve for \(y\) .\(8 \ x \ - \ 2 \ y= 10 ⇒- \ 2 \ y=10 \ - \ 8 \ x⇒y=4 \ x \ - \ 5\)
The slope of the line is \(4\).

The correct answer is \(32\)
Five years ago, Ann was three times as old as Michael . Michael is \(14\) years now. Therefore, \(5\) years ago Michael was \(9\) years. Five years ago, Ann was:A:\(=3 \ × \ 9=27\)
Now Amy is \(32\) years old:\(27 \  +  \  5 = 32\)

The correct answer is \(15\)
Let \(x\) be the number. Write the equation and solve for \(x\).
\(60\%\) of \(x=9⇒ 0.60 \ x=9⇒x=9 \ ÷ \ 0.60=15\)

The correct answer is \(x^{10}\)
The exponent "product rule" says that,
when multiplying two powers that have the same base, you can add the exponents:
\((x^6)(x^4 )= x^{(6 \ + \ 4)}=x^{10}\)

The correct answer is \(48\)
The amount of money that John earns for one hour: \(\frac{$\ 720}{45}=$\ 16\)
Number of additional hours that he needs to work in order to make enough money is: \(\frac{$\ 850 \ - \ $\ 720}{2.5 \ × \ $\ 16}=3\)
Number of total hours is: \(45 \ + \ 3=48\)
 

The correct answer is \(14\) hours
The distance between Mike and Alex is \(7\) miles.
Mike running at \(4.5\) miles per hour and Alex is running at the speed of \(5\) miles per hour.
Therefore, every hour the distance is \(0.5\) miles less.
\(7 \ ÷ \ 0.5 =14 \)

The correct answer is \(14\)
The formula for the area of the circle is: A\(=π \ r^2\)
The area is \(49 \ π\). Therefore:A\(=π \ r^2⇒49 \ π = π \ r^2\)
Divide both sides by \(π\):   \(49 = r^2⇒r=7\)
Diameter of a circle is \(2 \ x\) radius.
Then:Diameter \(= 2 \ × \ 7 = 14\)

The correct answer is \(29\%\)
\($\ 16\) is what percent of \($\ 54\) ?  \(16 \ ÷ \ 54 = 0.29 = 29\%\)

The correct answer is \(2400\)
Let \(x\) be the capacity of one tank.
Then, \(\frac{3}{6} x=300→x=\frac{300 \ × \ 6}{3}=600\) Liters
The amount of water in four tanks is equal to: \(4 \ × \ 600=2400\) Liters

The correct answer is \(60\) ft
Write a proportion and solve for \(x\).
\(\frac{5}{3}=\frac{x}{36}⇒3 \ x=5 \ × \ 36⇒x=60\) ft

The correct answer is \(79\%\)
The failing rate is \(15\) out of \(70 = \frac{15}{70}\)
Change the fraction to percent:\(\frac{15}{70} \ × \ 100\%=21\%\)
\(21\) percent of students failed. Therefore, \(79\) percent of students passed the test.