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.