Full Length HiSET Mathematics Practice Test

The correct answer is $4$
Simplify:$2(x \ + \ 3) \ = \ 4(x \ − \ 6) \ + \ 22 \ ⇒ \ 2x \ + 6 = 4x \ − \ 24 \ + \ 22 \ ⇒ \ 2x \ + \ 6 \ = \ 4x \ – \ 2$
Subtract $2x$ from both sides:$6 \ = \ 2x \ – \ 2$, Add $2$ to both sides:$8 \ = \ 2x \ ⇒ \ 4 \ = \ x$

The corret answer is $275$
Add the first $5$ numbers. $20 \ + \ 25 \ + \ 15 \ + \ 30 \ + \ 35 = 125$
To find the distance traveled in the next $5$ hours, multiply the average by number of hours.
Distance = Average × Rate $= 30 \ × \ 5 = 150$, Add both numbers.
$125 \ + \ 150 = 275$

The correct answer is $125$
$x=100 \ + \ 25=125$

The correct answer is $5$
Use Pythagorean Theorem: $a^2 \ + \ b^2 \ = \ c^2 \ ⇒ \ 4^2 \ + \ 3^2 \ = \ c^2 \ ⇒ \ 25 = c^2 ⇒ c = 5$

The correct answer is $6 \ x^2 \ + \ 19 \ x \ y \ + \ 10\ y^2$
Use FOIL (First, Out, In, Last)$(3x \ + \ 2y) \ (2x \ + \ 5y) \ = \ 6x^2 \ + \ 15xy \ + \ 4xy \ + \ 10y^2 \ = \ 6x^2 \ + \ 19xy \ + \ 10y^2$

The correct answer is $150$
Use percent formula:part $=\frac{ percent}{100}×$whole
$45= \frac{percent}{100} \ × \ 30 ⇒ 45 = \frac{percent \ × \ 30}{100}⇒45 = \frac{percent × \ 3}{10}$, multiply both sides by $10$.
$450 = percent \ × \ 3$, divide both sides by $3$ ⇒ $150=$ percent

The correct answer is $108\%$
To find the discount, multiply the number by ($100 \% \ –$ rate of discount).
Therefore, for the first discount we get: (D)  $(100\% \ – \ 10\%) =$ (D)   $(0.90) = 0.90$ D
For increase of $20\%: (0.90 D) \ (100\% \ + \ 20\%) = (0.90 D) \ (1.20) = 1.08 D = 108\%$ of D

The correct answer is $2$
$y = 3\ a \ b \ - \ 4 \ b^2$
Plug in the values of $a$ and $b$ in the equation: $a = 3$ and $b = 2$
$y = 3 \ (3) \ (2) \ - \ 4 \ (2)^2 = 18 \ - \ 4 \ (4) = 18 \ - \ 16 = 2$

The correct answer is $72$
$4.5\%$ of $1,600 = 0.045 \ × \ 1600 = 72$

The correct answer is $7$
The percent of girls playing tennis is: $35\% ×20\% = 0.35 \ × \ 0.20 = 0.07 = 7\%$

The correct answer is $22$ hours and $20$ minutes
Use distance formula:
Distance = Rate × time ⇒ $670 = 30 × T$, divide both sides by $30$ ⇒
$\frac{670}{30} = T$ ⇒ $T = 22.33$ hours.
Change hours to minutes for the decimal part. $0.33$ hours $= 0.33 \ × \ 60 = 20$

The correct answer is $24\%$
Use the formula for Percent of Change: $\frac{New \ Value \ - \ Old \ Value}{Old \ Value} \ × \ 100\%$
$\frac{38 \ - \ 50}{50} \ × \ 100\% = – \ 24\%$ (negative sign here means that the new price is less than old price).

The correct answer is $204 \ π \ in^2$
Surface Area of a cylinder  $= 2 \ π \ r \ (r \ + \ h)$,
The radius of the cylinder is $6$ inches and its height is $11$ inches.
Surface Area of a cylinder $= 2 \ (π) \ (6) \ (6 \ + \ 11) = 204 \ π$

The correct answer is $9$
Let $x$ be the number. Write the equation and solve for $x$.
$\frac{1}{2} \ × \ 12 \ = \ \frac {2}{3} \ x \ ⇒ \ \frac{1 \ × \ 12}{2}=\frac{2 \ x}{3}$
use cross multiplication to solve for $x$. $12 \ \times \ 3 \ = \ 2x \ \times \ 2 \ ⇒ \ 36 \ = \ 4x \ ⇒ \ x \ = \ 9$

The correct answer is $15 \ x \ y \ + \ 6 \ x$
Use distributive property: $3x(2 \ + \ 5y) \ = \ 6x \ + \ 15xy \ = \ 15xy \ + \ 6x$

The correct answer is $8$
The diagonal of the square is $4$. Let $x$ be the side.
Use Pythagorean Theorem: $a^2 \ + \ b^2 = c^2$
$x^2 \ + \ x^2 \ = \ 4^2 \ ⇒ \ 2x^2 \ = \ 4^2 \ ⇒ \ 2x^2 \ = \ 16 \ ⇒ \ x^2 \ = \ 8 \ ⇒ \ x= \ \sqrt{8}$
The area of the square is:
$\sqrt{8} \times \sqrt{8} \ = \ 8$

The correct answer is $$1000$
Use simple interest formula: (I = interest, p = principal, r = rate, t = time)
$I \ = \ (1000) \times (0.025) \times (4) = 1000$ 

The correct answer is $75$ cm$^3$
The formula of the volume of pyramid is: V $= \frac{l \ \times \ w \ \times \ h}{3}$
The length and width of the pyramid are $5$ cm and its height is $9$ cm.
Therefore:
V $= \frac{5 \ \times \ 5 \ \times \ 9}{3}=75$cm$^3$

The correct answer is $$500$
Let $x$ be the original price.
If the price of a laptop is decreased by $20\%$ to $$400$,
then: $80\%$ of $x \ = \ 400 \ ⇒ \ 0.80x \ = \ 400 \ ⇒ \ x \ = \ 400 \ ÷ \ 0.80 \ = \ 500$

The correct answer is $600$ ml
$6\%$ of the volume of the solution is alcohol.
Let $x$ be the volume of the solution.
Then: $6\%$ of $x \ = \ 36$ ml $⇒ \ 0.06x \ = \ 36 \ ⇒ \ x \ = \ 36 \div 0.06 \ = \ 600$

The correct answer is $2$
Solving Systems of Equations by Elimination
$2 \ x \ - \ 3 \ y = - \ 22$
$- \ x \ + \ 4 \ y =16$
Multiply the second equation by $2$, then add it to the first equation.
$2 \ x \ - \ 3 \ y = - \ 22$
$2 (- \ x \ + \ 4 \ y =16) ⇒ \ -2 \ x \ + \ 8 \ y =  32$  
$⇒ \ 5 \ y= 10 \ ⇒ \ y = 2$

The correct answer is $72$
The perimeter of the trapezoid is $40$.
So, the missing side (height) is $= 40 \ – \ 14 \ – \ 8 \ – \ 10 = 8$
Area of the trapezoid:
A $=\frac{1}{2} \ h \ (b_1 \ + \ b_2) = \frac{1}{2} (8) \ (10 \ + \ 8) = 72$

The correct answer is $300$
The ratio of boys to girls is $3:4$. Therefore, there are $3$ boys out of $7$ students.
To find the answer, first, divide the total number of students by $7$, then multiply the result by $3$.
$700 \ ÷ \ 7 = 100 ⇒ 100 × 3 = 300$

The correct answer is $8$
Write the numbers in order:   $3 \ , \ 4 \ , \ 5 \ , \ 8 \ , \ 11 \ , \ 15 \ , \ 16$
Since we have $7$ numbers ($7$ is odd),
then the median is the number in the middle, which is $8$.

The correct answer is $32$
average $= \frac{sum \ of \ terms}{number \ of \ terms}⇒ 16 = \frac{10 \ + \ 14 \ + \ 8 \ + \ x}{4 }⇒ 64  = 32 \ + \ x ⇒ x = 32$

The correct answer is $$\ 450$
Use simple interest formula: (I = interest, p = principal, r = rate, t = time)
$I=(6,000) \ (0.025) \ (3)=450$

The correct answer is $720$
Let $x$ be the original price.
If the price of the bed is decreased by $25\%$ to $$\ 540$,
then: $75\%$ of $x=540 ⇒ 0.75 \ x = 540 ⇒ x =540 \ ÷ \ 0.75=720$

The correct answer is $14 \ π$
Use the formula of areas of circles.
Area $= π \ r^2 ⇒49 \ π = π \ r^2⇒ 49 = r^2 ⇒ r = 7$
Radius of the circle is $7$.
Now, use the circumference formula:
Circumference $= 2 \ π \ r = 2 \ π (7)= 14 \ π$

The correct answer is $137$
The question is this:$1.85$ is what percent of $1.35$?
Use percent formula:part $= \frac{percent}{100} \ ×$ whole
$1.85 = \frac{percent}{100} \ × \ 1.35 ⇒1.85 = \frac{percent \ × \ 1.35}{100} ⇒ 185 = percent \ × \ 1.35$ ⇒
$percent = \frac{185}{1.35} = 137$

The correct answer is $0 \ , \ - \ 2 \ , \ - \ 1$ 
First factor the function:$x \ (x \ + \ 2) \ (x \ + \ 1)$
To find the zeros, $f(x)$ should be zero.$f(x)=x \ (x \ + \ 2) \ (x \ + \ 1)=0$
Therefore, the zeros are:$x=0$, $(x \ + \ 2)=0 ⇒x= - \ 2$ , $(x \ + \ 1)=0 ⇒x= - \ 1$

The correct answer is $I > 15000 \ x \ + \ 20000$
Let $x$ be the number of years. Therefore, $$\ 15,000$ per year equals $15000 \ x$.
starting from $$\ 20,000$ annual salary means you should add that amount to $15000 \ x$.
Income more than that is:$I > 15000 \ x \ + \ 20000$

The correct answer is $35$
Some of prime numbers are: $2 \ , \ 3 \ , \ 5 \ , \ 7 \ , \ 11 \ , \ 13$
Find the product of two consecutive prime numbers:
$2 \ × \ 3 = 6$ (not in the options)
$3 \ × \ 5 = 15$(not in the options),
$5 \ × \ 7 = 35$ (bingo!)

The correct answer is $18$
If the score of Jennifer was $72$, therefore the score of Kevin is $36$.
Since the score of Amy was half that of Kevin,
therefore, the score of Amy is $18$.

The correct answer is $52$
Let $x$ be the smallest number. Then, these are the numbers: $x \ , \ x \ + \ 1 \ , \ x \ + \ 2 \ , \ x \ + \ 3 \ , \ x \ + \ 4$
average $=\frac {sum \ of \ terms}{number \ of \ terms}⇒ 54 =\frac { x \ + \ (x \ + \ 1) \ + \ (x \ + \ 2) \ + \ (x \ + \ 3)\ + \ (x \ + \ 4)}{5} ⇒$
$54=\frac {5 \ x \ + \ 10}{5} ⇒ 270 = 5 \ x \ + \ 10 ⇒ 260 = 5 \ x ⇒ x=52$

The correct answer is $50$ feet
The relationship among all sides of a special right triangle
$30^° \ - \ 60^° \ - \ 90^°$ is provided in this triangle:
In this triangle, the opposite side of the $30^°$ angle is half of the hypotenuse.
Draw the shape of this question:
The latter is the hypotenuse. Therefore, the ladder is $50$ ft.

The correct answer is $400\%$
Write the equation and solve for B$:0.40$ A $= 0.10$ B,
divide both sides by $0.10$ ,
then you will have $\frac{0.40}{0.10}$ A = B,
therefore: B $= 4$ A, and B is $4$ times of A or it’s $400\%$ of A.

The correct answer is $7$
Let $x$ be the number. Write the equation and solve for $x$. $(35 \ – \ x) \ ÷ \ x= 4$
Multiply both sides by $x$.
$(35 \ – \ x) = 4 \ x$,
then add $x$ both sides. $35 = 5 \ x$,
now divide both sides by $5$ ⇒ $x = 7$

The correct answer is $40$
To find the number of possible outfit combinations, multiply the number of options for each factor:
$4 \ × \ 5 \ × \  2 =40$

The correct answer is $36$
The sum of supplement angles is $180$. Let $x$ be that angle.
Therefore, $x = \frac{1}{4}(180 \ - \ x) ⇒ x \ + \  4 \ x = 180 ⇒$
$5x \ = \ 180$ , divide both sides by $5$ : $x  = 36$

The correct answer is $16$
The area of the floor is: $4 \  cm \ × \ 28 \ cm = 112$ cm,
The number is tiles needed $= 112 \ ÷ \ 7 = 16$

The correct answer is $22.8$ ft
Use Pythagorean theorem: $a^2 \ + \ b^2 = c^2$ ,
$14^2 \ + \ 18^2= x^2$ , $196 \ + \ 324 = x^2$
$520 = x^2$ ⇒ $x = 22.8$

The correct answer is $245$ cm$^3$
The formula of the volume of a pyramid is:
V$=\frac {l \times w \times h}{3}$
The length and width of the pyramid are $7$ cm and its height is $14$ cm. Therefore:
V $= \frac{7 \ \times \ 7 \ \times \ 15}{3} = 245$ cm$^3$

The correct answer is $$\ 500$
Let $x$ be the original price.
If the price of a laptop is decreased by $20\%$ to $$\ 400$ ,
then: $80\%$  of  $x= 400 \ ⇒ \ 0.80x \ = \ 400 ⇒ x = 400 \ ÷ \ 0.80 \ = \ 500$

The correct answer is $5.25$
The weight of $10.5$ meters of this rope is: $10.5 \ × \ 500 \ g = 5250$ g
1 kg $= 1000$ g,
therefore, $5250$ g $÷ \ 1000 = 5.25$ kg

The correct answer is $71.2$
average $= \frac{sum \ of \ terms }{number \ of \ terms}$
The sum of the weight of all girls is: $24 \ × \ 70 = 1680$ kg
The sum of the weight of all boys is: $36 \ × \ 72 =2592$ kg
The sum of the weight of all students is: $1680 \ + \ 2592 =4272$ kg
average $= \frac{4272}{60}= 71.2$

The correct answer is $2 : 3$
The average speed of john is: $240 \ ÷ \ 8 = 30$
The average speed of Alice is: $270 \ ÷ \ 6 = 45$
Write the ratio and simplify.
$30 : 45 ⇒ 2 : 3$

The correct answer is $1728$ cm$^3$
If the length of the box is $36$, then the width of the box is one-third of it, $12$,
and the height of the box is $4$ (one-third of the width).
The volume of the box is: $V = l \ w \ h = (36) \ (12) \ (4) =1728$ cm$^3$

The corrrect answer is $20\%$
Use this formula: Percent of Change $=\frac{New \ Value \ - \ Old \ Value}{Old Value} \ × \ 100\%$
$\frac{16000 \ - \ 20000}{20000} \ × \ 100\% = 20\%$ and $\frac{12800 \ - \ 16000}{16000} \ × \ 100\% = 20\%$

The correct answer is $(2 \ , \ 5)$ , $(1 \ , \ 4)$ , $(- \ 3 \ , \ 7)$
Since the triangle ABC is reflected over the $y-$axis, then all values of $y$’s of the points don’t change
and the sign of all$x$’s change.
(remember that when a point is reflected over the $y-$axis, the value of $y$ does not change and when
a point is reflected over the $x-$axis, the value of $x$  does not change).
Therefore:
$(− \ 2,5)$ changes to $(2 \ , \ 5)$
$(− \ 1 \ ,  \ 4)$ changes to $(1 \ , \ 4)$
$(3 \ ,  \ 7)$ changes to$(− \ 3 \ , \ 7)$

The correct answer is $6.3 \ × \ 10^1$
$(4.2 \ × \ 10^5) \ × \ (1.5 \ × \ 10^{−4}) = (4.2 \ × \ 1.5) \ × \ (10^5 \ × \ 10^{−4}) = 6.3 \ × \ (10^{5 + (−4)} ) =$
$6.3 \ × \ 10^1$