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 \( 6.3 \ × \ 10^1\)
\((4.2 \ × \ 10^5) \ × \ (1.5 \ × \ 10^{−4}) = (4.2 \ × \ 1.5) \ × \ (10^5 \ × \ 10^{−4}) = 6.3 \ × \ (10^{5 + (−4)} ) =\)
\(6.3 \ × \ 10^1\)