Free Full Length TASC Mathematics Practice Test

The correct answer is $200\%$
Write the equation and solve for B:
$0.50$ A $= 0.25$ B, divide both sides by $0.25$, then:
$0.65/0.25$ A $=$ B, therefore:
B $=2$ A, and B is $2$ times of A or it’s $200\%$ of A.

The correct answer is $16$
average $= \frac{sum \ of \ terms}{ number \ of \ terms}=\frac{17 \ + \ 13 \ + \ 7 \ + \ 21 \ + \ 22}{5} = 805 = 16$

The correct answer is $2 : 1$
The average speed of john is: $180 \ ÷ \ 3=60$ km$/$h
The average speed of Alice is: $270 \ ÷ \ 9=30$ km$/$h
Write the ratio and simplify.
$60 : 30 ⇒ 2 : 1$

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 $=$ lwh $= (36) \ (12) \ (4) = 1728$

The correct answer is $5$
Let $x$ be the number.
Write the equation and solve for $x$.
$(25 \ – \ x) \ ÷ \ x = 4$
Multiply both sides by $x$.
$(25 \ – \ x) = 4 \ x$, then add both sides.
$25 = 5 \ x$, now divide both sides by 5.
$x = 5$

The correct answer is $2,401$
$7^4=7 \ × \ 7 \ × \ 7 \ × \ 7=2,401$

The correct answer is $90\%$
Use percent formula: part $=\frac{ percent}{100} \ ×$ whole
$27=\frac{percent}{100} \ × \ 30 ⇒$
$27=\frac{ percent \ × \ 30}{100} ⇒$
$27=\frac{percent \ × \ 3}{10}$, multiply both sides by $10$.
$270=$ percent $× \ 3$, divide both sides by $3$.
$90=$ percent

The correct answer is $13$ cm
Use Pythagorean Theorem: $a^2 \ + \ b^2=c^2$
$5^2 \ + \ 12^2 = c^2 ⇒$
$25 \ + \ 144=c^2 ⇒$
$169=c^2⇒$
$c=13$ cm

The correct answer is $20^\circ$
The sum of supplement angles is $180$.
Let $x$ be that angle.
Therefore, $x \ + \ 8\ x = 180$
$9 \ x = 180$, divide both sides by $9: \ x = 20^\circ$

The correct answer is $420$
Add the first $5$ numbers.
$35 \ + \ 40 \ + \ 45 \ + \ 25 \ + \ 50 = 195$
To find the distance traveled in the next $5$ hours, multiply the average by number of hours.
Distance $=$ Average $×$ Rate $= 45 \ × \ 5 = 225$
Add both numbers.
$225 \ + \ 195 = 420$

The correct answer is $$80$
$$12×8=$96$, Petrol use: $8 \ × \ 2=16$ liters
Petrol cost: $16 \ × \ $1=$16$
Money earned: $$96 \ − \ $16=$80$

The correct answer is $9$ hours and $30$ minutes
Use distance formula: Distance $=$ Rate $×$ time $⇒ 380 = 40 \ ×$ T, divide both sides by $40$.
$380 / 40 =$ T $⇒$ T $= 9.5$ hours.
Change hours to minutes for the decimal part.
$0.5$ hours $= 0.5 \ × \ 60 = 30$ minutes.

The correct answer is $50\%$
Use the formula for Percent of Change $\frac{New \ Value \ − \ Old \ Value}{old \ value} \ × \ 100\%$
$\frac{25−50}{50} \ × \ 100\%= \ – \ 50\%$ (Negative sign here means that the new price is less than old price).

The correct answer is $15$
The ratio of boy to girls is $3:8$. Therefore, there are $3$ boys out of $11$ students.
To find the answer, first divide the total number of students by $11$, then multiply the result by $3$.
$55 \ ÷ \ 11=5 ⇒ 5 \ × \ 3=15$
There are $15$ boys and $30 \ (55 \ – \ 15)$ girls.
So, $15$ more boys should be enrolled to make the ratio $1:1$

The correct answer is $9.240$ kg
The weight of $13.2$ meters of this rope is: $13.3 \ × \ 700$ g $=9,240$ g
$1$ kg $= 1,000$ g, therefore, $9,240$ g $÷ \ 1000=9.24$ kg

The correct answer is $64$ kg
average $=\frac{sum \ of \ terms}{ number \ of \ terms}$
The sum of the weight of all girls is: $15 \ × \ 60=900$ kg
The sum of the weight of all boys is: $30 \ × \ 66=1,980$ kg
The sum of the weight of all students is: $900 \ + \ 1,980=2,880$ kg
average $=\frac{2,880}{45}=64$

The correct answer is $15$
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)
$3 \ × \ 5 = 15$ (bingo!)
$5 \ × \ 7 = 35$ (not in the options)
$7 \ × \ 11 = 77$ (not in the options)

The correct answer is $10\%$
Use this formula: Percent of Change $\frac{New \ Value \ − \ Old Value}{pld \ value} \ × \ 100\%$
$\frac{18,000 \ − \ 20,000 }{20,000} \ × \ 100\%=10\%$ and
$\frac{16,200 \ − \ 18,000}{18000} \ × \ 100\%=10\%$

The correct answer is $50\%$
The question is this: $560.50$ is what percent of $1,121$?
Use percent formula:
part $=\frac{percent}{100} \ ×$ whole
$560.50= \frac{percent}{100} × \ 1,121 ⇒ 560.50=\frac{ percent \ × \ 1,121}{100 }⇒$
$56050 =$ percent $× \ 1.121 ⇒$
percent $=\frac{56050}{1,121}=50$
$560.50$ is $50\%$ of $1,121$.
Therefore, the discount is: $100\% \ – \ 50\%=50\%$

The correct answer is $$880$
Let $x$ be the original price.
If the price of the sofa is decreased by $15\%$ to $$748$, then:
$85\%$ of $x=748 ⇒ 0.85 \ x =748 ⇒$
$x=748 \ ÷ \ 0.85=880$

The correct answer is $15$
If the score of Mia was $90$, therefore the score of Ava is $45$.
Since, the score of Emma was one third as that of Ava, therefore, the score of Emma is $15$.

The correct answer is $30$
Let $x$ be the smallest number.
Then, these are the numbers:
$x, x \ + \ 1, x \ + \ 2, x \ + \ 3, x \ +\ 4$
average $= \frac{sum \ of \ terms}{ number \ of \ terms} ⇒ 32=\frac{x \ + \ (x \ + \ 1) \ + \ (x \ + \ 2) \ + \ (x \ + \ 3) \ + \ (x \ + \ 4)}{5}⇒32=\frac{5 \ x \ +10}{5 }⇒ 160=5 \ x \ + \ 10 ⇒ 150=5 \ x ⇒ x=30$

The correct answer is $$420$
Let $x$ be the original price.
If the price of a laptop is decreased by $10\%$ to $$378$, then:
$90\%$ of $x=378 ⇒ 0.90 \ x=378 ⇒ x=378 \ ÷ \ 0.90=420$

The correct answer is $9$
Write the numbers in order:
$4, 5, 8, 9, 13, 15, 18$
Since we have $7$ numbers ($7$ is odd), then the median is the number in the middle, which is $9$.

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 $6$
Let $x$ be the number.
Write the equation and solve for $x$.
$\frac{1}{3} \ × \ 12= \frac{2}{3} \ x$.
$x ⇒ \frac{1 \ × \ 12}{3}= \frac{2 \ x}{3}$ , use cross multiplication to solve for $x$.
$3 \ × \ 12=2 \ x \ × \ 3 ⇒36=6 \ x ⇒ x=6$

The correct answer is $28$
The area of the floor is: $8$ cm $× \ 35$ cm $= 280$ cm$^2$
The number of tiles needed $= 288 \ ÷ \ 10 = 28$

The correct answer is $x=- \ 24, \ y=18$
$\begin{cases}x \ + \ 2 \ y = 12\\3 \ x \ + \ 5 \ y= 18\end{cases} →$ Multiply the top equation by $- \ 3$ then,
$\begin{cases}- \ 3 \ x \ - \ 6 \ y = - \ 36\\3 \ x \ + \ 5 \ y= 18\end{cases} →$ Add two equations
$- \ y = - \ 18→y=18$ plug in the value of $y$ into the first equation
$x \ + \ 2 \ y = 12 → x \ + \ 2 \ (18) = 12→ x \ + \ 36 = 12$
Subtract $36$ from both sides of the equation. Then: $x \ + \ 36=12→x=- \ 24$

The correct answer is $600$ ml
$5\%$ of the volume of the solution is alcohol.
Let $x$ be the volume of the solution.
Then: $5\%$ of $x=30$ ml $⇒ 0.05 \ x =30 ⇒ x=30÷0.05=600$

The correct answer is $5$ cm
Formula for the Surface area of a cylinder is:
$SA=2 \ \pi \ r^2 \ + \ 2 \ \pi \ r \ h →150 \ 𝜋=2 \ \pi \ r^2 \ + \ 2 \ \pi \ r \ (10)→r^2 \ + \ 10 \ 𝑟 \ − \ 75=0 \ (r \ + \ 15) \ (𝑟 \ − \ 5)=0→𝑟=5$ or $𝑟= \ − \ 15$ (unacceptable)

The correct answer is $I \ > \ 4000 \ x \ + \ 21000$
Let $x$ be the number of years.
Therefore, $$2,000$ per year equals $2000 \ x$.
starting from $$24,000$ annual salary means you should add that amount to $2000 \ x$.
Income more than that is:
$I \ > \ 4000 \ x \ + \ 21000$

The correct answer is $840$
Use simple interest formula: $I=prt$
($I=$ interest, $p=$ principal, $r=$ rate,$t=$ time)
$I=(7,000) \ (0.04) \ (3)=840$

The correct answer is $50$ miles
Use the information provided in the question to draw the shape.
$40$ miles
Use Pythagorean Theorem: $a^2 \ + \ b^2 = c^2$
$40^2+ 30^2=c^2 ⇒ 1600 \ + \ 900= c^2 ⇒ 2500=c^2 ⇒ c=50$

The correct answer is $\frac{17}{18}$
If $17$ balls are removed from the bag at random, there will be one ball in the bag.
The probability of choosing a brown ball is $1$ out of $18$.
Therefore, the probability of not choosing a brown ball is $17$ out of $18$ and the probability of having not a brown ball after removing $17$ balls is the same.

The correct answer is $12 \ \pi$
Area of the circle is less than $49 \ π$.
Use the formula of areas of circles.
Area $= \pi \ r^2 ⇒ 49 \ \pi \ > \ \pi \ r^2⇒$
$49 > r^2⇒ r \ < \ 7$
Radius of the circle is less than $7$.
Let’s put $7$ for the radius.
Now, use the circumference formula:
Circumference $=2 \ \pi \ r =2 \ \pi \ (7)=14 \ \pi$
Since the radius of the circle is less than $7$.
Then, the circumference of the circle must be less than $14 \ \pi$.
Only choice A is less than $14 \ \pi$.

The correct answer is $\frac{2}{7}, \frac{3}{8}, \frac{5}{11}, \frac{3}{4}$
Let’s compare each fraction:
$\frac{2}{7} \ < \ \frac{3}{8} \ < \ \frac{5}{11} \ < \ \frac{3}{4}$
Only choice A provides the right order.

The correct answer is $0.88$ D
To find the discount, multiply the number by ($100\% \ –$ rate of discount).
Therefore, for the first discount we get: (D) ($100\% \ – \ 20\%) =$ (D) $(0.80) = 0.80$ D
For increase of $10\%: (0.85$ D) $(100\% \ + \ 10\%) = (0.85$ D) $(1.10) = 0.88$ D $= 88\%$ of D

The correct answer is $70$
To find the number of possible outfit combinations, multiply number of options for each factor: $7 \ × \ 2 \ × \ 5=70$

The correct answer is $(5, 7)$
The equation of a line is in the form of $y=m \ x \ + \ b$, where $m$ is the slope of the line and $b$ is the $y−$intercept of the line.
Two points $(5, 3)$ and $(6, 4)$ are on line A.
Therefore, the slope of the line A is:
slope of line $A=\frac{y_{2} \ − \ y_{1}}{x_{2} \ − \ x_{1}}= \frac{4 \ − \ 3}{6 \ − \ 5}=\frac{1}{1}=1$
The slope of line A is $1$.
Thus, the formula of the line A is:
$y=x \ + \ 𝑏$, choose a point and plug in the values of $x$ and $y$ in the equation to solve for .
Let’s choose point $(5, 3)$.
Then: $y=x \ + \ b→5=3 \ + \ b→b=5 \ − \ 3= 2$
The equation of line A is: $y=x \ + \ 2$
Now, let’s review the choices provided:
A. $(− \ 1, 2) \ \ y=x \ + \ 2→2=− \ 1 \ + \ 2=1$ This is not true.
B. $(5, 7) \ \ y=x \ + \ 2→7=5 \ + \ 2=7$ This is true!
C. $(3, 4) \ \ y=x \ + \ 2→4=3 \ + \ 2=5$ This is not true.
D. $(− \ 1, − \ 2) \ \ y=x \ + \ 2→− \ 2=− \ 1 \ + \ 2=1$ This is not true.

The correct answer is $46$ cm
The area of the trapezoid is: Area $=\frac{1}{2} \ h \ (b1 \ + \ b2)=\frac{1}{2} \ (x)(13+8)=126→10.5 \ x=126→x=12$
$y=\sqrt{5^2 \ + \ 12^2}=\sqrt{25 \ + \ 144}=\sqrt{169}=13$
The perimeter of the trapezoid is: $12 \ + \ 13 \ + \ 8 \ + \ 13=46$

The correct answer is $46$ cm
The area of the trapezoid is: Area $=\frac{1}{2} \ h \ (b1 \ + \ b2)=\frac{1}{2} \ (x)(13+8)=126→10.5 \ x=126→x=12$
$y=\sqrt{5^2 \ + \ 12^2}=\sqrt{25 \ + \ 144}=\sqrt{169}=13$
The perimeter of the trapezoid is: $12 \ + \ 13 \ + \ 8 \ + \ 13=46$

The correct answer is $26.75$
$2 \ x \ - \ 6=10.5→2 \ x=10.5+6=16.5→x=\frac{16.5}{2}=8.25$
Then; $3 \ x \ + \ 2=3 (8.25) \ + \ 2=24.75 \ + \ 2=26.75$

The correct answer is $- \ 2$
Use PEMDAS (order of operation):
$- \ 16 \ + \ 6 \ × \ (– \ 5) \ – \ [ \ 6 \ + \ 22 \ × \ (- \ 4) \ ] \ ÷ \ 2 \ + \ 5=$
$− \ 16 \ − \ 30 \ − \ [ \ 6 \ − \ 88 \ ] \ ÷ \ 2 \ + \ 5=$
$− \ 43 \ − \ [ \ − \ 82 \ ] \ ÷ \ 2 \ + \ 5=$
$− \ 48 \ +\ 82 \ ÷ \ 2 \ + \ 5=$
$− \ 48 \ + \ 41 \ + \ 5= \ - \ 2$

The correct answer is $21$
The input value is $3$.
Then: $x=3, \ 𝑓(x)=x^2 \ + \ 4 \ x→$
$f(3)=9 \ + \ 4 \ (3)=9 \ + 12=21$

The correct answer is $220$
The perimeter of the trapezoid is $58$.
Therefore, the missing side (height) is $= 58 \ – \ 16 \ – \ 12 \ – \ 10= 20$
Area of a trapezoid: A $= \frac{1}{2} \ h \ (b1 \ + \ b2) = \frac{1}{2} \ (20) \ (10 \ + \ 12) = 220$

The correct answer is $13$
Since $𝑁=5$, substitute $5$ for $N$ in the equation $\frac{x \ + \ 2}{3}=N$, which gives $\frac{x \ + \ 2}{3}=5$.
Multiplying both sides of $\frac{x \ + \ 2}{3}=5$ by $3$ gives $x \ + \ 2=15$ and then adding $- \ 2$ to both sides of
$x \ + \ 2=15$ then, $x=13$.

The correct answer is $\frac{3}{2}$
Let $x$ be the length of an edge of cube, then the volume of a cube is: $𝑉=x^3$
The surface area of cube is: $𝑆𝐴=6 \ x^2$
The volume of cube A is $\frac{1}{4}$ of its surface area. Then:
$x^3=\frac{6 \ x^2}{4}→x^3=\frac{3}{2} \ x^2$, divide both side of the equation by $x^2$.
Then: $\frac{x^3}{x^2}=\frac{3 \ x^2}{2 \ x^2}→x=\frac{3}{2}$

The correct answer is $8$
First draw an isosceles triangle.
Remember that two sides of the triangle are equal.
Let put $a$ for the legs. Then:
$𝑎=4⇒$ area of the triangle is $=\frac{1}{2}(4 \ × \ 4)=\frac{16}{2}=8$

The correct answer is $7$
average $=\frac{sum \ of \ terms}{ number \ of \ terms} ⇒$
$15=\frac{13 \ + \ 16 \ + \ 24 \ + \ x}{4}⇒$
$60=53 \ + \ x⇒x=7$

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

The correct answer is $150$
The question is this: $1.95$ is what percent of $1.30$?
Use percent formula:
part $= \frac{percent}{100 } \ ×$ whole
$1.95 = \frac{percent}{100} \ × \ 1.30 ⇒ 1.95 =\frac{ percent \ × \ 1.30}{100} ⇒195 =$ percent $× \ 1.30 ⇒$ percent $= \frac{195}{1.30} = 150$

The correct answer is $\frac{1}{5}$ or $0.2$
Write the ratio of $3 \ 𝑎$ to $4 \ b$.
$\frac{3 \ a}{6 \ b}=\frac{1}{10}$
Use cross multiplication and then simplify.
$3 \ a × 10= 6 \ b × 1 → 30 \ a = 6 \ b → a = \frac{6 \ b}{30} = \frac{ b}{5}$
Now, find the ratio of $a$ to $b$.
$\frac{a}{b} = \frac{\frac{ b}{5}}{b} →\frac{ b}{5} ÷ b =\frac{ b}{5} × \frac{1}{b} = \frac{b }{5 \ b} = \frac{1}{5} =0.2$

The correct answer is $33.75$ m
The rate of construction company $=\frac{50 \ cm}{1 \ min}=50$ cm$/$min
Height of the wall after $45$ minutes $=\frac{ 50 \ cm}{1 \ min}× \ 45$ min $=2,250$ cm
Let $x$ be the height of wall, then $\frac{2}{3} \ x=2,250$ cm $→x=\frac{3 \ × \ 2,250}{2}→x=3,375$ cm $= 33.75$ m