Full Length STAAR Grade 8 Practice Test

The correct answer is $7.32$
The weight of $12.2$ meters of this rope is:
$12.2 \ × \ 600$ g $= 7320$ g
$1$ kg $= 1000$ g, therefore, $7320$ g $÷ 1000 = 7.32$ kg

The correct answer is $600$
The ratio of boys to girls is $3:7$.
Therefore, there are $3$ boys out of $10$ students.
To find the answer, first divide the number of boys by $3$, then multiply the result by $10$.
$180 \ ÷ \ 3 = 60 ⇒$
$60 \ × \ 10 = 600$

The correct answer is $38$
the population is increased by $15\%$ and $20\%$.
$15\%$ increase changes the population to $115\%$ of original population.
For the second increase, multiply the result by $120\%$.
$(1.15) \ × \ (1.20) = 1.38 = 138\%$
$38$ percent of the population is increased after two years.

A linear equation is a relationship between two variables, $x$ and $y$, that can be put in the form $y = m \ x \ + \ b$.
A non-proportional linear relationship takes on the form $y = m \ x \ + \ b$, where $b ≠ 0$ and its graph is a line that does not cross through the origin.

The correct answer is $5, \ 10$
The perimeter of the rectangle is:
$2 \ x \ + \ 2 \ y=30→$
$x \ + \ y=15→$
$x=15 \ - \ y$
The area of the rectangle is:
$x \ × \ y=50→$
$(15 \ - \ y) \ (y)=50→$
$y^2 \ - \ 15 \ y \ + \ 50=0$
Solve the quadratic equation by factoring method.
$(y \ - \ 5) \ (y \ - \ 10)=0→$
$y=5$
(Unacceptable, because $y$ must be greater than $5$) or $y=10$
If $y=10 →$
$x \ × \ y=50→$
$x \ × \ 10=50→$
$x=5$

The correct answer is $120 \ x\ + \ 22.000 \ ≤ \ 40.000$
Let $x$ be the number of new shoes the team can purchase. Therefore, the team can purchase $240 \ x$.
The team had $$40,000$ and spent $$22,000$.
Now the team can spend on new shoes $$18,000$ at most.
Now, write the inequality: $120 \ x\ + \ 22.000 \ ≤ \ 40.000$

The correct answer is $10$ cm
Use the information provided in the question to draw the shape.
Use Pythagorean Theorem: $a^2 \ + \ b^2 = c^2$
$6^2 \ + \ 8^2 = c^2 ⇒$
$100 = c^2 ⇒ c = 10$

The correct answer is $25.5$
$3 \ x \ - \ 5=8.5→$
$3 \ x=8.5 \ + \ 5=13.5→$
$x=\frac{13.5}{3}=4.5$
Then; $5 \ x \ + \ 3=5 \ (4.5) \ + \ 3=22.5 \ + \ 3=25.5$

The correct answer is $$1800$
Use simple interest formula:
$I=prt$
($I =$ interest, $p =$ principal, $r =$ rate, $t =$ time)
$I=(8000) \ (0.045) \ (5)=1800$

The correct answer is $210$
Let $x$ be the number of soft drinks for $252$ guests.
Write the proportion and solve for $x$.
$\frac{10 \ soft \ drinks}{12 guests}= \frac{x}{252 \ guests}$
$x = \frac{252 \ × \ 10}{12} ⇒x=210$

The correct answer is $600$ ml
$4\%$ of the volume of the solution is alcohol.
Let $x$ be the volume of the solution.
Then: $4\%$ of $x = 24$ ml $⇒ 0.04 \ x = 24 ⇒$
$x = 24 \ ÷ \ 0.04 = 600$

The correct answer is $40$ ft.$^2$
Use the area of rectangle formula $(s = a \ × \ b)$.
To find area of the shaded region subtract smaller rectangle from bigger rectangle.
S$_{1} \ –$ S$_{2} = (10$ ft $× \ 8$ ft) $– \ (5$ ft $× \ 8$ ft) $⇒$ S$_{1} \ –$ S$_{2} = 40$ ft.$^2$

The correct answer is $30\%$
Use the formula for Percent of Change
$\frac{New \ Value-Old \ Value}{Old \ Value} \ × \ 100\%$
$\frac{28 \ - \ 40}{40} \ × \ 100\% = \ – \ 30\%$
(negative sign here means that the new price is less than old price).

The correct answer is $$1000$
Use simple interest formula:
$I=prt$
($I =$ interest, $p =$ principal, $r =$ rate, $t =$ time)
$I=(5000) \ (0.05) \ (4)=1000$

The correct answer is $8$
Use formula of rectangle prism volume.
$V =$ (length) (width) (height) $⇒ 2000 = (25) \ (10)$ (height) $⇒$
height $= 2000 \ ÷ \ 250 = 8$ feet

The correct 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 $20 \ \pi$
To find the area of the shaded region subtract smaller circle from bigger circle.
S $_{bigger} \ –$ S $_{smaller} = π \ (r _{bigger} )^2 \ – \ π \ (r _{smaller} )^2 ⇒$
S $_{bigger} \ –$ S $_{smaller} = π \ (6)^2 \ – \ π \ (4)^2 ⇒$
$36 \ π \ – \ 16 \ π = 20 \ π$

The correct answer is $18$
$a=6⇒$ area of the triangle is $=\frac{1}{2} \ (6 \ × \ 6)=\frac{36}{2}=18$ cm $^2$

The correct answer is $$70$
$$9 \ × \ 10=$90$
Petrol use:
$10 \ × \ 2=20$ liters
Petrol cost:
$20 \ × \ $1=$20$
Money earned:
$$90 \ - \ $20=$70$

The correct answer is $20$
Five years ago, Amy was three times as old as Mike.
Mike is $10$ years now.
Therefore, $5$ years ago Mike was $5$ years.
Five years ago, Amy was:
A $=3 \ × \ 5=15$
Now Amy is $20$ years old:
$15 \ + \ 5 = 20$

The correct answer is $22$
$\begin{cases}\frac{ - \ x}{2} \ + \ \frac{y}{4}=1\\ \frac{- \ 5 \ y}{6} \ + \ 2 \ x =4 \end{cases} \mapsto$ Multiply the top equation by $4$.
Then:
$\begin{cases}- \ 2 \ x \ + \ y=4\\ \frac{- \ 5 \ y}{6} \ + \ 2 \ x =4 \end{cases} \mapsto$ Add two equations.
$\frac{1}{6} \ y=8→y=48$ , plug in the value of $y$ into the first equation $→x=22$

The correct answer is $4.8$
Two triangles $\triangle$BAE and $\triangle$BCD are similar. Then:
$\frac{AE}{CD}=\frac{AB}{BC}→$
$\frac{4}{6}=\frac{x}{12}→$
$48 \ - \ 4 \ x=6 \ x→$
$10 \ x=48→$
$x=4.8$

The correct answer is $10$
$\frac{2}{5} \ × \ 25=\frac{50}{5}=10$

The correct answer is $y=x$
The slop of line A is: $m=\frac{y_{2} \ - \ y_{1}}{x_{2} \ - \ x_{1}}=\frac{3 \ - \ 2}{4 \ - \ 3}=1$
Parallel lines have the same slope and only choice D $(y=x)$ has slope of $1$.

The correct answer is $5$
$x$ is directly proportional to the square of $y$. Then:
$x=c \ y^2$
$12=c \ (2)^2→$
$12=4 \ c→$
$c=\frac{12}{4}=3$
The relationship between $x$ and $y$ is:
$x=3 \ y^2$
$x=75$
$75=3 \ y^2→$
$y^2=\frac{75}{3}=25→y=5$

The correct answer is $54$
The amount of money that jack earns for one hour:
$\frac{$616}{44}=$14$
$\frac{$826 \ - \ $616}{1.5 \ × \ $14}=10$
Number of total hours is:
$44 \ + \ 10=54$

The correct answer is $a= c$
Let’s find the mean (average), mode and median of the number of cities for each type of pollution.
Number of cities for each type of pollution: $6, \ 3, \ 4, \ 9, \ 8$
average (mean) $= \frac{sum \ of \ terms}{number \ of \ terms}= \frac{6 \ + \ 3 \ + \ 4 \ + \ 9 \ + \ 8}{5}=\frac{30}{5}=6$
Median is the number in the middle. To find median, first list numbers in order from smallest to largest.
$3, \ 4, \ 6, \ 8, \ 9$
Median of the data is $6$.
Mode is the number which appears most often in a set of numbers.
Therefore, there is no mode in the set of numbers.
Median $=$ Mean, then, $a= c$

The correct answer is $60\%, \ 40\%, \ 90\%$
Percent of cities in the type of pollution A: $\frac{6}{10} \ × \ 100=60\%$
Percent of cities in the type of pollution C: $\frac{4}{10} \ × \ 100=40\%$
Percent of cities in the type of pollution E: $\frac{9}{10} \ × \ 100=90\%$

The correct answer is $2$
Let the number of cities should be added to type of pollutions B be $x$. Then:
$\frac{x \ + \ 3}{8}=0.625→$
$x \ +\ 3=8 \ × \ 0.625→$
$x \ + \ 3=5→$
$x=2$

The correct answer is $\frac{1}{2}$
AB $=12$ And AC $=5$
BC $=\sqrt{12^2 \ + \ 5^2}=\sqrt{144\ +\ 25}=\sqrt{169}=13$
Perimeter $=5 \ + \ 12\ + \ 13=30$
Area $=\frac{5 \ × \ 12}{2}=5 \ × \ 6=30$
In this case, the ratio of the perimeter of the triangle to its area is: $\frac{30}{30}=1$
If the sides AB and AC become twice longer, then:
AB $=24$ And AC $=10$
BC $=\sqrt{24^2 \ + \ 10^2}=\sqrt{576 \ + \ 100}=\sqrt{676}=26$
Perimeter $=26 \ + \ 24 \ + \ 10=60$
Area $=\frac{10 \ × \ 24}{2}=10 \ × \ 12=120$
In this case the ratio of the perimeter of the triangle to its area is: $\frac{60}{120}=\frac{1}{2}$

The correct answer is $21$
The capacity of a red box is $20\%$ bigger than the capacity of a blue box and it can hold $30$ books.
Therefore, we want to find a number that $20\%$ bigger than that number is $30$.
Let $x$ be that number. Then:
$1.20 \ × \ x=30$, Divide both sides of the equation by $1.2$. Then:
$x=\frac{30}{1.20}=25$
Number of books in $30\%$ of red box $= \frac{30}{100} \ × \ 30=9→$
$30 \ - \ 9=21$

The correct answer is $- \ 5$
The smallest number is $- \ 15$.
To find the largest possible value of one of the other five integers, we need to choose the smallest possible integers for four of them. Let $x$ be the largest number. Then:
$- \ 70=(- \ 15) \ + \ (- \ 14) \ + \ (- \ 13) \ + \ (- \ 12) \ + \ (- \ 11) \ + \ x→$
$- \ 70=- \ 65 \ +\ x→$
$x=- \ 70 \ + \ 65=- \ 5$

The correct answer is $- \ 5$
$α=180^° \ - \ 112^°=68^°$
$β=180^° \ -\ 135^°=45^°$
$x \ + \ α \ + \ β=180^°→$
$x=180^° \ - \ 68^° \ - \ 45^°=67^°$

The correct answer is $f(x)=\sqrt{x} \ + \ 4$
A. $f(x)=x^2 \ - \ 5$      if $x=1→f(1)=(1)^2 \ - \ 5=1 \ - \ 5=- \ 4≠5$
B. $f(x)=x^2 \ - \ 1$      if $x=1→f(1)=(1)^2 \ - \ 1=1 \ - \ 1=0≠5$
C. $f(x)=\sqrt{x \ + \ 2}$    if $x=1→f(1)=\sqrt{1 \ + \ 2}=\sqrt{3}≠5$
D. $f(x)=\sqrt{x} \ + \ 4$   if $x=1→f(1)=\sqrt{1} \ + \ 4=5$

The correct answer is $$810$
Let $x$ be all expenses, then $\frac{22}{100} \ x=$660→$
$x=\frac{100 \ × \ $660}{22}=$3000$
He spent for his rent: $\frac{27}{100} \ × \ $3000=$810$

The correct answer is $\frac{100 \ x \ + \ 800}{x}$
The amount of money for $x$ bookshelf is: $100 \ x$
Then, the total cost of all bookshelves is equal to: $100 \ x \ + \ 800$
The total cost, in dollar, per bookshelf is:
$\frac{Total \ cost}{number \ of \ items}=\frac{100 \ x \ + \ 800}{x}$

The correct answer is $0$
$\sqrt{x}=4→x=16$
then; $\sqrt{x} \ - \ 7=\sqrt{16} \ - \ 7=4 \ - \ 7=- \ 3$ and $\sqrt{x \ - \ 7}=\sqrt{16 \ - \ 7}=\sqrt{9}=3$
Then: $(\sqrt{x \ - \ 7}) \ + \ (\sqrt{x \ - \ 7})=3 \ + \ (-\ 3)=0$

The correct answer is $25$
The angles on a straight line add up to $180$ degrees. Then:
$x \ + \ 25 \ + \ y \ + \ 2 \ x \ + \ y=180$
Then, $3 \ x \ + \ 2 \ y=180 \ - \ 25→$
$3 \ (35) \ + \ 2y=155→$
$2 \ y=155 \ - \ 105=50→$
$y=25$

The correct answer is $37$
Square root of $16$ is $\sqrt{16}=4\ < \ 6$
Square root of $25$ is $\sqrt{25}=5 \ < \ 6$
Square root of $37$ is $\sqrt{37}=\sqrt{36 \ + \ 1} \ >\ \sqrt{36}=6$
Square root of $49$ is $\sqrt{49}=7 \ > \ 6$
Since, $\sqrt{37} \ < \ \sqrt{49}$, then the answer is C.

The correct answer is $11$
$|- \ 12 \ -\ 5| \ - \ |- \ 8 \ + \ 2|=|- \ 17| \ - \ |- \ 6|=17 \ - \ 6=11$