Full Length STAAR Grade 7 Practice Test

The correct answer is $39 \ π$ cm$^2$
To find the area of the shaded region, find the difference of the area of two circles.
(S$_{1}$: the area of bigger circle. S$_{2}$: the area of the smaller circle)
Use the area of circle formula.
S $= π \ r^2$
S$_{1} \ -$ S$_{2} = π \ ( 5 \ + \ 3$cm)$^2 \ - \ π \ (5$ cm)$^2 ⇒$
S$_{1} \ -$ S$_{2} = π \ 64$ cm$^2 \ - \ π \ 25$ cm$^2 ⇒$
S$_{1} \ -$ S$_{2} = 39 \ π$ cm$^2$

The correct answer is $\frac{5}{8}$
William ate $\frac{1}{4}$ of $8$ parts of his pizza that it means $2$ parts out of $8$ parts ( $\frac{1}{4}$ of $8$ parts $= x ⇒ x = 2$) and left $6$ parts.
Ella ate $\frac{1}{2}$ of $8$ parts of her pizza that it means $4$ parts out of $8$ parts ( $\frac{1}{2}$ of $8$ parts $= x ⇒ x = 4$) and left $4$ parts.
Therefore, they ate $(4 \ + \ 2)$ parts out of $(8 \ + \ 8)$ parts of their pizza and left $(6 \ + \ 4)$ parts out of $(8 \ + \ 8)$ parts of their pizza.
It means: $\frac{ 10}{16}$
After simplification we have: $\frac{5}{8}$

The correct answer is $48 \ x^8 \ y^6$
Simplify.
$3 \ y^2 \ (2 \ x^2 \ y)^4=$
$3 \ y^2 \ (16 \ x^8 \ y^4 ) =$
$48 \ x^8 \ y^6$

The correct answer is $17$ cm
Use Pythagorean Theorem: $a^2 \ + \ b^2 = c^2$
$8^2 \ + \ 15^2 = c^2 ⇒$
$64 \ + \ 225 = c^2 ⇒$
$c^2 =289 ⇒$
$c=17$

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 $10\%: \ (0.80$ D) $(100\% \ + \ 10\%) = (0.85$ D) $(1.10) = 0.88$ D $= 88\%$ of D

The correct answer is $– \ 126$
Use PEMDAS (order of operation):
$\left[ \ 6 \ × \ (– \ 24) \ + \ 12 \ \right] \ – \ (4) \ + \ \left[ \ 4 \ × \ 5 \ \right] \ ÷ \ 2 =$
$\left[ \ – \ 144 \ + \ 12 \ \right] \ – \ 4 \ + \ \left[ \ 20 \ \right] \ ÷ \ 2 =$
$\left[ \ – \ 144 \ + \ 12 \ \right] \ – \ 4 \ + \ 10 =$
$\left[ \ – \ 132 \ \right] \ – \ 4 \ + \ 10 = \left[ \ – \ 132 \ \right] \ – \ 4 \ + \ 10 = – \ 126$

The correct answer is $16 \ π$
Use the formula of areas of circles.
Area $= π \ r^2 ⇒$
$64 \ π = π \ r^2 ⇒$
$64 = r^2 ⇒ r = 8$
Radius of the circle is $8$.
Now, use the circumference formula:
Circumference $= 2 \ π \ r = 2 \ π \ (8) = 16 \ π$

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 $140\%$
The question is this:
$1.75$ is what percent of $1.25$?
Use percent formula:
part $= \frac{percent}{100} \ ×$ whole
$= \frac{percent}{100} \ × 1.25 ⇒$
$1.75 = \frac{percent \ × \ 1.25}{100} ⇒$
$175 =$ percent $× \ 1.25 ⇒$
percent $= \frac{175}{1.25} = 140$

The correct answer is $10\%$
Let $x$ be the amount of students in the class.
$40\%$ of $x =$ girls
$25\%$ of girls $=$ tennis player
Find $25\%$ of $40\%$. Then:
$25\%$ of $40\%=0.25 \ × \ 0.40=0.10=10\%$

The correct answer is $28$
Write the numbers in order:
$2, \ 19, \ 28, \ 28, \ 35, \ 44, \ 67$
Since we have $7$ numbers ($7$ is odd), then the median is the number in the middle, which is $28$.

The correct answer is $60000$
Three times of $24,000$ is $72,000$.
One sixth of them cancelled their tickets.
One sixth of $72,000$ equals $12,000 (1/6 \ × \ 72000 = 12000)$.
$60,000 (72000 \ – \ 12000 = 60000)$ fans are attending this week

The correct answer is $7$
Write the ratio and solve for $x$.
$\frac{45}{40} =\frac{2 \ x \ + \ 4}{16} ⇒$
$40 \ (2 \ x \ + \ 4)=45 \ × \ 16 ⇒ x=7$

The correct answer is $8 \ (4 \ − \ x)=96$
Only option B is correct. Other options don’t work in the equation.
$8 \ (4 \ - \ (- \ 8))=96$

The correct answer is $8$
Let $x$ be the number of balls. Then:
$\frac{1}{3} \ x \ + \ \frac{1}{6} \ x \ + \ \frac{1}{4} \ x \ + \ 12 = x$
$(\frac{1}{3} \ + \ \frac{1}{6} \ + \ \frac{1}{4}) \ x \ + \ 12 = x$
$(\frac{9}{12}) \ x + 12 = x$
$x = 48$
In the bag of small balls $\frac{1}{6}$ are white, then: $\frac{48}{6} = 8$
There are $8$ white balls in the bag.

The correct answer is $50$
Use the information provided in the question to draw the shape.
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 $15\%$
The question is this:
$530.40$ is what percent of $624$?
Use percent formula:
part $= \frac{percent}{100} \ ×$ whole
$530.40 =\frac{ percent}{100} \ × 624 ⇒$
$530.40 = \frac{percent \ × \ 624}{100} ⇒$
$53040 =$ percent $× \ 624 ⇒$
percent $= \frac{53040}{624 }= 85$
$530.40$ is $85\%$ of $624$.
Therefore, the discount is: $100\% \ – \ 85\% = 15\%$

The correct answer is $15$
If the score of Mia was $60$, then the score of Ava is $30$.
Since, the score of Emma was half as that of Ava, therefore, the score of Emma is $15$.

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 $7.32$
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 $600$ 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 $400$
Let $x$ be the original price.
If the price of a laptop is decreased by $10\%$ to $$360$, then:
$90\%$ of $x=360 ⇒$
$0.90 \ x=360 ⇒$
$x=360 \ ÷ \ 0.90=400$

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 $$300$
Let $L$ be the price of laptop and $C$ be the price of computer.
$3 \ (L) =5 \ (C)$ and $L = $200 \ + \ C$
Therefore, $3 \ ($200 \ + \ C) =5 \ C ⇒$
$$600 \ + \ 3C = 5C ⇒$
$C=$300$

The correct answer is $97.6$
Use the area of square formula.
S $= a^2 ⇒ 595.36 = a^2 ⇒ a = 24.4$
One side of the square is $24.4$ feet.
Use the perimeter of square formula.
P $= 4 \ a ⇒$ P $= 4(24.4) ⇒$ P $= 97.6$

The correct answer is $6$ hours
The distance between Jason and Joe is $9$ miles.
Jason running at $5.5$ miles per hour and Joe is running at the speed of $7$ miles per hour.
Therefore, every hour the distance is $1.5$ miles less.
$9 \ ÷ \ 1.5 = 6$

The correct answer is $80\%$
The failing rate is $11$ out of $55 = \frac{11}{55}$
Change the fraction to percent:
$\frac{11}{55} \ × \ 100\%=20\%$
$20$ percent of students failed.
Therefore, $80$ percent of students passed the exam.

The correct answer is $60$
Jason needs an $75\%$ average to pass for five exams.
Therefore, the sum of $5$ exams must be at least $5 \ × \ 75 = 375$
The sum of $4$ exams is:
$68 \ + \ 72 \ + \ 85 \ + \ 90 = 315$.
The minimum score Jason can earn on his fifth and final test to pass is:
$375 \ – \ 315 = 60$

The correct answer is $840$
Use simple interest formula:
$I = prt$
($I =$ interest, $p =$ principal, $r =$ rate, $t =$ time)
$I=(12000) \ (0.035) \ (2)=840$

The correct answer is $44$
Let $x$ be the integer. Then:
$2 \ x \ – \ 5 = 83$
Add $5$ both sides: $2 \ x = 88$
Divide both sides by $2: \ x = 44$

The correct answer is $(- \ 1, \ 3)$
Input the points instead of $x$ and $y$ in the formula.
Only option B works in the equation.
$4 \ x \ + \ 6 \ y=14$
$4 \ (– \ 1) \ + \ 6 \ (3) =14$

The correct answer is $90$
To find the number of possible outfit combinations, multiply number of options for each factor:
$6 \ × \ 3 \ ×\ 5 = 90$

The correct answer is $30$
The sum of supplement angles is $180$.
Let $x$ be that angle. Therefore,
$x \ + \ 5 \ x = 180$
$6 \ x = 180$, divide both sides by $6: \ x = 30$

The correct answer is $5 : 9$
The average speed of John is: $150 \ ÷ \ 6 = 25$ km
The average speed of Alice is: $180 \ ÷ \ 4 = 45$ km
Write the ratio and simplify.
$25: 45 ⇒ 5: 9$

The correct answer is $210$
Let $x$ be the number of soft drinks for $252$ guests.
It’s needed to have a proportional ratio to find $x$.
$\frac{10 \ soft \ drinks}{12 \ guests} = \frac{x}{252 \ guests}$
$x = \frac{252 \ × \ 10}{12 }⇒x=210$

The correct answer is $$23.8$
Let $x$ be the number of cans.
Write a proportion and solve for $x$.
$\frac{5 \ cans}{$3.40) }= \frac{35 \ cans}{x}$
$x =\frac{3.40\ × \ 35}{5} ⇒x=$23.8$

The correct answer is $5$
$x\%$ of $24$ is $1.2$, then:
$x\% 24 =1.2 ⇒$
$0.24 \ x=1.2 ⇒$
$x=1.2 \ ÷ \ 0.24=5$

The correct answer is Mathematics
Compare each score:
In Algebra Joe scored $20$ out of $25$ in Algebra that it means $80\%$ of total mark.
$\frac{20}{25} = \frac{x}{100} ⇒x= 80$
Joe scored $30$ out of $40$ in science that it means $75\%$ of total mark.
$\frac{30}{40} = \frac{x}{100} ⇒x= 75$
Joe scored $68$ out of $80$ in mathematic that it means $85\%$ of total mark.
$\frac{68}{80} = \frac{x}{100} ⇒x= 85$
Therefore, his score in mathematic is higher than his other scores.

The correct answer is $480$ m$^3$
Use the volume of square pyramid formula.
$V= \frac{1}{3} \ a^2 \ h ⇒$
$V= \frac{1}{3} \ (12$ m)$^2 \ × \ 10$ m $⇒ V= 480$ m$^3$

The correct answer is $480$ m$^3$
Use the volume of square pyramid formula.
$V= \frac{1}{3} \ a^2 \ h ⇒$
$V= \frac{1}{3} \ (12$ m)$^2 \ × \ 10$ m $⇒ V= 480$ m$^3$