# Full-Length 7th Grade STAAR Math Practice Test-Answers and Explanations

Did you take the 7th Grade STAAR Math Practice Test? If so, then it’s time to review your results to see where you went wrong and what areas you need to improve.

## 7th Grade STAAR Math Practice Test Answers and Explanations

1- Choice C is correct
If the score of Mia was 90, then the score of Ava is 30. Since, the score of Emma was one and a half as that of Ava, therefore, the score of Emma is $$1.5×30=45$$.

2- Choice A is correct
Write the ratio and solve for $$x$$. $$\frac{60}{50}=\frac{5x+2}{10}⇒ 12=5x+2 ⇒12-2=5x⇒ x=\frac{10}{5}=2$$

3- Choice B is correct
Let x be the number of students in the class. $$40\%$$ of $$x$$ = girls, $$25\%$$ of girls = tennis player,
Find $$25\%$$ of $$40\%$$. Then: $$25\%$$ of $$40\%$$$$=0.25×0.40=0.1=10\%$$ or $$\frac{10}{100}=\frac{1}{10}$$

4- Choice C is correct
Use the information provided in the question to draw the shape.
Use Pythagorean Theorem: $$a^2+b^2=c^2$$
$$30^2+40^2=c^2⇒ 900+1600= c^2⇒2500= c^2⇒c=50$$

5- Choice A is correct
Write a proportion and solve for $$x$$. $$\frac{12 \space Cans}{ 7.40}=\frac{30 \space Cans}{x}, x= \frac{7.40×30}{12}⇒x=18.5$$

6- Choice D is correct
Use the volume of square pyramid formula.
$$V= \frac{1}{3} a^2 h ⇒V=\frac{1}{3} (12m)^2×20m ⇒ V=960 m^3$$

7- Choice C is correct
Let x be the number of soft drinks for 240 guests. Write a proportional ratio to find x. $$\frac{6 \space soft \space drinks}{8 \space guests} =\frac{x}{240 \space guests}$$,
$$x=\frac{240×6}{8}⇒x=180$$

8- Choice B is correct
Use the formula for Percent of Change: $$\frac{New \space Value-Old \space Value}{Old \space Value}×100\%$$,
$$\frac{1.75-1.4}{cd}×100\%=25\%$$

9- The answer is: -99
Use PEMDAS (order of operation): $$[8×(-14)+15]-(10)+[4×6]÷3=[-122+15]-(10)+8=-97-10+8=-99$$

10- Choice D is correct
Simplify. $$5x^2 y(2xy^3)^4=5x^2 y(16x^4 y^{12 })=80x^6 y^{13}$$

$11.99 Satisfied 102 Students 11- Choice C is correct The distance between Jason and Joe is 14 miles. Jason running at 6 miles per hour and Joe is running at the speed of 8 miles per hour. Therefore, every hour the distance is 2 miles less. $$14÷2=7$$ 12- Choice A is correct Let x be the integer. Then: $$5x-9=101$$, Add 9 both sides: $$5x=110$$, Divide both sides by 5: $$x=22$$ 13- Choice D is correct Two and half times of $$18,000$$ is $$45,000$$. One fifth of them cancelled their tickets. One sixth of $$45,000$$ equals $$9,000(\frac{1}{5} ×45000=9000)$$. $$36,000(45000-9000=36000)$$ fans are attending this week 14- Choice C is correct Write the numbers in order: 25,12,13,18,22,36,22 Since we have 7 numbers (7 is odd), then the median is the number in the middle, which is 22. 15- Choice D is correct The question is: 615 is what percent of 820? Use percent formula: part$$=\frac{percent}{100}×whole$$ $$615=\frac{percent}{100}×820 ⇒ 615=\frac{percent ×820}{100}⇒61,500=percent×820$$⇒ percent$$=\frac{61,500}{820}=75, 615$$ is $$75\%$$ of $$820$$. Therefore, the discount is: $$100\%-75\%=25\%$$ 16- The answer is $$22 \frac{1}{3}$$ miles. Robert runs $$4 \frac{1}{3}$$ miles on Saturday and $$2(4 \frac{1}{3} )$$ miles on Monday and Wednesday. Robert wants to run a total of 35 miles this week. Therefore, subtract $$4 \frac{1}{3}+2(4 \frac{1}{3} )$$ from 35. $$35-(4 \frac{1}{3}+2(4 \frac{1}{3} ))=35-12\frac{2}{3}=22 \frac{1}{3}$$ miles 17- Choice B is correct 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. $$S=πr^2$$ $$S_1- S_2=π(6cm)^2- π(4cm)^2⇒S_1- S_2=36π \space cm^2-16π \space cm^2 ⇒ S_1- S_2 =20π \space cm^2$$ 18- Choice A is correct Use Pythagorean Theorem: $$a^2+b^2=c^2$$, $$12^2+5^2=c^2⇒ 144+25= c^2 ⇒ c^2=169 ⇒c=13$$ 19- Choice A is correct Let L be the price of laptop and C be the price of computer. $$4(L) =7(C)$$ and $$L = 240 + C$$ Therefore, $$4(240 + C) =7C ⇒ 960 + 4C = 7C ⇒ C=320$$ 20- The answer is 70. Jason needs an $$75\%$$ average to pass five exams. Therefore, the sum of 5 exams must be at least $$5×75=375$$, The sum of 4 exams is: $$62+73+82+88=305$$. The minimum score Jason can earn on his fifth and final test to pass is: $$375-305=70$$ ## Best 7th Grade STAAR Math Prep Resource for 2022$36.99
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21- Choice B is correct
Let $$x$$ be the original price. If the price of a laptop is decreased by $$15\%$$ to $$425$$, then:
$$85\%\ of x=425 ⇒ 0.85x=425 ⇒ x=425÷0.85=500$$

22- Choice C is correct
The weight of 12 meters of this rope is: $$12×450 \space g=5,400\space g$$
$$1\space kg=1,000 \space g$$, therefore, $$5,400 \space g÷1,000=5.4\space kg$$

23- Choice D is correct
Only option D is correct. Other options don’t work in the equation. $$(4x-2)x=42$$

24- Choice C is correct
Compare each score: In Algebra Joe scored 24 out of 32 in Algebra that it means $$75\%$$ of total mark. $$\frac{24}{32}= \frac{x}{100}⇒x=75$$
Joe scored 28 out of 40 in science that it means $$70\%$$ of total mark. $$\frac{28}{40}=\frac{x}{100}⇒x=70$$
Joe scored 72 out of 90 in mathematic that it means $$80\%$$ of total mark. $$\frac{72}{90}=\frac{x}{100} ⇒x=80$$
Therefore, his score in mathematics is higher than his other scores.

25-Choice B is correct
To find the discount, multiply the number by ($$100\%$$-rate of discount).
Therefore, for the first discount we get: $$(D)(100\%-25\%)=(D)(0.75)=0.75$$
For increase of $$15\%$$: $$(0.75D)(100\%+15\%)=(0.75D)(1.15)=0.8625$$
$$D=86.25\%$$ of D

26-Choice B is correct
Write the numbers in order: 42,21,15,28,43,34,26 Since we have 7 numbers (7 is odd), then the median is the number in the middle, which is 28.

27-Choice C is correct
The average speed of John is: $$210÷7=30$$ km, The average speed of Alice is: $$160÷5=32$$ km, Write the ratio and simplify. 30∶ $$32 ⇒ 15∶16$$

28-Choice D is correct
Use the formula for Percent of Change: $$\frac{New \space Value-Old \space Value}{Old \space Value}×100\%$$
$$\frac{42-56}{56}×100\%=-25\%$$ (negative sign here means that the new price is less than old price).

29-Choice C is correct
Use the formula of areas of circles.$$Area=πr^2 ⇒ 121π= πr^2 ⇒ 121= r^2⇒ r=11$$ Radius of the circle is 11. Now, use the circumference formula: Circumference =$$2πr=2π(11)=22π$$

30-Choice B is correct
Let x be the number of balls. Then: $$\frac{1}{2}x+\frac{1}{5}x+\frac{1}{10} x+12=x$$
$$(\frac{1}{2}+\frac{1}{5}+\frac{1}{10})x+12=x$$, $$\frac{8}{10}x+12=x,x=60$$, In the bag of small balls $$\frac{1}{5}$$ are white, then: $$\frac{60}{5}=12$$, There are $$12$$ white balls in the bag.

31-Choice A is correct
William ate $$\frac{4}{5}$$ of 10 parts of his pizza that it means 8 parts out of 10 parts
($$\frac{4}{5}$$ of 10 parts =x ⇒ x=8) and left 2 parts.
Ella ate $$\frac{1}{2}$$ of 10 parts of her pizza that it means 5 parts out of 10 parts ($$\frac{1}{2}$$ of 10 parts = x ⇒ x=5) and left 5 parts. Therefore, they ate (5+2) parts out of (10+10) parts of their pizza and left (5+2) parts out of (10 + 10) parts of their pizza. It means: $$\frac{7}{20}$$, After simplification we have: $$\frac{7}{20}$$

32-Choices D is correct.
The failing rate is 14 out of 50=$$\frac{14}{50}$$, Change the fraction to percent: $$\frac{14}{50} ×100\%=28\%$$
28 percent of students failed. Therefore, 72 percent of students passed the exam.

33-Choice C is correct
$$x\%$$ of 50 is 6.2, then: $$0.50x=6.2 ⇒x=6.2÷0.50=12.4$$

34-The answer is 56
Use the area of the square formula. $$S=a^2 ⇒ 196= a^2 ⇒ a=14$$ One side of the square is 14 feet. Use the perimeter of the square formula. $$P=4a ⇒ P=4(14) ⇒ P=56$$

35-Choice B is correct.
Input the points instead of x and y in the formula. Only option B works in the equation.
$$6x-14=4y, 4(2)-14=4(-\frac{1}{2})⇒-2=-2$$

36- Choice B is correct
The sum of supplement angles is 180. Let $$x$$ be that angle. Therefore, $$x+4x=180$$
$$5x=180$$, divide both sides by 5: $$x=36$$

37- Choice B is correct
Use simple interest formula: I=prt (I=interest,p=principal,r= rate,t=time)
$$I=(16,000)(0.035)(3)=1,680$$

38- Choice B is correct.
Total number of way is6×6=36.favorable cases is (1,6),(2,5),(3,4),(4,3),(5,2),(6,1). Thus probability that sum of two tice get 7 is $$\frac{6}{36}=\frac{1}{6}$$

39- The answer is 168.
To find the number of possible outfit combinations, multiply number of options for each factor: $$3×8×7=168$$

40- Choice B is correct.
$$7\%$$ of the volume of the solution is alcohol. Let $$x$$ be the volume of the solution.
Then: $$7\%$$ of $$x=35$$ ml ⇒ $$0.07 x=35$$ ⇒ $$x=35 ÷ 0.07=500$$

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