Free Full Length STAAR Grade 7 Practice Test

The correct answer is \(2\)
The equation of a line in slope intercept form is: \(y=m \ x \ + \ b\)
Solve for \(y\).
\(2 \ x \ - \ y=12 ⇒\)
\(- \ y=12 \ - \ 2 \ x ⇒\)
\(y=(12 \ - \ 2 \ x) \ ÷ \ (- \ 1) ⇒\)
\(y=2 \ x \ - \ 6\)
The slope of this line is \(2\).
Parallel lines have same slopes.

The correct answer is \(36\)
Simplify:
\(5 \ (x\ - \ 2 \ y) \ + \ (2 \ - \ x)^2 = \)
\((5 \ x \ - \ 10 \ y) \ + \ (4 \ - \ 4 \ x \ + \ x^2) =\)
\(x \ - \ 10 \ y \ + \ 4 \ + \ x^2\)
When \(x=3\) and \(y=- \ 2\) ,therefore:
\(x \ - \ 10 \ y \ + \ 4 \ + \ x^2 =3 \ + \ 20 \ + \ 4 \ + \ 9 =36\)

The correct answer is \( 87.5\)
average (mean) \(=\frac{sum \ of \ terms}{number \ of \ terms}⇒\)
\(88 = \frac{sum \ of \ terms}{50} ⇒\)
sum \(= 88 \ × \ 50 = 4400\)
The difference of \(94\) and \(69\) is \(25\).
Therefore, \(25\) should be subtracted from the sum.
\(4400 \ – \ 25 = 4375\)
mean \(=\frac{sum \ of \ terms}{number \ of \ terms}⇒\)
mean \(=\frac{4375}{50 }= 87.5\)

The correct answer is \(729\)
If the length of the box is \(27\), then the width of the box is one third of it, \(9\), and the height of the box is \(3\) (one third of the width).
The volume of the box is:
\(V = lwh = (27) \ (9) \ (3) = 729\)

The correct answer is \(475\)
Add the first \(5\) numbers.
\(40 \ + \ 45 \ + \ 50 \ + \ 35 \ + \ 55 = 225\)
To find the distance traveled in the next \(5\) hours, multiply the average by number of hours.
Distance \(=\) Average \(×\) Rate \(= 50 \ × \ 5 = 250\)
Add both numbers.
\(250 \ + \ 225 = 475\)

The correct answer is \(240\)
The ratio of boy to girls is \(2:3\).
Therefore, there are \(2\) boys out of \(5\) students.
To find the answer, first divide the total number of students by \(5\), then multiply the result by \(2\).
\(600 \ ÷ \ 5 = 120 ⇒\)
\(120 \ × \ 2 = 240\)

The correct answer is \(130\)
The perimeter of the trapezoid is \(54\) cm.
Therefore, the missing side (high) is \(= 54 \ – \ 18 \ – \ 12 \ – \ 14 = 10\)
Area of a trapezoid: A \(= \frac{1}{2} \ h \ (b1 \ + \ b2) = \frac{1}{2} \ (10) \ (12 \ + \ 14) = 130\)

The correct answer is \(I \ > \ 2000 \ x \ + \ 24000\)
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:
\(I \ > \ 2000 \ x \ + \ 24000\)

Solve for \(x\).
\(- \ 2 \ ≤ \ 2 \ x \ - \ 4 \ < \ 8 ⇒\)
(add \(4\) all sides) \(-\ 2 \ + \ 4 \ ≤ \ 2 \ x \ - \ 4 \ + \ 4 \ < \ 8 \ + \ 4 ⇒\)
\(2 \ ≤ \ 2 \ x \ < \ 12 ⇒\)
(divide all sides by \(2\)) \(1 \ ≤ \ x \ < \ 6\)
\(x\) is between \(1\) and \(6\).

The correct answer is \(120 \ x \ + \ 14,000 \ ≤ \ 20,000\)
Let \(x\) be the number of new shoes the team can purchase. Therefore, the team can purchase \(120 \ x\).
The team had \($20,000\) and spent \($14000\).
Now the team can spend on new shoes \($6000\) at most.
Now, write the inequality:
\(120 \ x \ + \ 14,000 \ ≤ \ 20,000\)

The correct answer is \(\frac{1}{4}\)
The options to get sum of \(6: \ (1\) & \(5)\) and \((5\) & \(1), \ (2\) & \(4)\) and \((4\) & \(2), \ (3\) & \(3)\), so we have \(5\) options
The options to get sum of \(9: \ (3\) & \(6)\) and \((6\) & \(3), \ (4\) & \(5)\) and \((5\) & \(4)\), we have \(4\) options.
To get the sum of \(6\) or \(9\) for two dice, we have \(9\) options: \(5 \ + \ 4 = 9\)
Since, we have \(6 \ × \ 6 = 36\) total options, the probability of getting a sum of \(6\) and \(9\) is \(9\) out of \(36\) or \(\frac{9}{36}=\frac{1}{4}\).

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

For each option, choose a point in the solution part and check it on both inequalities.
A. Point \((– \ 4, \ – \ 4)\) is in the solution section. Let’s check the point in both inequalities.
\(– \ 4 \ ≤ \ – \ 4 \ + \ 4\), It works
\(2 \ (– \ 4) \ + \ (– \ 4) \ ≤ \ – \ 4 ⇒ – \ 12 \ ≤ \ – \ 4\), it works (this point works in both)
B. Let’s choose this point \((0, \ 0)\)
\(0 \ ≤ \ 0 \ + \ 4\), It works
\(2 \ (0) \ + \ (0) \ ≤ \ – \ 4\), That’s not true!
C. Let’s choose this point \((– \ 5, \ 0)\)
\(0 \ ≤ \ – \ 5 \ + \ 4\), That’s not true!
D. Let’s choose this point \((0, \ 5)\)
\(5 \ ≤ \ 0 \ + \ 4\), That’s not true!

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 \(\frac{1}{4}\)
The probability of choosing a Hearts is \(\frac{13}{52} =\frac{1}{4}\)

The correct answer is \(8\) hours and \(24\) minutes
Use distance formula:
Distance \(=\) Rate \(×\) time \(⇒ 420 = 50 \ ×\) T, divide both sides by \(50\).
\(\frac{420}{50} =\) T \(⇒\) T \(= 8.4\) hours.
Change hours to minutes for the decimal part.
\(0.4\) hours \(= 0.4 \ × \ 60 = 24\) minutes.

The correct answer is \(472\)
\(11 \ × \ 36 \ + \ 6 \ × \ 12 \ + \ 4 = 472\)

The correct answer is \((200) \ (0.85) \ (0.85)\)
To find the discount, multiply the number by (\(100\% \ –\) rate of discount).
Therefore, for the first discount we get: \((200) (100\% \ – \ 15\%) = (200) \ (0.85) = 170\)
For the next \(15\%\) discount: \((200) \ (0.85) \ (0.85)\)

The correct answer is \((- \ 1, \ 3)\)
Input \((- \ 1, \ 3)\) in the \(2 \ x \ + \ 4 \ y = 10\) formula instead of \(x\) and \(y\). So we have:
\(2(- \ 1) \ + \ 4 \ (3) = 10\)
\(- \ 2 \ + \ 12 = 10\)

The correct answer is \(- \ 30\)
Use PEMDAS (order of operation):
\(5 \ + \ 8 \ × \ (– \ 2) \ – \ [ \ 4 \ + \ 22 \ × \ 5 \ ] \ ÷ \ 6 =\)
\(5 \ + \ 8 \ × \ (– \ 2) \ – \ [ \ 4 \ + \ 110 \ ] \ ÷ \ 6 =\)
\(5 \ + \ 8 \ × \ (– \ 2) \ – \ [ \ 114 \ ] \ ÷ \ 6 =\)
\(5 \ + \ (– \ 16) \ – \ 19 =\)
\(5 \ + \ (– \ 16) \ – \ 19 =\)
\(– \ 11 \ – \ 19 = \ – \ 30\)

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 \(40\)
Plug in \(104\) for F and then solve for C.
C \(= \frac{5}{9}\) (F \(– \ 32) ⇒\)
C \(= \frac{5}{9} \ (104 \ – \ 32) ⇒\)
C \(= \frac{5}{9} \ (72) = 40\)

The correct answer is \(\frac{125}{512}\)
The square of a number is \(\frac{25}{64}\), then the number is the square root of \(\frac{25}{64}\)
\(\sqrt{\frac{25}{64}}= \frac{5}{8}\)
The cube of the number is:
\((\frac{5}{8})^3 = \frac{125}{512}\)

The correct answer is \(66 \ π\)
Surface Area of a cylinder \(= 2 \ π \ r \ (r \ + \ h)\),
The radius of the cylinder is \(3 \ (6 \ ÷ \ 2)\) inches and its height is \(8\) inches.
Therefore, Surface Area of a cylinder \(= 2 \ π \ (3) \ (3 \ + \ 8) = 66 \ π\)

The correct answer is \( \frac{1}{4}\)
\(\frac{2}{3} \ x \ + \ \frac{1}{6}=\frac{1}{3}⇒\)
\(\frac{2}{3} \ x= \frac{1}{6} ⇒\)
\(x= \frac{1}{6} \ × \ \frac{3}{2} ⇒ x= \frac{1}{4}\)

The correct answer is \(27\)
Solve for the sum of five numbers.
average \(=\frac{sum \ of \ terms}{number \ of \ terms} ⇒\)
\(24 = \frac{sum \ of \ 5 \ numbers}{5} ⇒\)
sum of \(5\) numbers \(= 24 \ × \ 5 = 120\)
The sum of \(5\) numbers is \(120\).
If a sixth number \(42\) is added, then the sum of \(6\) numbers is
\(120 \ + \ 42 = 162\)
average \(= \frac{sum \ of \ terms}{number \ of \ terms}= \frac{162}{6} = 27\)

The correct answer is \(\frac{1}{4}\)
Probability \(= \frac{number \ of \ desired \ outcomes}{number \ of \ total \ outcomes}= \frac{18}{12 \ + \ 18 \ + \ 18 \ + \ 24} = \frac{18}{72} = \frac{1}{4}\)

The correct answer is \(\frac{2}{3}, \ 67\%, \ 0.68, \ \frac{4}{5}\)
Change the numbers to decimal and then compare.
\(\frac{2}{3} = 0.666…\)
\(0.68\)
\(67\% = 0.67\)
\(\frac{4}{5} = 0.80\)
Therefore: \(\frac{4}{5} \ > \ 68\% \ > \ 0.67 \ > \frac{2}{3}\)

The correct answer is \(60\)
To find the number of possible outfit combinations, multiply number of options for each factor:
\(3 \ × \ 5 \ × \ 4 = 60\)

The correct answer is \(24\)
\(4 \ ÷ \ \frac{1}{6} = 24\)

The correct answer is \(32\)
The diagonal of the square is \(8\).
Let \(x\) be the side.
Use Pythagorean Theorem: \(a^2 \ + \ b^2 = c^2\)
\(x^2 \ + \ x^2 = 82 ⇒\)
\(2 \ x^2 = 82 ⇒\)
\(2 \ x^2 = 64 ⇒\)
\(x^2 = 32 ⇒\)
\(x= \sqrt{32}\)
The area of the square is:
\(\sqrt{32} \ × \ \sqrt{32} = 32\)

The correct answer is \(12\)
The ratio of boy to girls is \(4:7\).
Therefore, there are \(4\) boys out of \(11\) students.
To find the answer, first divide the total number of students by \(11\), then multiply the result by \(4\). 
\(44 \ ÷ \ 11 = 4 ⇒\)
\(4 \ × \ 4 = 16\)
There are \(16\) boys and \(28 \ (44 \ – \ 16)\) girls. So, \(12\) more boys should be enrolled to make the ratio \(1:1\)

The correct answer is \(40\) ft.\(^2\)
Use the area of rectangle formula \((s=a \ × \ b)\).
To find area of the shaded region subtract the 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 \(\frac{1}{22}\)
\(2,500\) out of \(55,000\) equals to \(\frac{2500}{55000} = \frac{25}{550} = \frac{1}{22}\)

The correct answer is \(6\)
Let the number be \(x\). Then:
\(\frac{24 \ - \ x}{x} = 3→\)
\(3 \ x=24 \ - \ x→\)
\(4 \ x=24→\)
\(x = 6\)

The correct answer is \(120\) cm\(^3\)
Volume of a box \(=\) length \(×\) width \(×\) height \(= 4 \ × \ 5 \ × \ 6 = 120\) cm\(^3\)

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.

The correct answer is \(405\)
The ratio of boy to girls is \(4:5\).
Therefore, there are \(4\) boys out of \(9\) students.
To find the answer, first divide the number of boys by \(4\), then multiply the result by \(9\).
\(180 \ ÷ \ 4 = 45 ⇒\)
\(45 \ × \ 9 = 405\)

The correct answer is \(18\)
The area of the floor is: \(6\) cm \(× \ 24\) cm \(= 144\) cm\(^2\)
The number of tiles needed \(= 144 \ ÷ \ 8 = 18\)

The correct answer is \(1004.8\)
Surface Area of a cylinder \(= 2 \ π \ r \ (r \ + \ h)\),
The radius of the cylinder is \(8\) inches and its height is \(12\) inches.
\(π\) is about \(3.14\). Then:
Surface Area of a cylinder \(= 2 \ (π) \ (8) \ (8 \ + \ 12) =\)
\(320 \ π = 1004.8\)