Full Length SHSAT Mathematical Practice Test

The correct answer is \(8\) cm\(^2\)
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 \(=\frac{1}{2} \ (4 \ × \ 4)=\frac{16}{2}=8\) cm\(^2\)

The correct answer is \((700) \ (0.65) \ (0.95)\)
To find the discount, multiply the number by (\(100\% \ –\) rate of discount).
Therefore, for the first discount we get: \((700) \ (100\% \ – \ 35\%) = (700) \ (0.65) \)
For the next \(5\%\) discount: \((700) \ (0.65) \ (0.95)\)

The correct answer is \((− \ 2,3)\)
Plug in each pair of numbers in the equation: \(4 \ x \ + \ 6 \ y=10\)
A. \((-\ 2, 3): \)       \(4 \ (-\ 2) \ + \ 6 \ (3) = 10\)
B. \((– \ 1, 2):\)    \(4 \ (– \ 1) \ + \ 6 \ (2) = 8\)
C. \((– \ 2, 2):\)    \(4 \ (– \ 2) \ + \ 6 \ (2) = 4\)
D. \((2, 2): \)       \(4 \ (2) \ + \ 6 \ (2) = 20\)

The correct answer is \(21.1\)
\(8 \ x \ - \ 6=12.5→3 \ x=12.5 \ + \ 6=18.5→x=\frac{18.5}{8}=2.3\) 
Then; \(7 \ x \ + \ 5=7 \ (2.3) \ + \ 5=16.1\ + \ 5=21.1\)

The correct answer is \(− \ 83\)
Use PEMDAS (order of operation):
\(- \ 17 \ + \ 5 \ × \ (– \ 7) \ – \ \left[ \ 2 \ - \ 20 \ × \ (- \ 3) \ \right] \ ÷ \ 2=\)
\(- \ 17 \ - \ 35 \ - \ \left[ \ 2 \ + \ 60\ \right] \ ÷ \ 2=\)
\(- \ 52 \ - \ \left[  62 \right] \ ÷ \ 2=\)
\(- \ 52\ - \ 62  \ ÷ \ 2=\)
\(- \ 52 \ - \ 31= \ - \ 83 \)

The correct answer is \(− \ 83\)
Use PEMDAS (order of operation):
\(- \ 17 \ + \ 5 \ × \ (– \ 7) \ – \ \left[ \ 2 \ - \ 20 \ × \ (- \ 3) \ \right] \ ÷ \ 2=\)
\(- \ 17 \ - \ 35 \ - \ \left[ \ 2 \ + \ 60\ \right] \ ÷ \ 2=\)
\(- \ 52 \ - \ \left[  62 \right] \ ÷ \ 2=\)
\(- \ 52\ - \ 62  \ ÷ \ 2=\)
\(- \ 52 \ - \ 31= \ - \ 83 \)

The correct answer is \(8\)
average \(= \frac{sum \ of \ terms}{number \ of \ terms} ⇒\)
\(19.5 = \frac{22 \ + \ 45 \ + \ 3 \ + \ x}{4} ⇒\)
\(78= 70 \ + \ x ⇒ x = 8\)

The correct answer is \(5\)
Let \(x\) be the number. Write the equation and solve for \(x\).
\((35 \ – \ x) \ ÷ \ x = 6\)
Multiply both sides by \(x\). 
\((35 \ – \ x) = 6 \ x\), then add \(x\) both sides.
\(35 =7 \ x\), now divide both sides by \(7\). 
\(x = 5\)

The correct answer is \($60\)
\($7 \ × \ 15=$105\)
Petrol use: \(15 \ × \ 1.5=22.5\) liters
Petrol cost: \(22.5 \ × \ $2=$45\)
Money earned: \($105 \ - \ $45=$60\)

The correct answer is \($800\)
Let \(x\) be the original price.
If the price of the sofa is decreased by \(30\%\) to \($476\), then: \(70\%\) of \(x=560 ⇒\)
\(0.7 \ x=560 ⇒\)
\(x=560 \ ÷ \ 0.7=800\)

The correct answer is \(7 : 9\)
The average speed of john is: \(140 \ ÷ \ 5 = 26\) km
The average speed of Alice is: \(190 \ ÷ \ 2 = 45\) km
Write the ratio and simplify. \(35 : 45 ⇒ 7 : 9\)

The correct answer is \(3\%\)
The percent of girls playing tennis is: \(30\% \ × \ 10\% = 0.03 \ × \ 0.1 = 0.03 = 3\%\)

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 \(10\) cm
Use Pythagorean Theorem: \(a^2 \ + \ b^2=c^2\)
\(8^2 \ + \ 6^2 = c^2 ⇒\)
\(64 \ + \ 36=c^2 ⇒\)
\(100=c^2⇒c=10\)

The correct answer is \(10\)
Solving Systems of Equations by Elimination
\(\cfrac{\begin{align} 6 \ x \ - \ 4 \ y \ = - \ 10 \\ - \ x \ + \  y \ = \ 5 \end{align}}{} \)
Multiply the second equation by \(6\), then add it to the first equation.
\(\cfrac{\begin{align} 6 \ x \ - \ 4 \ y \ =  - \ 10 \\ 6 \ ( \ - \ x \ + \  y \ = 30) \end{align}}{}\) ⇒ 
\(\cfrac{ \begin{align} 6 \ x \ - \ 4 \ y \ =  - \ 10 \\ - \ 6\ x \ + \ 6 \ y \ = 30 \end{align} }{\begin{align} 2\ y \ =  20 \\ ⇒ y \ = \ 10 \end{align}} \)

The correct answer is \(8 \ π\) and \(12 \ π\)
(If you selected \(3\) choices and \(2\) of them are correct, then you get one point.
If you answered \(2\) or \(3\) choices and one of them is correct, you receive one point.
If you selected more than \(3\) choices, you won’t get any point for this question.)
Area of the circle is less than \(12 \ π\).
Use the formula of areas of circles.
Area \(= π \ r^2 ⇒ 36 \ π \ > \ π \ r^2⇒ 36 \ > \ r^2⇒ r \ < \ 6\)
Radius of the circle is less than \(8\).
Let’s put \(6\) for the radius.
Now, use the circumference formula:
Circumference \(=2 \ π \ r=2 \ π \ (6)=12 \ π\)
Since the radius of the circle is less than \(6\).
Then, the circumference of the circle must be less than \(12 \ π\). Online choices A and B are less than \(12 \ π\).

The correct answer is \(512\) cm\(^3\)
If the length of the box is \(32\), then the width of the box is one Fourth of it, \(8\), and the height of the box is \(2\) (one third of the width).
The volume of the box is: \(V = lwh = (32) \ (8) \ (2) = 512\) cm\(^3\)

The correct answer is \(25\%\)
Use this formula: Percent of Change: \(\frac{New \ Value \ - \ Old \ Value}{Old \ Value} \ × \ 100\%\)
\(\frac{22000 \ - \ 17600}{17600} \ × \ 100\% = 25\%\) and;
\(\frac{27500 \ - \ 22000}{22000} \ × \ 100\% = 25\%\)

The correct answer is \($5040\)
Use simple interest formula: \(I=prt\)
(\(I =\) interest, \(p =\) principal, \(r =\) rate, \(t =\) time)
\(I=(12,000) \ (0.06) \ (7)=5,040\)

The correct answer is \(200\%\)
Write the equation and solve for B: \(0.80\) A \(= 0.40\) B, divide both sides by \(0.40\), then:
\(\frac{0.80}{0.40}\) A \(=\) B, therefore: B \(= 2\) A, and B is \(2\) times of A or it’s \(200\%\) of A.

The correct answer is \(15625\)
\(5^6 = 5 \ × \ 5 \ × \ 5 \ × \ 5 \times 5 \times 5 = 1,5625\)

The correct answer is \(64\)
To find the number of possible outfit combinations, multiply number of options for each factor:
\(8 \ × \ 4 \ × \ 2 = 64\)

The correct answer is \(270\)
The perimeter of the trapezoid is \(54\).
Therefore, the missing side (height) is \(= 64\ – \ 16 \ – \ 10 \ – \ 8 = 30\)
Area of a trapezoid: A \(= \frac{1}{2} \ h \ (b1 \ + \ b2) = \frac{1}{2} \ (30) \ (10 \ + \ 8) = 270\)

The correct answer is \(317\) km
Add the first \(5\) numbers.
\(30 \ + \ 62 \ + \ 43 \ + \ 5 \ + \ 52 = 192\)
To find the distance traveled in the next \(5\) hours, multiply the average by number of hours.
Distance \(=\) Average \(×\) Rate \(= 25 \ × \ 5 = 125\), Add both numbers. \(125 \ + \ 192 = 317\)

The correct answer is \(150\%\)
Use percent formula: part \(= \frac{percent}{100} \ ×\) whole
\(45 = \frac{percent}{100} \ × \ 30 ⇒\)
\(45 = \frac{percent \ × \ 30}{100} ⇒\)
\(45 = \frac{percent \ × \ 3}{10}\), multiply both sides by \(10\).
\(450 =\) percent \(× \ 3\), divide both sides by \(2\). 
\(150 =\) percent

The correct answer is\(( 7, - \ 8)\)  and \((3, 4)\)
(If you selected \(3\) choices and \(2\) of them are correct, then you get one point.
If you answered \(2\) or \(3\) choices and one of them is correct, you receive one point.
If you selected more than \(3\) choices, you won’t get any point for this question.)
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 \((3,4)\) and \((2,3)\) are on line A.
Therefore, the slope of the line A is:
slope of line A \(=\frac{y_{2} \ - \ y_{1}}{x_{2} \ - \ x_{1 }} = \frac{3 \ - \ 4}{2 \ - \ 3}=\frac{- \ 1}{- \ 1}=1\)
The slope of line A is \(1\).
Thus, the formula of the line A is: \(y=m \ x \ + \ b=x \ + \ b\), choose a point and plug in the values of \(x\) and \(y\) in the equation to solve for b.
Let’s choose point \((3, 4)\). Then:
\(y=x \ + \ b→4=3 \ + \ b→b=4 \ - \ 3= 1\)
The equation of line A is: \(y=x \ + \ 1\)
Now, let’s review the choices provided:
A. \((- \ 1, 2)\) \(y=x \ +\ 1→2= \ - \ 1 \ + \ 1= 0\) This is not true.
B. \((5, 7)\) \(y=x \ + \ 1→7=5 \ + \ 1=6\) This is not true.
C. \((3, 4)\) \(y=x \ + \ 1→4=3 \ + \ 1=4\) This is true.
D. \((- \ 1, - \ 2)\) \(y=x \ + \ 1→ \ - \ 2= \ - \ 1 \ + \ 1= 0\) This is not true!
E. \(( 7, - \ 8)\) \(y=x \ + \ 1→ \ - \ 8= 7 \ + \ 1= \ - \ 8\) This is true!

The correct answer is \(10\) hours and \(36\) minutes
Use distance formula: Distance \(=\) Rate \(×\) time \(⇒ 640 = 60 \ ×\) T, divide both sides by \(60\).
\(\frac{640}{ 60} =\) T \(⇒\) T \(= 10.6\) hours.
Change hours to minutes for the decimal part.
\(0.6\) hours \(= 0.6 \ × \ 60 = 36\) minutes.

The correct answer is \(0.94\) D
To find the discount, multiply the number by (\(100\% \ –\) rate of discount).
Therefore, for the first discount we get: (D) \((100\% \ – \ 10\%) =\) (D) \((0.90) = 0.90\) D
For increase of \(5\%: (0.90\) D\() \ (100\% \ + \ 5\%) = (0.90\) D\() \ (0.05) = 0.94\) D \(= 94\%\) of D

The correct answer is \(15\)
Let \(x\) be the number.
Write the equation and solve for \(x\). 
\(\frac{2}{3} \ × \ 30= \frac{ 4}{3}\).
\(x ⇒ \frac{2 \ × \ 30}{3}= \frac{4 \ x}{3}\), use cross multiplication to solve for \(x\).
\(3 \ × \ 60=4 \ x \ × \ 3 ⇒180=12 \ x ⇒ x=15\)

The correct answer is \(13\%\)
Use the formula for Percent of Change: \(\frac{New \ Value \ - \ Old \ Value}{Old \ Value} \ × \ 100\%\)
\(\frac{26 \ - \ 30}{30} \ × \ 100\% = \ – \ 13\%\) (negative sign here means that the new price is less than old price).

The correct answer is \(30\%\)
The question is this: \(404.60\) is what percent of \(578\)? 
Use percent formula: part \(= \frac{percent}{100 } \ ×\) whole
\(404.60 = \frac{percent}{100} \ × \ 578 ⇒\)
\(404.60 = \frac{percent \ × \ 578}{100} ⇒\)
\(40460 =\) percent \(× \ 578 ⇒\) 
percent \(= \frac{40460}{578} = 70\)
\(404.60\) is \(70\%\) of \(578\)
Therefore, the discount is: \(100\% \ – \ 70\% = 30\%\)

The correct answer is \(38\)
Let \(x\) be the smallest number. Then, these are the numbers:
\(x, x \ + \ 1, x \ + \ 2, x \ + \ 3, x \ + \ 4\)
average \(= \frac{sum \ of \ terms}{number \ of \ terms}⇒\)
\(40 = \frac{x \ + \ (x \ + \ 1) \ + \ (x \ + \ 2) \ + \ (x \ + \ 3) \ + \ (x \ + \ 4)}{5}⇒\)
\(40=\frac{5 \ x \ + \ 10}{5} ⇒\)
\(200= 5 \ x \ + \ 10 ⇒\)
\(190 = 5 \ x ⇒ x=38\)

The correct answer is \(11.2\)
The weight of \(14\) meters of this rope is: \(14 \ × \ 800\) g \(= 11,200\) g
\(1\) kg \(= 1,000\) g, therefore, \(11,200\) g \(÷ \ 1000 = 11.2\) kg

The correct answer is \(15\) and \(77\)
(If you selected \(3\) choices and \(2\) of them are correct, then you get one point.
If you answered \(2\) or \(3\) choices and one of them is correct, you receive one point. If you selected more than \(3\) choices, you won’t get any point for this question.)
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)
\(7 \ × \ 11 = 77\) (yes!)
Choices D and F are correct.

The correct answer is \(\frac{21}{22}\)
If \(21\) 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 \(22\).
Therefore, the probability of not choosing a brown ball is \(21\) out of \(22\) and the probability of having not a brown ball after removing \(21\) balls is the same.

The correct answer is \(210\)
The ratio of boy to girls is \(3:4\).
Therefore, there are \(3\) boys out of \(7\) students.
To find the answer, first divide the total number of students by \(5\), then multiply the result by \(3\). 
\(490 \ ÷ \ 7= 70 ⇒ 70 \ × \ 3 = 210\)

The correct answer is \(540\) ml
\(8\%\) of the volume of the solution is alcohol. 
Let \(x\) be the volume of the solution. 
Then: \(8\%\) of \(x = 36\) ml \(⇒ 0.08 \ x = 36 ⇒ x = 36 \ ÷ \ 0.08 = 540\)

The correct answer is \(20\)
If the score of Maryam was \(80\), therefore the score of John  is \(40\).
Since, the score of Alex  was half as that of John, therefore, the score of Alex is \(20\).

The correct answer is \(80\)
The area of the floor is: \(8\) cm \(× \ 30\) cm \(= 240\) cm\(^2\)
The number of tiles needed \(= 240 \ ÷ \ 3 = 80\)

The correct answer is \(10\)
Write the numbers in order: \(3, 5, 7, 10, 12, 14, 16\)
Since we have \(7\) numbers (\(7 \) is odd), then the median is the number in the middle, which is \(10\).

The correct answer is \(100\) miles
Use the information provided in the question to draw the shape.
Use Pythagorean Theorem: \(a^2 \ + \ b^2 = c^2\)
\(80^2 \ + \ 60^2 = c^2 ⇒\)
\(6400 \ + \ 3600 = c^2 ⇒\)
\(10000 = c^2 ⇒ c = 100\)

The correct answer is \(125\%\)
The question is this: \(2.5\) is what percent of \(2\)?
Use percent formula: part \(= \frac{percent}{100} \ ×\) whole 
\(2.5 = \frac{percent}{100} \ × \ 2 ⇒\)
\(2.5 = \frac{percent \ × \ 2}{100} ⇒\)
\(250 =\) percent \(× \ 2 ⇒\)
percent \(= \frac{250}{2} = 125\)

The correct answer is \(63.2\)
average \(= \frac{sum \ of \ terms}{number \ of \ terms}\)
The sum of the weight of all girls is: \(17 \ × \ 50 = 850\) kg
The sum of the weight of all boys is: \(33 \ × \ 70 = 2310\) kg
The sum of the weight of all students is: \(850 \ + \ 2310 = 3160\) kg
average \(= \frac{3160}{50} = 63.2\)

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 \(800\)
Let \(x\) be the original price.
If the price of a laptop is decreased by \(25\%\) to \($600\), then: 
\(75\%\) of \(x=600⇒ 0.75 \ x=600 ⇒ x=600 \ ÷ \ 0.75=800\)

The correct answer is \(𝐼 \ > \ 3000 \ x \ + \ 30000\)
Let \(x\) be the number of years.
Therefore, \($3,000\) per year equals \(3000 \ x\). 
starting from \($30,000\) annual salary means you should add that amount to \(3000 \ x\). 
Income more than that is: \(𝐼 \ > \ 3000 \ x \ + \ 30000\)

The correct answer is \(753.6\)
Surface Area of a cylinder \(= 2 \ π \ r \ (r \ + \ h)\),
The radius of the cylinder is \(6\) inches and its height is \(14\) inches.
\(π\) is \(3.14\). Then: 
Surface Area of a cylinder \(= 2 \ (3.14) \ (6) \ (6 \ + \ 14) = 753.6\)