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 $= 2 \ (3.14) \ (6) \ (6 \ + \ 14) = 753.6$