Full Length HSPT Mathematics Practice Test

The correct answer is $2$
$3 \ a \ + \ 24 = 30 →$
$3 \ a = 30 \ - \ 24 →$
$3 \ a = 6 → a = 2$

The correct answer is $242$ pounds
$220 \ + \ 22 = 242$

The correct answer is $28$
A. $\frac{18}{6} = 3$
B. $\frac{28}{6} = 4.66$
C. $\frac{12}{6} = 2$
D. $\frac{30}{6} = 5$

The correct answer is $3$
$\frac{3^3}{x} = \frac{3^3}{9} = \frac{27}{9} = 3$

The correct answer is $3$
$8 \ x \ – \ 4 = 20$
$8 \ x = 24$
$x = \frac{24}{8} = 3$

The correct answer is $2 \times 2 \times 5 \times 7$
Find the value of each choice:
A. $2 \times 2 \times 5 \times 7 = 140$
B. $2 \times 2 \times 2 \times 2 \times 5 \times 7 = 560$
C. $2 \times 2 \times 7 = 28$
D. $2 \times 2 \times 2 \times 5 \times 7 = 280$

The correct answer is $40$
$\frac{20}{100} \ 200 = x$
$x = \frac{20 \ \times \ 200}{100} = 40$

The correct answer is $750$
Area of a rectangle $=$ width $\times$ length $= 30 \times 25 = 750$

The correct answer is $8$
$240 \div 30 = 8$

The correct answer is $14$
$\frac{15 \ + \ 10 \ + \ 5 \ + \ 19 \ + \ 21}{5} = \frac{70}{5} = 14$

The correct answer is $20$
Mary $=$ Ashly $– \ 8$
Mary $=$ David $– \ 7$
Ashly $+$ Mary $+$ David $= 75$
Ashly $+ \ 8 =$ Mary $⇒$ Ashly $=$ Mary $– \ 8$
Ashly $+$ Mary $+$ David $= 75$
Now, replace the ages of Mary and David by Mary. Then:
Mary $+ \ 8 \ +$ Mary $+$ Mary $+ \ 7 = 75$
$3$Mary $+ \ 15 = 75 ⇒ 3$ Mary $= 75 \ – \ 15$
$3$Mary $= 60$
Mary $= 20$

The correct answer is $23$
The difference of $3$ and $5$ is $2$.
The difference of $5$ and $9$ is $4$ and the difference of $9$ and $15$ is $6$.
Then, the difference of $15$ and the next number should be $8$.
The answer is $23$. $15 \ + \ 8 = 23$

The correct answer is $23$
A. $10$ is not prime.     It is divisible by $2$.
B. $15$ is not prime.   It is divisible by $3$.
C. $18$ is not prime.   It is divisible by $3$.
D. $23$ is prime!

The correct answer is $\frac{5}{3}$
$\frac{1}{\frac{3}{5}} = \frac{5}{3}$

The correct answer is $a^{7}$
$(a^2) \ . \ (a^5) = a^{2 \ + \ 5} = a^{7}$

The correct answer is $4.8$
$0.95 \ + \ 1.7 \ + \ 2.15 = 4.8$

The correct answer is $3 \ (N \ – \ 4)$
Let $x$ and $y$ be the numbers. Then:
$x \ + \ y = N, \ x = 4→$
$4 \ + \ y = N→$
$y = N \ – \ 4$
$3 \ y = 3 \ (N \ – \ 4)$

The correct answer is $18\%$
$0.18 \times 100 = 18\%$

The correct answer is $13$
Circumference $= π \ d ⇒ C = 4.2 \ π = 13.188 \cong 13$

The correct answer is $\frac{4}{3}$
$\frac{20}{15} = \frac{4}{3}$

The correct answer is $- \ 4$
$11 \ + \ x = 7$
$x = 7 \ – \ 11$
$x = - \ 4$

The correct answer is $\frac{3}{2}$
A. $\frac{2}{5} = 0.4$
B. $\frac{1}{7} = 1.14$
C. $\frac{5}{8} = 0.62$
D. $\frac{3}{2} = 1.5$

The correct answer is $9$
 $2 \ x \ + \ 15 = 2 \ (- \ 3) \ + \ 15 =  - \ 6 \ + \ 15 = 9$ 

The correct answer is $5,040$
$7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5,040$

The correct answer is $6$
$\sqrt{36} = 6$

The correct answer is $7$
$(9 \ + \ 5) \div (4^{2} \div 8) = (14) \div (2) = 7$

The correct answer is $9.5$
$7 \ < \ x \ ≤ \ 9$, then $x$ cannot be equal to $9.5$ . 

The correct answer is $32$
$2^{5} = 2 \times 2 \times 2 \times 2 \times 2 = 32$

The correct answer is $6$
The difference of each number and next number is $6$.
$\left\{18, \ 15, \ 12, \ 9, \ 6\right\}$

The correct answer is $40$
$x \ + \ y = 10$
$4 \ x \ + \ 4 \ y = 4 (x \ + \ y) →$
$10 \times 4 = 40$

The correct answer is $3,584$
$112 \times 32 = 3,584$

The correct answer is $6$
$8 \ + \ x \ ≥ \ 14 →$
$x \ ≥ \ 14 \ - \ 8 → x \ ≥ \ 6$

The correct answer is $- \ 5$
$- \ 5 \ a = 25$
$a = \frac{25}{- \ 5} = - \ 5$

The correct answer is $168$
$2$ABC $= 2 \ (7) \ (2) \ (6) = 168$

The correct answer is $2.25$ weeks
$1$ quart $= 0.25$ gallon
$27$ quarts $= 27 \times 0.25 = 6.75$ gallons
then: $\frac{6.75}{3} = 2.25$ weeks

The correct answer is $(x \ + \ 4)( x \ – \ 2)$
$x^2 \ + \ 2 \ x \ – \ 8 = (x \ + \ 4)( x \ – \ 2)$

The correct answer is $22$
Write a proportion and solve.
$\frac{6}{1} = \frac{132}{x} →$
$x = \frac{132}{6} = 22$

The correct answer is $270$
$15 \times 18 = 270$

The correct answer is $\frac{45}{10}$
$\frac{45}{10} = 4.5$

The correct answer is $3! =3 \times 2 \times 1$

The correct answer is $3 \ \frac{ 3}{10}$
$\frac{4}{10} \ + \ \frac{5}{2} \ + \ \frac{2}{5} = \frac{4 \ + \ 5(5) \ + \ 2(2)}{10} = \frac{33}{10}= 3 \ \frac{ 3}{10}$

The correct answer is $180$
Since Lucy gives $8$ pieces of candy to each of her friends, then, then number of pieces of candies must be divisible by $8$.
A. $128 \div 5 = 25.6$
B. $180\div 5 = 36$
C. $426 \div 5 = 85.2$
D. $264 \div 5 =52.8$
Only choice B gives a whole number.

The correct answer is $x^{2} \ + \ 7 \ x \ + \ 12$
$(x \ + \ 3)(x \ + \ 4) = x^{2} \ + \ 4 \ x \ + \ 3 \ x \ + \ 12 = x^{2} \ + \ 7 \ x \ + \ 12$ 

The correct answer is $(3, \ 18)$
Let’s review the choices provided.
Put the values of $x$ and $y$ in the equation.
A. $(2, \ 6) ⇒ x = 2 ⇒ y = 6$                         This is true!
B. $(− \ 2, \ − \ 10) ⇒ x = - \ 2 ⇒ y = - \ 11$   This is not true!
C. $(1, \ 2) ⇒ x = 1 ⇒ y = 2$                        This is true!
D. $(3, \ 10) ⇒ x = 3 ⇒ y = 10$                       This is true!

The correct answer is $\frac{5}{10}$
$\frac{5}{10} = 0.5$

The correct answer is $0.63$
$\frac{12}{19} = 0.63$

The correct answer is $12$
$(6 \ x \ + \ 7) \ - \ (6 \ x \ - \ 5) = 6 \ x \ + \ 7 \ - \ 6 \ x \ + \ 5 = 12$

The correct answer is $45$
Perimeter of a triangle $=$ side $1 \ +$ side $2  \ +$ side $3 = 15 \ + \ 15\ + \ 15 = 45$

The correct answer is $128$ pounds
$110 \ + \ 12 \ + \ 6 = 128$

The correct answer is $- \ 6$
$x^2 \ – \ 36 = 0$
$x^2 = 36$
$x = 6$ or $- \ 6$

The correct answer is $30^{◦}$
Angle b and angle $135$ are supplementary angles. (their sum is $180$ degrees)
Angle b $= 180 \ – \ 150 = 30$

The correct answer is $11$
The line is from $- \ 9$ to $+ \ 2$.
The difference of these two numbers is:
$2 \ –\ (– \ 9) = 2 \ + \ 9 = 11$

The correct answer is $x^{8}$
$(x^4)^2 = x^{8}$

The correct answer is $525$
Perimeter of rectangles $= 2$ (width $+$ length)
Area of a rectangles $=$ width . length
Perimeter of rectangles $= 2$(width $+$ length) $→ 100 = 2(15 \ +$ length) →
$100 = 30 \ + \ 2$ (length) $→ 70 = 2$ (length) $→$ length $= 35$
Area of a rectangles $=$ width . length $= 15 \times 35 = 525$

The correct answer is $64$
$4 \times 4 \times 4 = 64$

The correct answer is $10$
The factors of $10$ are: $\left\{ 1, \ 2, \ 5, \ 10\right\}$
The factors of $20$ are: $\left\{1, 4 , \ 5, 10 ,\ 20\right\}$
Then: Greatest Common Factor $= 10$

The correct answer is $18$
$\sqrt{36} \times \sqrt{9} = 6 \times 3 = 18$

The correct answer is $9$
The difference between any number and its next number is $3$.
$\left\{21, \ 18, \ 15, \ 12, \ 9\right\}$

The correct answer is $7325.3$
The tenth value is $2$.
$7325.25$ is closer to $7325.3$ than $7325.2$

The correct answer is $65$
Plug in the value of x in the expression.
Then: $7 \ x^2 \ +\ 4 \ x \ – \ 10 = 7(3)^2 \ + \ 4(3) \ – \ 10 = 65$

The correct answer is $2.39$ cm
Use circle circumference formula:
C $= 2 \ π \ r$
$15= 2 \ π \ r$
$r = \frac{15}{2 \ π} = 2.38 \cong 2.39$

The correct answer is $6$
$\sqrt[3]{216} = \sqrt[3]{6^3} = 6$

The correct answer is $y = x \ + \ 1$
Plug in the values of $x$ and $y$ in the equations provided:
A. $y = 1 \ – \ x → y = 1 \ – \ (- \ 1) = 2$     This is true!
B. $y = x \ + \ 1 → y =(- \ 1) \ + \ 1 = 0$ This is NOT true!
C. $x = - \ 1 → (- \ 1) = - \ 1$                  This is true!
D. $y = x \ +\ 3 → y =(- \ 1) \ + \ 3 = 2$ This is true!

The correct answer is $105$
$180  \ – \ 75 = 105$