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 \(105\)
\(180  \ – \ 75 = 105\)