Full Length HSPT Mathematics Practice Test

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HSPT Mathematics Practice Test 3 64 questions Total time for this section: 45 Minutes Calculators are not allowed at the test.
1-	$3 \ a \ + \ 24 = 30 , a =$ ?
(A)	$1$
(B)	$10$
(C)	$2$
(D)	$5$
2-	A trash container, when empty, weighs $22$ pounds. If this container is filled with a load of trash that weighs $220$ pounds, what is the total weight of the container and its contents?
(A)	$250$ pounds
(B)	$120$ pounds
(C)	$186$ pounds
(D)	$242$ pounds
3-	Which of the following is not a multiple of $6$?
(A)	$18$
(B)	$28$
(C)	$12$
(D)	$30$
4-	If $x = 9$, then $\frac{3^3}{x} =$
(A)	$3$
(B)	$12$
(C)	$8$
(D)	$5$
5-	Solve for $x: \ 8 \ x \ – \ 4 = 20$
(A)	$6$
(B)	$9$
(C)	$3$
(D)	$7$
6-	What is the prime factorization of $140$?
(A)	$2 \times 2 \times 5 \times 7$
(B)	$2 \times 2 \times 2 \times 2 \times 5 \times 7$
(C)	$2 \times 2 \times 7$
(D)	$2 \times 2 \times 2 \times 5 \times 7$
7-	If $x$ is $20\%$ percent of $200$, what is $x$?
(A)	$33$
(B)	$40$
(C)	$55$
(D)	$80$
8-	If a rectangle is $25$ feet by $30$ feet, what is its area?
(A)	$750$
(B)	$360$
(C)	$1,358$
(D)	$1,700$
9-	A writer finishes $240$ pages of his manuscript in $30$ hours. How many pages is his average?
(A)	$7$
(B)	$10$
(C)	$8$
(D)	$20$
10-	Find the average of the following numbers: $15, \ 10, \ 5, \ 19, \ 21$
(A)	$14$
(B)	$20$
(C)	$11$
(D)	$17$
11-	Ashly is $8$ years older than her sister Mary, and Mary is $7$ years younger than her brother David. If the sum of their ages is $75$, how old is Michelle?
(A)	$20$
(B)	$12$
(C)	$18$
(D)	$24$
12-	The first four terms in a sequence are shown below. What is the fifth term in the sequence? $\left\{3, \ 5, \ 9, \ 15, \ ...\right\}$
(A)	$32$
(B)	$23$
(C)	$28$
(D)	$20$
13-	Which of the following is a prime number?
(A)	$10$
(B)	$15$
(C)	$18$
(D)	$23$
14-	If $x = \frac{3}{5}$ then $\frac{1}{x} =$ ?
(A)	$\frac{5}{3}$
(B)	$\frac{3}{5}$
(C)	$\frac{1}{4}$
(D)	$\frac{1}{5}$
15-	$(a^{2}) \ . \ (a^{5}) =$ ___
(A)	$2 \ a^3$
(B)	$2 \ a^7$
(C)	$a^7$
(D)	$a^{25}$
16-	$0.95 \ + \ 1.7 \ + \ 2.15 =$?
(A)	$6.25$
(B)	$5.5$
(C)	$7.35$
(D)	$4.8$
17-	The sum of two numbers is N. If one of the numbers is $4$, then what is three times the other number?
(A)	$3 \ N$
(B)	$3 \ (N \ - \ 4)$
(C)	$3 \ (N \ + \ 4)$
(D)	$(N \ + \ 4)$
18-	Convert $0.18$ to a percent.
(A)	$0.018\%$
(B)	$0.18\%$
(C)	$1.8\%$
(D)	$18\%$
19-	A circle has a diameter of $4.2$ inches. What is its approximate circumference?
(A)	$15$
(B)	$13$
(C)	$8$
(D)	$19$
20-	In the simplest form, $\frac{20}{15}$ is:
(A)	$\frac{4}{13}$
(B)	$\frac{4}{3}$
(C)	$\frac{14}{3}$
(D)	$\frac{3}{4}$
21-	What number belongs in the box? $11 \ + \Box = 7$
(A)	$8$
(B)	$5$
(C)	$- \ 4$
(D)	$4$
22-	Which of the following fractions is the largest?
(A)	$\frac{2}{5 }$
(B)	$\frac{1}{7}$
(C)	$\frac{5}{8}$
(D)	$\frac{3}{2}$
23-	Evaluate $2 \ x \ + \ 15$, when $x= - \ 3$
(A)	$9$
(B)	$4$
(C)	$11$
(D)	$6$
24-	What is the value of $7!$ ?
(A)	$5,040$
(B)	$504$
(C)	$3,254$
(D)	$4,500$
25-	$\sqrt{36}$ is equal to:
(A)	$4$
(B)	$9$
(C)	$6$
(D)	$3$
26-	$( 9 \ + \ 5) \div (4^{2} \div 8) =$ ___
(A)	$6$
(B)	$9$
(C)	$3$
(D)	$7$
27-	If $7 \ < \ x \ ≤ \ 9$, then $x$ cannot be equal to:
(A)	$9.5$
(B)	$8$
(C)	$7.5$
(D)	$9$
28-	Which of the following is the equivalent of $2^{5}$?
(A)	$2 \times 2 \times 2$
(B)	$5 \times 5 \times 5$
(C)	$32$
(D)	$60$
29-	What's the next number in the series $\left\{18, \ 15, \ 12, \ 9, \ ?\right\}$
(A)	$6$
(B)	$8$
(C)	$5$
(D)	$7$
30-	If $x \ + \ y = 10$, what is the value of $4 \ x \ + \ 4 \ y$?
(A)	$65$
(B)	$78$
(C)	$40$
(D)	$32$
31-	$112 \times 32 =$?
(A)	$3,548$
(B)	$3,485$
(C)	$3,480$
(D)	$3,584$
32-	If $8 \ + \ x \ ≥ \ 14$, then $x \ ≥$ ?
(A)	$7$
(B)	$6$
(C)	$9$
(D)	$4$
33-	If $- \ 5 \ a = 25$, then $a =$ ___
(A)	$- \ 4$
(B)	$- \ 5$
(C)	$5$
(D)	$8$
34-	If A $= 7$, B $= 2$ and C $= 6$, then $2$ABC $=$?
(A)	$168$
(B)	$185$
(C)	$130$
(D)	$197$
35-	I’ve got $27$ quarts of milk and my family drinks $3$ gallons of milk per week. How many weeks will that last us?
(A)	$5$ weeks
(B)	$4.5$ weeks
(C)	$2.25$ weeks
(D)	$3$ weeks
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36-	Factor this equation: $x^{2} \ + \ 2 \ x \ – \ 8$
(A)	$x \ (4 \ + \ 2)$
(B)	$(x \ + \ 4) \ (x \ - \ 3)$
(C)	$(x \ + \ 4) \ (x \ - \ 2)$
(D)	$x^2(3 \ + \ 4) \ (x \ - \ 2)$
37-	A baker uses $6$ eggs to bake a cake. How many cakes will he be able to bake with $132$ eggs?
(A)	$25$
(B)	$24$
(C)	$28$
(D)	$22$
38-	Which of the following is the product of $15$ and $18$?
(A)	$238$
(B)	$270$
(C)	$35$
(D)	$9$
39-	Which of the following is equal to $4.5$?
(A)	$3 \frac{1}{10}$
(B)	$5$
(C)	$\frac{45}{10}$
(D)	$\frac{45}{100}$
40-	Which of the following is the correct calculation for $3!$?
(A)	$3 \times 2 \times 1$
(B)	$3 \times 2$
(C)	$1 \times 2 \times 3$
(D)	$2 \times 3$
41-	What is the sum of $\frac{4}{10} \ + \ \frac{5}{2} \ + \ \frac{2}{5}$ ?
(A)	$3$
(B)	$3.10$
(C)	$2 \frac{3}{10}$
(D)	$3 \ \frac{3}{10}$
42-	Lucy gives $5$ pieces of candy to each of her friends. If Lucy gives all her candy away, which amount of candy could have been the amount she distributed?
(A)	$128$
(B)	$180$
(C)	$426$
(D)	$264$
43-	$(x \ + \ 3)(x \ + \ 4) =$ ?
(A)	$x^{2} \ + \ 7 \ x \ + \ 12$
(B)	$x^{2} \ + \ 12 \ x \ + \ 7$
(C)	$x^{2} \ - \ 12 \ x \ - \ 7$
(D)	$x^{2} \ - \ 7 \ x \ + \ 12$
44-	The equation of a line is given as : $y = 4 \ x \ – \ 2$. Which of the following points does not lie on the line?
(A)	$2 , 6$
(B)	$- \ 2 , - \ 10$
(C)	$1 \ , \ 2$
(D)	$3 \ , \ 10$
45-	The number $0.5$ can also represented by which of the following?
(A)	$\frac{5}{10}$
(B)	$\frac{5}{100}$
(C)	$\frac{5}{1000}$
(D)	$\frac{5}{10,000}$
46-	$\frac{12}{19}$ is equal to:
(A)	$6.3$
(B)	$0.6$
(C)	$0.63$
(D)	$0.06$
47-	How much greater is the value of $6 \ x \ + \ 7$ than the value of $6 \ x \ – \ 5$?
(A)	$6$
(B)	$12$
(C)	$15$
(D)	$8$
48-	What is the perimeter of the triangle in the provided diagram?
(A)	$50$
(B)	$45$
(C)	$72$
(D)	$36$
49-	A woman weighs $110$ pounds. She gains $12$ pounds one month and $6$ pounds the next month. What is her new weight?
(A)	$172$ Pounds
(B)	$156$ Pounds
(C)	$128$ Pounds
(D)	$135$ Pounds
50-	$x^{2} \ – \ 36 = 0 \ , \ x$ could equal:
(A)	$- \ 6$
(B)	$- \ 8$
(C)	$10$
(D)	$36$
51-	In the diagram provided, what is the value of b?
(A)	$120^{◦}$
(B)	$45^{◦}$
(C)	$30^{◦}$
(D)	$85^{◦}$
52-	How long is the line segment shown on the number line below?
(A)	$8$
(B)	$6$
(C)	$9$
(D)	$11$
53-	$(x^{4})^{2} =$ ?
(A)	$x^{6}$
(B)	$2 \ x^{6}$
(C)	$x^{8}$
(D)	$x^{2}$
54-	If a rectangular swimming pool has a perimeter of $100$ feet and is $15$ feet wide, what is its area?
(A)	$565$
(B)	$1,458$
(C)	$525$
(D)	$712$
55-	The cube of $4$ is ___.
(A)	$72$
(B)	$81$
(C)	$32$
(D)	$64$
56-	What’s the greatest common factor of the $20$ and $10$?
(A)	$10$
(B)	$14$
(C)	$8$
(D)	$18$
57-	What is $\sqrt{36} \times \sqrt{9}$
(A)	$\sqrt{6}$
(B)	$3 \ \sqrt{6}$
(C)	$18$
(D)	$10$
58-	What's the next number in the series $\left\{21, \ 18, \ 15, \ 12, \ ?\right\}$
(A)	$9$
(B)	$7$
(C)	$25$
(D)	$10$
59-	What is $7,325.2598$ rounded to the nearest tenth?
(A)	$7325.260$
(B)	$7325$
(C)	$7325.25$
(D)	$7325.3$
60-	If $x = 3$ what’s the value of $7 \ x^{2} \ + \ 4 \ x \ – \ 10$?
(A)	$98$
(B)	$65$
(C)	$35$
(D)	$72$
61-	The circumference of a circle is $15$ cm. what is the approximate radius of the circle?
(A)	$3.54$ cm
(B)	$2.39$ cm
(C)	$4.5$ cm
(D)	$3.75$ cm
62-	What is the radicand in $\sqrt[3]{216}$ ?
(A)	$9$
(B)	$5$
(C)	$3$
(D)	$6$
63-	Line l passes through the point $(− \ 1, \ 2)$. Which of the following CANNOT be the equation of line l?
(A)	$y = - \ 1$
(B)	$y = x \ + \ 3$
(C)	$y = x \ + \ 1$
(D)	$y = 1 \ - \ x$
64-	What is the difference between $180$ and $75$?
(A)	$105$
(B)	$75$
(C)	$62$
(D)	$87$

HSPT Mathematics Practice Test Answers and Explanations

1- Choice C is correct

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

2- Choice D is correct

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

3- Choice B is correct

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

4- Choice A is correct

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

5- Choice C is correct

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

6- Choice A is correct

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. $2 \times 2 \times 2 \times 5 \times 7 = 280$

7- Choice B is correct

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

8- Choice A is correct

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

9- Choice C is correct

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

10- Choice A is correct

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

11- Choice A is correct

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 $= 20$

12- Choice B is correct

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 $23$. $15 \ + \ 8 = 23$

13- Choice D is correct

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!

14- Choice A is correct

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

15- Choice C is correct

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

16- Choice D is correct

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

17- Choice B is correct

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

18- Choice D is correct

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

19- Choice B is correct

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

20- Choice B is correct

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

21- Choice C is correct

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

22- Choice D is correct

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. $\frac{3}{2} = 1.5$

23- Choice A is correct

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

24- Choice A is correct

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

25- Choice C is correct

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

26- Choice D is correct

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

27- Choice A is correct

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

28- Choice C is correct

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

29- Choice A is correct

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

30- Choice C is correct

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

31- Choice D is correct

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

32- Choice B is correct

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

33- Choice B is correct

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

34- Choice A is correct

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

35- Choice C is correct

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

36- Choice C is correct

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

37- Choice D is correct

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

38- Choice B is correct

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

39- Choice C is correct

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

40- Choice A is correct

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

41- Choice D is correct

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

42- Choice B is correct

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.

43- Choice A is correct

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

44- Choice B is correct

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!

45- Choice A is correct

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

46- Choice C is correct

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

47- Choice B is correct

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

48- Choice B is correct

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

49- Choice C is correct

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

50- Choice A is correct

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

51- Choice C is correct

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

52- Choice D is correct

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

53- Choice C is correct

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

54- Choice C is correct

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 $= 15 \times 35 = 525$

55- Choice D is correct

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

56- Choice A is correct

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 $= 10$

57- Choice C is correct

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

58- Choice A is correct

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

59- Choice D is correct

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

60- Choice B is correct

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

61- Choice B is correct

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

62- Choice D is correct

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

63- Choice C is correct

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!

64- Choice A is correct

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

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