FTCE General Knowledge Mathematics Subtest Assessment Practice Test
1. Which of the following is considered a rational number?
o A) 2\sqrt{2}2
o B) 13\frac{1}{3}31
o C) −5-\sqrt{5}−5
o D) π\piπ
Answer: B) 13\frac{1}{3}31
Explanation: Rational numbers can be expressed as a fraction ab\frac{a}{b}ba where aaa and bbb are
integers and b≠0b \neq 0b=0. 13\frac{1}{3}31 fits this definition, while 2\sqrt{2}2, −5-\sqrt{5}−5, and π\
piπ are irrational numbers.
2. What is the sum of the natural numbers from 1 to 10?
o A) 45
o B) 55
o C) 50
o D) 60
Answer: B) 55
Explanation: The sum of the first nnn natural numbers is given by the formula n(n+1)2\frac{n(n + 1)}
{2}2n(n+1). For n=10n = 10n=10, it is 10(10+1)2=10×112=55\frac{10(10 + 1)}{2} = \frac{10 \times 11}{2} =
55210(10+1)=210×11=55.
3. Which property is demonstrated by the equation a+b=b+aa + b = b + aa+b=b+a?
o A) Associative Property
o B) Commutative Property
o C) Distributive Property
o D) Identity Property
Answer: B) Commutative Property
Explanation: The Commutative Property states that the order in which two numbers are added does not
change the sum, hence a+b=b+aa + b = b + aa+b=b+a.
4. Which of the following numbers is an integer?
o A) 4.5
o B) -3
o C) 72\frac{7}{2}27
o D) 9\sqrt{9}9
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, FTCE General Knowledge Mathematics Subtest Assessment Practice Test
Answer: B) -3
Explanation: Integers are whole numbers that can be positive, negative, or zero. -3 fits this definition,
while 4.5 is a decimal, 72\frac{7}{2}27 is a fraction, and 9\sqrt{9}9 equals 3 (which is an integer, but -3 is
the correct choice given the context).
5. Which property is illustrated by 2(3+4)=2×3+2×42(3 + 4) = 2 \times 3 + 2 \times
42(3+4)=2×3+2×4?
o A) Associative Property
o B) Commutative Property
o C) Distributive Property
o D) Inverse Property
Answer: C) Distributive Property
Explanation: The Distributive Property states that multiplying a number by a sum is the same as
multiplying each addend individually and then adding the results.
6. What is the identity element for addition?
o A) 0
o B) 1
o C) -1
o D) None of the above
Answer: A) 0
Explanation: The identity element for addition is 0, as adding 0 to any number aaa does not change its
value: a+0=aa + 0 = aa+0=a.
7. Which of the following is an example of an irrational number?
o A) 58\frac{5}{8}85
o B) 0
o C) 16\sqrt{16}16
o D) 7\sqrt{7}7
Answer: D) 7\sqrt{7}7
Explanation: Irrational numbers cannot be expressed as a fraction of two integers. 7\sqrt{7}7 is not a
perfect square and cannot be simplified to a fraction, while the others are either rational or whole
numbers.
8. Which number is a whole number but not a natural number?
o A) 0
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, FTCE General Knowledge Mathematics Subtest Assessment Practice Test
o B) -2
o C) 1
o D) 5
Answer: A) 0
Explanation: Whole numbers include all natural numbers (0, 1, 2, ...) and the number 0. Natural
numbers start from 1, so 0 is not a natural number.
9. If a=−4a = -4a=−4 and b=3b = 3b=3, what is a+ba + ba+b?
o A) -7
o B) -1
o C) 1
o D) 7
Answer: B) -1
Explanation: The sum of aaa and bbb is −4+3=−1-4 + 3 = -1−4+3=−1.
10. Which property allows the rearrangement of terms in multiplication?
o A) Associative Property
o B) Commutative Property
o C) Distributive Property
o D) Identity Property
Answer: B) Commutative Property
Explanation: The Commutative Property allows the terms in a multiplication operation to be rearranged
without changing the product: a×b=b×aa \times b = b \times aa×b=b×a.
11. What is the value of −2+(−3)-2 + (-3)−2+(−3)?
o A) -5
o B) 5
o C) -1
o D) 1
Answer: A) -5
Explanation: Adding two negative numbers results in a more negative number: −2+(−3)=−5-2 + (-3) = -
5−2+(−3)=−5.
12. If x=5x = 5x=5 and y=2y = 2y=2, what is xyxyxy?
o A) 3
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, FTCE General Knowledge Mathematics Subtest Assessment Practice Test
o B) 10
o C) 7
o D) 25
Answer: B) 10
Explanation: The product of xxx and yyy is 5×2=105 \times 2 = 105×2=10.
13. Which of the following statements is true regarding the number 1?
o A) It is a natural number.
o B) It is an irrational number.
o C) It is an integer.
o D) Both A and C.
Answer: D) Both A and C.
Explanation: The number 1 is both a natural number and an integer. It is not irrational since it can be
expressed as 11\frac{1}{1}11.
14. Which of the following numbers is not a rational number?
o A) 0.750.750.75
o B) 8
o C) 23\frac{2}{3}32
o D) 5\sqrt{5}5
Answer: D) 5\sqrt{5}5
Explanation: 5\sqrt{5}5 is an irrational number because it cannot be expressed as a fraction of integers.
15. Which property is used in the statement (a+b)+c=a+(b+c)(a + b) + c = a + (b + c)(a+b)+c=a+
(b+c)?
o A) Commutative Property
o B) Associative Property
o C) Distributive Property
o D) Identity Property
Answer: B) Associative Property
Explanation: The Associative Property states that the way in which numbers are grouped does not
change their sum or product.
16. What is the result of 7+5×27 + 5 \times 27+5×2 using the order of operations?
o A) 12
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1. Which of the following is considered a rational number?
o A) 2\sqrt{2}2
o B) 13\frac{1}{3}31
o C) −5-\sqrt{5}−5
o D) π\piπ
Answer: B) 13\frac{1}{3}31
Explanation: Rational numbers can be expressed as a fraction ab\frac{a}{b}ba where aaa and bbb are
integers and b≠0b \neq 0b=0. 13\frac{1}{3}31 fits this definition, while 2\sqrt{2}2, −5-\sqrt{5}−5, and π\
piπ are irrational numbers.
2. What is the sum of the natural numbers from 1 to 10?
o A) 45
o B) 55
o C) 50
o D) 60
Answer: B) 55
Explanation: The sum of the first nnn natural numbers is given by the formula n(n+1)2\frac{n(n + 1)}
{2}2n(n+1). For n=10n = 10n=10, it is 10(10+1)2=10×112=55\frac{10(10 + 1)}{2} = \frac{10 \times 11}{2} =
55210(10+1)=210×11=55.
3. Which property is demonstrated by the equation a+b=b+aa + b = b + aa+b=b+a?
o A) Associative Property
o B) Commutative Property
o C) Distributive Property
o D) Identity Property
Answer: B) Commutative Property
Explanation: The Commutative Property states that the order in which two numbers are added does not
change the sum, hence a+b=b+aa + b = b + aa+b=b+a.
4. Which of the following numbers is an integer?
o A) 4.5
o B) -3
o C) 72\frac{7}{2}27
o D) 9\sqrt{9}9
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, FTCE General Knowledge Mathematics Subtest Assessment Practice Test
Answer: B) -3
Explanation: Integers are whole numbers that can be positive, negative, or zero. -3 fits this definition,
while 4.5 is a decimal, 72\frac{7}{2}27 is a fraction, and 9\sqrt{9}9 equals 3 (which is an integer, but -3 is
the correct choice given the context).
5. Which property is illustrated by 2(3+4)=2×3+2×42(3 + 4) = 2 \times 3 + 2 \times
42(3+4)=2×3+2×4?
o A) Associative Property
o B) Commutative Property
o C) Distributive Property
o D) Inverse Property
Answer: C) Distributive Property
Explanation: The Distributive Property states that multiplying a number by a sum is the same as
multiplying each addend individually and then adding the results.
6. What is the identity element for addition?
o A) 0
o B) 1
o C) -1
o D) None of the above
Answer: A) 0
Explanation: The identity element for addition is 0, as adding 0 to any number aaa does not change its
value: a+0=aa + 0 = aa+0=a.
7. Which of the following is an example of an irrational number?
o A) 58\frac{5}{8}85
o B) 0
o C) 16\sqrt{16}16
o D) 7\sqrt{7}7
Answer: D) 7\sqrt{7}7
Explanation: Irrational numbers cannot be expressed as a fraction of two integers. 7\sqrt{7}7 is not a
perfect square and cannot be simplified to a fraction, while the others are either rational or whole
numbers.
8. Which number is a whole number but not a natural number?
o A) 0
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, FTCE General Knowledge Mathematics Subtest Assessment Practice Test
o B) -2
o C) 1
o D) 5
Answer: A) 0
Explanation: Whole numbers include all natural numbers (0, 1, 2, ...) and the number 0. Natural
numbers start from 1, so 0 is not a natural number.
9. If a=−4a = -4a=−4 and b=3b = 3b=3, what is a+ba + ba+b?
o A) -7
o B) -1
o C) 1
o D) 7
Answer: B) -1
Explanation: The sum of aaa and bbb is −4+3=−1-4 + 3 = -1−4+3=−1.
10. Which property allows the rearrangement of terms in multiplication?
o A) Associative Property
o B) Commutative Property
o C) Distributive Property
o D) Identity Property
Answer: B) Commutative Property
Explanation: The Commutative Property allows the terms in a multiplication operation to be rearranged
without changing the product: a×b=b×aa \times b = b \times aa×b=b×a.
11. What is the value of −2+(−3)-2 + (-3)−2+(−3)?
o A) -5
o B) 5
o C) -1
o D) 1
Answer: A) -5
Explanation: Adding two negative numbers results in a more negative number: −2+(−3)=−5-2 + (-3) = -
5−2+(−3)=−5.
12. If x=5x = 5x=5 and y=2y = 2y=2, what is xyxyxy?
o A) 3
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, FTCE General Knowledge Mathematics Subtest Assessment Practice Test
o B) 10
o C) 7
o D) 25
Answer: B) 10
Explanation: The product of xxx and yyy is 5×2=105 \times 2 = 105×2=10.
13. Which of the following statements is true regarding the number 1?
o A) It is a natural number.
o B) It is an irrational number.
o C) It is an integer.
o D) Both A and C.
Answer: D) Both A and C.
Explanation: The number 1 is both a natural number and an integer. It is not irrational since it can be
expressed as 11\frac{1}{1}11.
14. Which of the following numbers is not a rational number?
o A) 0.750.750.75
o B) 8
o C) 23\frac{2}{3}32
o D) 5\sqrt{5}5
Answer: D) 5\sqrt{5}5
Explanation: 5\sqrt{5}5 is an irrational number because it cannot be expressed as a fraction of integers.
15. Which property is used in the statement (a+b)+c=a+(b+c)(a + b) + c = a + (b + c)(a+b)+c=a+
(b+c)?
o A) Commutative Property
o B) Associative Property
o C) Distributive Property
o D) Identity Property
Answer: B) Associative Property
Explanation: The Associative Property states that the way in which numbers are grouped does not
change their sum or product.
16. What is the result of 7+5×27 + 5 \times 27+5×2 using the order of operations?
o A) 12
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