High School Assessment (HLA) Mathematics Pre-Calculus Honors (6–
12 Grade) Practice Exam
1. Which of the following is an example of the Commutative Property of
addition?
A. a+b=b+aa + b = b + aa+b=b+a
B. a+(b+c)=(a+b)+ca + (b + c) = (a + b) + ca+(b+c)=(a+b)+c
C. a+0=aa + 0 = aa+0=a
D. a+(−a)=0a + (-a) = 0a+(−a)=0
Answer: A. a+b=b+aa + b = b + aa+b=b+a
Explanation: The Commutative Property states that the order of numbers in addition or
multiplication does not affect the result. In this case, adding aaa and bbb is the same as adding
bbb and aaa.
2. Which of the following operations does not apply to real numbers?
A. Addition
B. Subtraction
C. Division
D. Division by zero
Answer: D. Division by zero
Explanation: Real numbers can be added, subtracted, and divided (except by zero). Division by
zero is undefined in the real number system.
3. What is the value of (−2)3(-2)^3(−2)3?
A. -6
B. -8
C. 8
D. 2
Answer: B. -8
Explanation: (−2)3=(−2)×(−2)×(−2)=−8(-2)^3 = (-2) \times (-2) \times
(-2) = -8(−2)3=(−2)×(−2)×(−2)=−8. When a negative number is raised
to an odd power, the result is negative.
4. Which of the following is equivalent to 16\sqrt{16}16?
1
, High School Assessment (HLA) Mathematics Pre-Calculus Honors (6–
12 Grade) Practice Exam
A. 16
B. -16
C. 4
D. -4
Answer: C. 4
Explanation: The square root of 16 is 4, because 42=164^2 = 1642=16. By definition, the
square root symbol represents the principal (positive) root.
5. What is the value of 343^434?
A. 12
B. 81
C. 64
D. 27
Answer: B. 81
Explanation: 34=3×3×3×3=813^4 = 3 \times 3 \times 3 \times 3 = 8134=3×3×3×3=81.
6. Which of the following is written in scientific notation?
A. 5×1065 \times 10^65×106
B. 500000050000005000000
C. 5,000,0005,000,0005,000,000
D. 5000000.05000000.05000000.0
Answer: A. 5×1065 \times 10^65×106
Explanation: Scientific notation expresses numbers as a product of a coefficient (between 1 and
10) and a power of 10. 5×1065 \times 10^65×106 is the scientific notation for 5 million.
7. Simplify 2523\frac{2^5}{2^3}2325.
A. 282^828
B. 222^222
C. 252^525
D. 232^323
2
, High School Assessment (HLA) Mathematics Pre-Calculus Honors (6–
12 Grade) Practice Exam
Answer: B. 222^222
Explanation: Using the quotient rule for exponents, 2523=25−3=22\frac{2^5}{2^3} =
2^{5-3} = 2^22325=25−3=22.
8. Which of the following is the Additive Inverse of 7?
A. 7
B. 0
C. -7
D. 1
Answer: C. -7
Explanation: The Additive Inverse of a number is the number that, when added to the original
number, results in 0. For 7, the additive inverse is -7.
9. What is the result of 12×103\frac{1}{2} \times 10^321×103 written in decimal
notation?
A. 500
B. 0.5
C. 5000
D. 5
Answer: A. 500
Explanation: 12×103=0.5×1000=500\frac{1}{2} \times 10^3 = 0.5 \times 1000 = 50021
×103=0.5×1000=500.
10. Which of the following expressions is not a valid use of exponents?
A. 232^323
B. 3−23^{-2}3−2
C. 51/25^{1/2}51/2
D. 000^000
Answer: D. 000^000
Explanation: 000^000 is an indeterminate form and is not defined in mathematics.
3
, High School Assessment (HLA) Mathematics Pre-Calculus Honors (6–
12 Grade) Practice Exam
11. Which property of real numbers is illustrated by the equation (a+b)+c=a+
(b+c)(a + b) + c = a + (b + c)(a+b)+c=a+(b+c)?
A. Commutative Property
B. Associative Property
C. Distributive Property
D. Identity Property
Answer: B. Associative Property
Explanation: The Associative Property states that the grouping of numbers in addition or
multiplication does not affect the result. This property is illustrated by the equation (a+b)+c=a+
(b+c)(a + b) + c = a + (b + c)(a+b)+c=a+(b+c).
12. What is 25+3\sqrt{25} + 325+3?
A. 5
B. 8
C. 28
D. 6
Answer: B. 8
Explanation: 25=5\sqrt{25} = 525=5, and 5+3=85 + 3 = 85+3=8.
13. Which of the following represents 4.5×1034.5 \times 10^34.5×103 in standard
form?
A. 4500
B. 45
C. 450
D. 0.045
Answer: A. 4500
Explanation: 4.5×1034.5 \times 10^34.5×103 means moving the decimal point 3 places to the
right, so the result is 4500.
14. Simplify 52×535^2 \times 5^352×53.
A. 555^555
B. 565^656
4
12 Grade) Practice Exam
1. Which of the following is an example of the Commutative Property of
addition?
A. a+b=b+aa + b = b + aa+b=b+a
B. a+(b+c)=(a+b)+ca + (b + c) = (a + b) + ca+(b+c)=(a+b)+c
C. a+0=aa + 0 = aa+0=a
D. a+(−a)=0a + (-a) = 0a+(−a)=0
Answer: A. a+b=b+aa + b = b + aa+b=b+a
Explanation: The Commutative Property states that the order of numbers in addition or
multiplication does not affect the result. In this case, adding aaa and bbb is the same as adding
bbb and aaa.
2. Which of the following operations does not apply to real numbers?
A. Addition
B. Subtraction
C. Division
D. Division by zero
Answer: D. Division by zero
Explanation: Real numbers can be added, subtracted, and divided (except by zero). Division by
zero is undefined in the real number system.
3. What is the value of (−2)3(-2)^3(−2)3?
A. -6
B. -8
C. 8
D. 2
Answer: B. -8
Explanation: (−2)3=(−2)×(−2)×(−2)=−8(-2)^3 = (-2) \times (-2) \times
(-2) = -8(−2)3=(−2)×(−2)×(−2)=−8. When a negative number is raised
to an odd power, the result is negative.
4. Which of the following is equivalent to 16\sqrt{16}16?
1
, High School Assessment (HLA) Mathematics Pre-Calculus Honors (6–
12 Grade) Practice Exam
A. 16
B. -16
C. 4
D. -4
Answer: C. 4
Explanation: The square root of 16 is 4, because 42=164^2 = 1642=16. By definition, the
square root symbol represents the principal (positive) root.
5. What is the value of 343^434?
A. 12
B. 81
C. 64
D. 27
Answer: B. 81
Explanation: 34=3×3×3×3=813^4 = 3 \times 3 \times 3 \times 3 = 8134=3×3×3×3=81.
6. Which of the following is written in scientific notation?
A. 5×1065 \times 10^65×106
B. 500000050000005000000
C. 5,000,0005,000,0005,000,000
D. 5000000.05000000.05000000.0
Answer: A. 5×1065 \times 10^65×106
Explanation: Scientific notation expresses numbers as a product of a coefficient (between 1 and
10) and a power of 10. 5×1065 \times 10^65×106 is the scientific notation for 5 million.
7. Simplify 2523\frac{2^5}{2^3}2325.
A. 282^828
B. 222^222
C. 252^525
D. 232^323
2
, High School Assessment (HLA) Mathematics Pre-Calculus Honors (6–
12 Grade) Practice Exam
Answer: B. 222^222
Explanation: Using the quotient rule for exponents, 2523=25−3=22\frac{2^5}{2^3} =
2^{5-3} = 2^22325=25−3=22.
8. Which of the following is the Additive Inverse of 7?
A. 7
B. 0
C. -7
D. 1
Answer: C. -7
Explanation: The Additive Inverse of a number is the number that, when added to the original
number, results in 0. For 7, the additive inverse is -7.
9. What is the result of 12×103\frac{1}{2} \times 10^321×103 written in decimal
notation?
A. 500
B. 0.5
C. 5000
D. 5
Answer: A. 500
Explanation: 12×103=0.5×1000=500\frac{1}{2} \times 10^3 = 0.5 \times 1000 = 50021
×103=0.5×1000=500.
10. Which of the following expressions is not a valid use of exponents?
A. 232^323
B. 3−23^{-2}3−2
C. 51/25^{1/2}51/2
D. 000^000
Answer: D. 000^000
Explanation: 000^000 is an indeterminate form and is not defined in mathematics.
3
, High School Assessment (HLA) Mathematics Pre-Calculus Honors (6–
12 Grade) Practice Exam
11. Which property of real numbers is illustrated by the equation (a+b)+c=a+
(b+c)(a + b) + c = a + (b + c)(a+b)+c=a+(b+c)?
A. Commutative Property
B. Associative Property
C. Distributive Property
D. Identity Property
Answer: B. Associative Property
Explanation: The Associative Property states that the grouping of numbers in addition or
multiplication does not affect the result. This property is illustrated by the equation (a+b)+c=a+
(b+c)(a + b) + c = a + (b + c)(a+b)+c=a+(b+c).
12. What is 25+3\sqrt{25} + 325+3?
A. 5
B. 8
C. 28
D. 6
Answer: B. 8
Explanation: 25=5\sqrt{25} = 525=5, and 5+3=85 + 3 = 85+3=8.
13. Which of the following represents 4.5×1034.5 \times 10^34.5×103 in standard
form?
A. 4500
B. 45
C. 450
D. 0.045
Answer: A. 4500
Explanation: 4.5×1034.5 \times 10^34.5×103 means moving the decimal point 3 places to the
right, so the result is 4500.
14. Simplify 52×535^2 \times 5^352×53.
A. 555^555
B. 565^656
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