Number Types & Properties

2. Which of the following inequalities orders the numbers 0.2, 0.03, and from least to greatest?

2015 June(73C) Math Question 2

2. The graph below shows the number of students who were present on Thursday from each of the 5 groups in Ms. Meagan's class. What is the probability that a student selected at random from the class on Thursday is in Group 4 ?

2017 December(A10) Math Question 2

2. What is the sum of the complex numbers 3 – 4i and 5 + 3i?

2018 April(A09) Math Question 2

3. Which of the following inequalities orders the numbers 0.1, 0.04, and 1/6 from least to greatest?

2014 December(72G) Math Question 3

3. Which of the following integers is NOT a factor of 132?

2013 June(71C) Math Question 3

4. Which of the following numbers has the greatest value?

2016 April(73E) Math Question 4

2011 April(67F) Math Question 5

6. The square root of a certain number is approximately 9.2371. The certain number is between what 2 integers?

2015 June(73C) Math Question 6

2020 July(C01) Math Question 12

14. Which of the following integers is closest to

2017 June(74C) Math Question 14

15. What is the smallest integer greater than V85 ?

2018 June(A11) Math Question 15

2010 April(68G) Math Question 15

16. What is the largest possible product for 2 even integers whose sum is 18 ?

Adding, subtracting, multiplying and dividing positive and negative numbers

2020 December(D03) Math Question 16

2014 April(71H) Math Question 17

18. For which of the following conditions will the sum of integers in and n always be an odd integer?

2017 April(74F) Math Question 18

2011 April(67F) Math Question 19

20. One of the following values for a makes the expression (2a+5)/(a2+1) undefined. Which one?

Complex Number

Undefined fraction

2021 April(D05) Math Question 20

21. What is the least positive number that has a remainder of 3 when divided by 5 and a remainder of 7 when divided by 9 ?

Remainders

2021 April(D05) Math Question 21

2010 December(69A) Math Question 23

28. Which of the following operations will produce the largest result when substituted for the blank in the

2016 December(74H) Math Question 28

2009 December(68A) Math Question 28

2018 December(B05) Math Question 29

2012 December(71A) Math Question 30

31. What is the 322nd digit after the decimal point in the repeating decimal 0.1357 ?

Repeating decimal

2021 June(D06) Math Question 31

2019 April(Z15) Math Question 32

2012 June(70C) Math Question 32

2012 April(70G) Math Question 32

32. What is the complex conjugate of the number below?

Division of imaginary numbers (the use of conjugates)

2021 April(D05) Math Question 32

33. What is the least positive number that has a remainder of 3 when divided by 6 and a remainder of 6 when divided by 9 ?

2020 December(D03) Math Question 33

35. For which of the equations below is its solution an integer?

2015 April(73G) Math Question 35

36. Which of the following arranges the numbers f, 1.8,
1.08, and 1.08 into ascending order? (Note: The
overbar notation shows that the digits under the bar
will repeat. For example, 1.73 == 1.737373 ... )

2019 June(B02) Math Question 36

2019 April(B04) Math Question 36

36. Among the following rational numbers, which has the greatest value?

2013 June(71C) Math Question 36

36. Given that i is the imaginary unit, which of the following complex numbers is equal to (7 + 6i)2 ?

2020 December(D03) Math Question 36

38. Which of the following expressions, when evaluated, equals an irrational number?

2017 April(74F) Math Question 38

2010 December(69A) Math Question 40

2009 April(66F) Math Question 40

2011 June(69F) Math Question 41

2009 April(66F) Math Question 41

43. What is the smallest positive integer having exactly
5 different positive integer divisors?

2019 June(B02) Math Question 43

2012 December(71A) Math Question 43

43. For i = square root of -1, (1 + 2i)^2 = ?

2016 April(73E) Math Question 43

2021 June(D06) Math Question 44

2010 December(69A) Math Question 45

2011 April(67F) Math Question 46

2020 July(C01) Math Question 46

2021 June(D06) Math Question 46

46. Let A, B, and C represent the digits in the hundreds, tens, and ones places, respectively, of a certain 3-digit whole number. Let D, E, and F represent the digits in the hundreds, tens, and ones places, respectively, of a different 3-digit whole number. The positive difference between the 2  numbers is greater than 100. Which of the following inequalities must be true?

Absolute value

2021 December(E23) Math Question 46

2009 December(68A) Math Question 47

2013 December(71E) Math Question 48

2009 April(66F) Math Question 48

49. If x < y and y < 4, then what is the greatest possible integer value of x + y ?

2018 June(A11) Math Question 49

2013 April(71G) Math Question 51

2012 June(70C) Math Question 51

52. Let x be a negative odd integer. The expression xy3 is a positive even integer whenever y is any member of which of the following sets?

2014 December(72G) Math Question 52

52. What is the 275th digit after the decimal point in the repeating decimal 0.6295 _____ ?

2021 April(Z04) Math Question 52

53. An integer is abundant if its positive integer factors, excluding the integer itself, have a sum that is greater than the integer. How many of the integers 6, 8, 10, and 12 are abundant?

2018 June(A11) Math Question 53

53. The product of 2 numbers is 25. If 1 of the numbers is the complex number 4 + 3i, what is the other number?

2014 April(71H) Math Question 53

53. Given that b is rational and i = √••−1 , the product of the expression (3 + bi) and which of the following expressions must be a rational number?

2021 December(E23) Math Question 53

2020 June(C02) Math Question 53

2013 April(71G) Math Question 54

2020 June(C02) Math Question 54

2021 April(Z04) Math Question 55

2020 June(C02) Math Question 56

57. What is the distance, in coordinate units, between 2 + 6i and —4 + 3i in the complex plane?

2016 December(74H) Math Question 57

58. The equation (x — 7)2 + (y — 8)2 = 10 is that of a circle that lies in the standard (x,y) coordinate plane. One endpoint of a diameter of the circle has y-coordinate 11. What is the y-coordinate of the other endpoint of that diameter?

2017 December(A10) Math Question 58

58. Karie is inventing a new notation in math. She has decided to use n.L to denote the sum of the first a positive integers. For example, 51 means 5 + 4 + 3 + 2 + 1. Karie has written 3 statements that she is investigating as possible properties of

2018 April(A09) Math Question 58

2020 July(C01) Math Question 58

58. For all real numbers x and the imaginary number i, which of the following expressions is equivalent to

2017 June(74C) Math Question 58

58. Given a positive integer n such that i^n = 1, which of the following statements about n must be true? (Note: i² = – 1)

Number Types & PropertiesThere are 71 ACT math questions under Number Types & Properties

Sub-topics

2015 June(73C) Math Question 2

2017 December(A10) Math Question 2