ACT - Math Vocab
If 2 consecutive prime numbers have a sum of 42, what is the larger number? A. 17 B. 19 C. 23 D. 27 E. 29
The correct answer is C. Assume the problem is asking something easy. Just list a bunch of prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 and look for two in a row (consecutive) that add up to 42. 19 + 23 = 42. Just stay relaxed, focused, and confident.
If the sum of three consecutive odd integers is 33, what is the value of the largest of the three integers? A. 7 B. 9 C. 11 D. 13 E. 15
The correct answer is D. Just list the possibilities 7, 9, 11, 13, 15 or "Use the Answers." Either way, don't get intimidated and realize that you know the vocab — 9 + 11 + 13 = 33. Make sure to underline the vocab terms and choose the largest of the three integers.
For all real numbers x, how many values of x are odd positive prime numbers less than 20 ? A. 3 B. 5 C. 6 D. 7 E. 8
The correct answer is D. List the primes less than 20: 2, 3, 5, 7, 11, 13, 17, 19. All are odd except 2. Remember that 1 is not a prime number. So there are 7 odd prime numbers less than 20.
Constant
This word really throws some kids, but it just means a letter in place of specific, fixed number, just like a variable. Sometimes we may know the numerical value of the constant, sometimes we won't.
Real number
Any number without an "i" to mean "imaginary number." or ∞. Examples: −3, −2.2, 0, 2.75, 3.1415926535897932348...(pi again!), and 2⎯⎯√
Rational number
A number that can be expressed as the quotient of two integers and has a finite number of decimal places, or has decimal values that repeat in a pattern.
Irrational number
A number that cannot be expressed as the quotient of two integers and has an infinite number of decimal places. Examples: 3.1415926535897932348..., e (2.7182818284590...), etc.
Prime
A number whose only factors are 1 and itself. The numbers 2, 3, 5, 7, 11, 13, 17, ...are prime.
Units digit
Just a fancy term for the "ones" digit in a number, like the 2 in 672.
Consecutive numbers
Numbers that are next to each other: 5 and 6, 100 and 101, 9 and 10...you get the picture. Just add 1 to get from the first number to the second. If a question problem says "Two consecutive numbers" and doesn't tell you what they are, label them as "x" and "x + 1." If they ask for "Three consecutive numbers," label them as "x" and "x + 1" and "x + 2."
Integer
Numbers without decimals or fractions. Also known as awhole number. Examples: −3, −2, −1, 0, 1, 2, 3...
Consecutive even/odd numbers
Pairs of even numbers and odd numbers that are next to each other (skipping the odd and even numbers, respectively, between them): 2 and 4, 57 and 59, 100 and 102...you get the picture. Just add 2 between each number. If a problem says "Two consecutive even numbers" or "Two consecutive odd numbers" and doesn't tell you what they are, label them as "x" and "x + 2." If it asks you for "three consecutive even/odd numbers," that means "x," "x + 2," and "x + 4".
Which of the following is a list of all positive integers between 40 and 46 that do not include a member of the pair of consecutive odd prime numbers? A. 42, 44, and 45 B. 42, 43, and 44 C. 41, 42, 43, and 44 D. 41 and 45 E. 42 and 44
The correct answer is A. Make a list of the integers between 40 and 46: 41, 42, 43, 44, 45. Cross out any consecutive odd prime numbers: 41 and 43. So 42, 44, and 45 are the integers between 40 and 46 that are not consecutive odd prime numbers.
Two consecutive odd integers have a sum of −32. Which of the following is NOT a justified conclusion? A. Both numbers are negative. B. The lesser number is −15. C. Both numbers are greater than −20. D. Both numbers are less than −10. E. One of the numbers is a factor of 60.
The correct answer is B. Probably best to just find the 2 numbers. If that seems difficult, "Use the Answers" as hints; that is, try −15 and numbers close to −15. The two numbers are indeed −15 and −17. Choice B (−15) might seem less than −17, since 15 is less than 17, but the bigger the negative number, the less it really is; like the more you owe, the bigger the debt, and the less you have. All other choices are justifiable. This is a great question to use the process of elimination; eliminate choices that you are sure are incorrect (in this case the ones that you are sure are justified) and then choose the best from what's left.
For all real numbers x, what integer values satisfy the equation 2x^2 = 50 ? A. −5 only B. −5 and 5 C. −5, 5, and 25 D.5 only E. 25 only
The correct answer is B. You can do the algebra and solve for x, or you can just "Use the Answers." Most people know that since (2)(52) = 50, there is at least one answer to this question. But (2)(−5)2 = 50 also. So there are two possible answers to the question, 5 and −5. This is a great reminder to try all the answers and not just pick the first one that works.
