Mathlete's Quiz 5 - Algebraic Reasoning (L-Z)

Write an algebraic expression for the phrase “the sum of 8 times a number r and 3”.

• 8r + 3

• 11r

• 24r

• 3r + 8

Answer explanation

The phrase "the sum of 8 times a number r and 3" translates to the expression 8r + 3, where 8r represents 8 times the number r, and adding 3 gives the final expression. Thus, the correct answer is 8r + 3.

Bobby’s age is 7 less than his sister’s age, a. Write an algebraic expression to represent Bobby’s age.

• a - 7

• a + 7

• 7 - a

• a * 7

Answer explanation

Bobby’s age is 7 less than his sister’s age, represented by 'a'. Therefore, to find Bobby's age, we subtract 7 from 'a', resulting in the expression 'a - 7', which is the correct choice.

Write the verbal phrase for the algebraic expression 4k – 9.

• 9 less than the product of 4 and k

• The sum of 4 times k and 9

• 9 more than the product of 4 and k

• The difference of 4k and 9

Answer explanation

The expression 4k - 9 represents the difference between 4 times k and 9. Thus, it can be described as '9 less than the product of 4 and k', which matches the correct answer choice.

Maddie is a hockey fan and wants to go to the playoff games. When she researched the price of tickets, they cost more than $215. Which inequalities could represent the ticket price, t, that Maddie will pay to attend a playoff hockey game? Select all that apply.

• t ≤ $215

• $215 > t

• $215 < t

• t > $215

• t ≤ $215

Answer explanation

Maddie found tickets cost more than $215, so the correct inequalities are $215 > t (tickets are less than $215) and $215 < t (tickets are more than $215). The other options do not accurately represent her situation.

What inequality is represented on the number line?

• y > 6

• y < 6

• y = 6

• y ≥ 6

Answer explanation

The number line shows an open circle at 6, indicating that 6 is not included. This represents the inequality y > 6, meaning y can take any value greater than 6.

In order to participate in a youth camp, children must be at most 12 years old. Write an inequality to show how old children, c, have to be to attend this camp.

• c ≤ 12

• c < 12

• c ≥ 12

• c > 12

Answer explanation

The camp requires children to be at most 12 years old, meaning they can be 12 or younger. This is represented by the inequality c ≤ 12, indicating that c can equal 12 or be less than 12.

Evaluate the expression -2d³ - 3r where d = 3 and r = 4.

• -66

• -20

• -6

• 42

Answer explanation

Substituting d = 3 and r = 4 into the expression -2d^3 - 3r gives -2(3^3) - 3(4) = -2(27) - 12 = -54 - 12 = -66. Thus, the correct answer is -66.

Evaluate the expression 4a² + b² - 3 where a = 2 and b = 1.

• 14

• 10

• 12

• 16

Answer explanation

Substituting a = 2 and b = 1 into the expression: 4(2)² + (1)² - 3 = 4(4) + 1 - 3 = 16 + 1 - 3 = 14. Thus, the correct answer is 14.

• -2

• -1

• 0

• 1

Answer explanation

Substituting n = -2 and p = 11 into the expression \( \frac{5n - 12}{p} \): \( \frac{5(-2) - 12}{11} = \frac{-10 - 12}{11} = \frac{-22}{11} = -2 \). Thus, the correct answer is -2.

Select all of the equivalent expressions to: 6n + 2(2n - 1).

• 6n + 4n - 1

• 9n

• 11n

• 10n - 2

• 6n + 4n - 2

Answer explanation

To simplify 6n + 2(2n - 1), distribute to get 6n + 4n - 2, which equals 10n - 2. The expression 6n + 4n - 2 is equivalent as well. Thus, the correct choices are 10n - 2 and 6n + 4n - 2.