Benchmark #2 Review

Solving

100

- 4 + x = - (x + 8)

x = -2

200

-4x + 12 + 5x = 7 + x

no solution

300

(k+7)/3 = (k+1)/5

k = -16

400

DAILY DOUBLE

2x + 22 < 4(5x + 1)

x > 1

500

A = 4xy, solve for y

y = A/4x

Sequences

100

Find the explicit formula for the arithmetic sequence if a₁ = 18 and d = 7

an=7n+11

or 

an=18+(n−1)⋅7  

200

Which of the following is a geometric sequence?

A. -1, 3, 7, 11,..

B. (1/2), 0, (-1/2), -1,..

C. 1, 4, 9, 16,..

D. (1/3), 1, 3, 9,..

D.

300

Write the explicit formula for the sequence

-2, -4, -8, -16,..

an=−2⋅(2)^n-1

400

Given a geometric sequence where a₂ = 6 and r = - 3, find a₈.

4,374

500

Given the following sequence, {0.5, -2, 8, -32,..}

Find the fourteenth term.

−33,554,432

Practical and Applied

100

Maria is collecting stamps and starts her collection with 100 stamps. Every month, she decides to sell 12 stamps to make some extra money.

How many stamps will Maria have after 6 months?

40 stamps

200

The Williams family just bought a home for $350,000. If the value of the home increases at a rate of 5% per year, use an exponential function to find the approximate value of the home after 8 years. 

$517,109.41

300

Sierra purchased a car for $9,000 in 1999. The value of the car depreciated by 8% each year thereafter. Use an exponential function to find the approximate value of the car in 2005.

$5,457

400

A tree nursery has a special variety of trees that doubles in height every year. The nursery starts with a tree that is 2 feet tall.

If this growth pattern continues, what will be the height of the tree after 5 years?

64 ft

500

Emma is planning a charity event and wants to accommodate no more than 300 guests. The venue has two types of seating arrangements: one that accommodates 5 people and another that accommodates 15 people. The venue can hold a maximum of 40 seating arrangements in total. Let x represent the number of 5-person seating arrangements and y represent the number of 15-person seating arrangements.

Write a system of inequalities that can be used to determine the possible combinations of seating arrangements that will ensure there are enough seats for all the guests.

5x+15y≤300 

x+y≤40

Functions and Equations

100

Evaluate the function for the given value

 f(x) = 5x - 2; f(-1)

-7

200

DAILY DOUBLE

Convert this equation into slope-intercept form, 

4x + 10y = 20

y = -(2/5)x + 2

300

Write the linear equation in slope-intercept form given the following: (-3, 7); slope = -9

y = −9x − 20

400

The graph of an arithmetic sequence would look like a(n) ____________ function.

Linear

500

The function y = 4.5 + 6.5x represents the price y for a train ride of x miles. What is a reasonable domain value for this function?

[0, infinity)

Random

100

This mountain range, stretching over 1,500 miles along the western coast of South America, is home to the highest peak in the Americas, Aconcagua.

Andes Mountains

200

This artist, known for hits like "Shake It Off" and "Blank Space," gained fame for her catchy songs and personal songwriting, transitioning from country to pop music.

Taylor Swift

300

This small, social primate, native to Madagascar, is known for its large, reflective eyes and ability to leap between trees.

Lemur

400

This event, which began in 1914 and involved many of the world's great powers, was marked by trench warfare and significant loss of life, ultimately leading to major geopolitical changes.

World War I

500

This Hall of Fame wide receiver holds records for the most career receptions (1,549), receiving yards (22,895), and touchdowns (197), primarily playing for the San Francisco 49ers and earning three Super Bowl rings.

Jerry Rice