2018. Category 2: Computations & Algebraic Relationships

Jerry has a new job and earns a salary of $45,000. Victoria has a new job and earns a salary of $54,000. Jerry will receive a salary increase of $2,500 per year, and Victoria will receive a salary increase of $1,500 per year.

Which equation can be used to find x, the number of years it will take Jerry to earn the same salary as Victoria?

• 45,000 + 2,500x = 54,000x + 1,500x

• 45,000x + 2,500 = 54,000x + 1,500

• 45,000 + 2,500x = 54,000 + 1,500x

• 45,000 + 2,500x = 54,000x + 1,500

A relation contains the points

(1, 2), (2, -1), (3, 0), and (5, -1).

Which statement accurately describes this relation?

• The relation does not represent y as a function of x, because each value of x is associated with a single value of y.

• The relation represents y as a function of x, because on value of y is associated with two values of x.

• The relation does not represent y as a function of x, because each value of y is associated with two values of x.

• The relation represents y as a function of x, because each value of x is associated with a single value of y.

Julie started with 20 pieces of gum and gave away x pieces. Conrad started with 35 pieces of gum and gave away twice as many pieces as Julie did.

How many pieces of gum did Julie give away if they had the same number of pieces of gum left?

• 18

• 5

• 15

• 8

Which function is best represented by this graph?

• $y=\frac{1}{4}x+8$
  

• $y=\frac{1}{4}x-2$

• $y=4x-2$

• $y=4x+8$

A hot-air balloon is released at ground level, and it rises into the air at a constant rate. After 5 seconds the height of the balloon is 20 feet. The balloon continues to rise at the same rate.

Which table shows the relationship between the time in seconds, x, and the height of the balloon in feet, y?

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Rudolfo has 15 toys in his toy box, and he adds 2 new toys every month. Based on this information, which representation best shows this relationship between the number of toys Rudolfo has in his toy box, y, and the number of months that have passe, x?

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A gym charges a membership fee plus an additional fee per yoga class. The table shows the linear relationship between the number of yoga classes taken and the total cost including the membership fee.

Which statement is true?

• The additional fee per yoga class is $3.75.

• The additional fee per yoga class is $8.25.

• The membership fee is $35.00.

• The membership fee is $42.50.

Joseph ran a 6-mile race in 48 minutes. Which graph has a slope that best represents Joseph's average rate of speed during the race?

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Which situation can be represented by this equation?

7x + 1 = 10x

• Brody ran at a constant rate of 7 miles per hour in a race. Candice ran at a constant rate of 10 miles per hour in a race that started 1 mile in front of the starting point. What is x, the number of hours that Brody and Candice would have to run in order for their distance to be the same?

• Brody played a game where he scored 8 points per hour. Candice played the game and scored 10 points per hour. What is x, the number of hours that Brody and Candice would each have to play the game in order for their scores to be the same?

• Brody went to two different amusement parks. The first park charged $7 per hour and gave a 1% discount for showing a student ID. The other park charged $10 per hour. What is x, the number of hours that Brody would have to stay at each park to have to pay the same amount?

• Brody rode his bicycle on two different days. The first day he rode 7 miles per hour and started 1 mile from his house. The second day he started from his house and rode 10 miles per hour. What is x, the number of hours that Brody would have to ride his bicycle to travel the same distance on both days?

The ticket sales for a concert started at 4:00 PM. The table shows the linear relationship between the number of tickets remaining and the number of hours since 4:00 PM.

Which function can be used to find y, the number of tickets remaining x hours since 4:00 PM?

• y = 3,000x + 12,000

• y = 3,000x + 15,000

• y = -3,000 + 12,000

• y = -3,000x + 15,000