2018 Grade 6 Math Regents

1. An equation is shown below.
$12 - 9 + c =12$

What value of $c$ makes the equation true?

A. $0$
B. $3$
C. $9$
D. $12$

2. Kate has a coin collection. She keeps $7$ of the coins in a box, which is only $5\%$ of her entire collection. What is the total number of coins in Kate’s coin collection?

A. $12$
B. $14$
C. $120$
D. $140$

3. What is the greatest common factor of $36$ and $90$ ?

A. $6$
B. $18$
C. $36$
D. $180$

4. The relationship between Robert’s age, $r$ , and Julia’s age, $j$ , can be represented by the equation shown below.
$r = j + 3$

Which table of values represents the relationship between Robert’s age and Julia’s age?

A.
B.
C.
D.

15. All the students in the sixth grade either purchased their lunch or brought their lunch from home on Monday.
$\bullet 24\%$ of the students purchased their lunch.
$\bullet 190\%$ students brought their lunch from home.

How many students are in the sixth grade?

A. $76$
B. $166$
C. $214$
D. $250$

16. Joe walks on a treadmill at a constant rate. The equation below describes the relationship between $t$ , the time he walks in hours, and $d$ , the distance he walks in miles.
$d = 4t$

Which graph represents the relationship between the amount of time Joe walks and the distance he walks?

A.
B.
C.
D.

19. There are $230$ calories in $4$ ounces of a type of ice cream. How many calories are in $6$ ounces of that ice cream?

A. $232$
B. $236$
C. $345$
D. $460$

22. A shape is made of $12$ right triangles of equal size. Each right triangle has a base of $4$ cm and a height of $5$ cm. What is the total area, in square centimeters, of the shape?

A. $10$
B. $60$
C. $120$
D. $240$

25. Pat bounces a basketball $25$ times in $30$ seconds. At that rate, approximately how many times will Pat bounce the ball in $150$ seconds?

A. $120$
B. $125$
C. $144$
D. $145$

26. Which expression is equivalent to $5(4x + 3) - 2x$ ?

A. $18x + 15$
B. $18x + 3$
C. $7x + 8$
D. $2x + 8$

27. Mark graphed points on the coordinate plane below to represent the locations of his school and a bank.

Mark wants to add the location of the library on the coordinate plane. The distance from the library to the school is the same as the distance from the bank to the school. Which ordered pair could be the coordinates of the library?

A. $(2,4)$
B. $(2,8)$
C. $(4,4)$
D. $(6,8)$

28. A student draws the net below to show the dimensions of a container that is shaped like a right rectangular prism.

What is the surface area, in square inches, of the container?

A. $19$
B. $30$
C. $38$
D. $62$

29. Which two expressions are equivalent?

A. $x + x + x$ and $x^{3}$
B. $14x + 10 - 2x$ and $16x + 10$
C. $12x + 16x$ and $4(3x + 4x)$
D. $12x^{2} + 5x + 10$ and $17x^{2} + 10$

30. A machine fills boxes at a constant rate. At the end of $35$ minutes, it has filled $5$ boxes. Which table represents the relationship between the number of minutes the machine fills boxes and the number of boxes it has filled?

A.
B.
C.
D.

31. Which expression represents the perimeter of the figure below?

A. $5x + 2y$
B. $x + y + z$
C. $5x + 2y + z$
D. $(5 + 2 + 1)(x + y + z)$

32. The elevations, in feet, of three cities are marked on the number line shown below.

The point $0$ on the number line represents sea level. Which statement must be true?

A. City P and City Q are above sea level.
B. City Q and City R are below sea level.
C. City P is above sea level and City Q is below sea level.
D. City P is above sea level and City R is below sea level.

33. A basketball player attempts $15$ baskets in a game. He makes $9$ of the attempted baskets. Which ratio describes the number of baskets the player made to the number of baskets the player attempted?

A. $\dfrac{3}{5}$
B. $\dfrac{5}{3}$
C. $\dfrac{2}{5}$
D. $\dfrac{5}{2}$

34. Which number line shows a graph of the inequality $x \textless -25$ ?

A.
B.
C.
D.

35. The coordinates of the points below represent the vertices of a rectangle.

$P:(2,2)$ ,
$Q:(6,2)$ ,
$R:(6,5)$ ,
$S:(2,5)$ ,

What is the perimeter, in units, of a rectangle $PQRS$ ?

A. $8$
B. $12$
C. $14$
D. $16$

36. Carol has $1\dfrac{5}{8}$ cups of yogurt to make smoothies. Each smoothies uses $\dfrac{1}{3}$ cup of yogurt. What is the maximum number of smoothies that Carol can make with the yogurt?