Algebra STAAR Review #2 A2DEF

Front

What does it mean when we say 'y varies directly as x'?

Back

It means that as x increases, y increases proportionally. This can be expressed mathematically as y = kx, where k is a constant.

Front

If y = 6 when x = 27, what is the constant of variation (k)?

Back

k = y/x = 6/27 = 2/9.

Tags

CCSS.HSF-LE.A.1B

Front

How do you find the value of x when y = 2, given that y varies directly as x and k = 2/9?

Back

Use the formula y = kx. Substitute y = 2 and k = 2/9: 2 = (2/9)x. Solving for x gives x = 9.

Front

If 4 apples cost $0.45, what is the cost of 1 apple?

Back

Cost of 1 apple = $0.45 / 4 = $0.1125.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

Front

How do you find the cost of 12 apples if 4 apples cost $0.45?

Back

First, find the cost of 1 apple ($0.1125), then multiply by 12: $0.1125 * 12 = $1.35.

Tags

CCSS.6.RP.A.3B

Front

What is the formula for direct variation?

Back

The formula for direct variation is y = kx, where k is the constant of variation.

Front

If x = 24 when y = 8, what is the value of y when x = 33?

Back

First, find k: k = y/x = 8/24 = 1/3. Then use y = kx: y = (1/3) * 33 = 11.

Front

What is the relationship between mass and size in direct variation problems?

Back

In direct variation, if one quantity increases, the other quantity increases proportionally. For example, if the mass of a box increases, its size also increases.

Front

If a 20 cubic centimeter box has a mass of 40 kg, what is the size of the box if the mass is 100 kg?

Back

First, find k: k = size/mass = 20/40 = 0.5. Then use size = k * mass: size = 0.5 * 100 = 50 cubic centimeters.

Front

How do you estimate the number of hours a store would take to earn $23,000 if it earns $11,500 in 4 hours?

Back

Set up a proportion: 11,500/4 = 23,000/x. Cross-multiply and solve for x: x = 8 hours.

Tags

CCSS.7.RP.A.2C