TSI Math Review

Front

What is the formula for the area of a rectangle?

Back

Area = length × width.

Front

What is the formula for the perimeter of a rectangle?

Back

Perimeter = 2(length + width).

Front

If the area of a rectangle is 45 and its perimeter is 28, how do you find the length of the longer side?

Back

Set up the equations: length × width = 45 and 2(length + width) = 28. Solve for length and width.

Front

What does it mean for y to vary inversely as x?

Back

It means that as x increases, y decreases, and vice versa. The relationship can be expressed as y = k/x, where k is a constant.

Front

If y = 4.5 when x = 10, how do you find the constant k in the inverse variation?

Back

Use the formula: k = y × x. So, k = 4.5 × 10 = 45.

Front

How do you find x when y = 5 in the inverse variation y = k/x?

Back

Rearrange the equation to x = k/y. Substitute k = 45 and y = 5 to find x.

Front

What does it mean for y to vary directly as x?

Back

It means that as x increases, y also increases. The relationship can be expressed as y = kx, where k is a constant.

Front

If x = 3 when y = 24, how do you find the constant k in the direct variation?

Back

Use the formula: k = y/x. So, k = 24/3 = 8.

Front

How do you find y when x = 10 in the direct variation y = kx?

Back

Substitute k = 8 and x = 10 into the equation: y = 8 × 10 = 80.

Front

What is the difference between direct and inverse variation?

Back

In direct variation, y increases with x; in inverse variation, y decreases as x increases.