Foundation of Math 3

Front

What is the formula for the area of a sector of a circle?

Back

Area = (θ/360) * π * r², where θ is the central angle in degrees and r is the radius.

Front

How do you find the area of a shaded sector with a radius of 6 inches and a central angle of 100°?

Back

Area = (100/360) * π * (6)² ≈ 31.4 sq. in.

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction.

Front

How do you solve the equation 2|x + 3| - 2 = 10?

Back

First, isolate the absolute value: 2|x + 3| = 12, then |x + 3| = 6. This gives x + 3 = 6 or x + 3 = -6, leading to x = 3 or x = -9.

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number.

Front

Rewrite log₂8 = 3 in exponential form.

Back

2³ = 8.

Front

What is the relationship between exponential and logarithmic forms?

Back

If b^y = x, then log_b(x) = y.

Front

How do you solve the equation |2x + 9| = 15?

Back

Split into two cases: 2x + 9 = 15 and 2x + 9 = -15. This gives x = 3 and x = -12.

Front

What is the definition of a central angle in a circle?

Back

A central angle is an angle whose vertex is at the center of the circle and whose sides are radii.

Front

How do you convert an exponential equation to logarithmic form?

Back

If a^b = c, then log_a(c) = b.