ACT/SAT Math Practice #3

Front

What is the probability of selecting a non-green racquetball from Herbie's practice bag?

Back

To find the probability of selecting a non-green racquetball, calculate the total number of non-green racquetballs (4 blue + 1 red = 5) and divide by the total number of racquetballs (4 blue + 1 red + 6 green = 11). Thus, the probability is \( \frac{5}{11} \approx 0.45 \).

Front

What is the result of squaring the complex number (3 - i)?

Back

To square the complex number (3 - i), use the formula: \( (a - b)^2 = a^2 - 2ab + b^2 \). Here, \( a = 3 \) and \( b = i \). Thus, \( (3 - i)^2 = 3^2 - 2(3)(i) + (i)^2 = 9 - 6i - 1 = 8 - 6i \).

Front

How do you convert the equation of a line from standard form to slope-intercept form?

Back

To convert from standard form \( Ax + By = C \) to slope-intercept form \( y = mx + b \), solve for y. For example, from \( 5x - y = -2 \), rearranging gives \( y = 5x + 2 \).

Front

How do you calculate the total number of lunch combinations at the cafeteria?

Back

To find the total combinations, multiply the number of choices for each category: \( 3 \) salads \( \times 5 \) main dishes \( \times 2 \) desserts = \( 30 \) different lunches.

Front

What is the best strategy to achieve a high SAT score?

Back

The best strategy is to try your best and not give up. This includes practicing regularly, managing your time effectively during the test, and staying calm.

Front

What is the formula for calculating probability?

Back

The formula for probability is: \( P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \).

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form \( a + bi \), where \( a \) and \( b \) are real numbers, and \( i \) is the imaginary unit with the property that \( i^2 = -1 \).

Front

What does slope-intercept form represent in a linear equation?

Back

Slope-intercept form \( y = mx + b \) represents a linear equation where \( m \) is the slope of the line and \( b \) is the y-intercept, the point where the line crosses the y-axis.

Front

How do you find the slope of a line given its equation in standard form?

Back

To find the slope from the standard form \( Ax + By = C \), rearrange to slope-intercept form and identify the coefficient of x. The slope is \( -\frac{A}{B} \).

Front

What is the significance of the imaginary unit 'i' in complex numbers?

Back

The imaginary unit 'i' is significant because it allows for the extension of the real number system to include solutions to equations like \( x^2 + 1 = 0 \), which have no real solutions.