MCAS Grade 10 Math flashcards
MCAS Grade 10 Math · Build recall with a focused review session.
32 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Rational number
- A number that can be written as a fraction a/b, where a and b are integers and b is not zero; its decimal form terminates or repeats.
- Irrational number
- A real number that cannot be written as a fraction of two integers; its decimal form neither terminates nor repeats, such as pi or the square root of two.
- Scientific notation
- A way to write numbers as a times ten to a power, where a is at least one and less than ten; used for very large or small values.
- Exponent product rule
- When multiplying powers with the same base, add the exponents: a^m times a^n equals a^(m+n). The base stays unchanged.
- Negative exponent rule
- A base raised to a negative exponent equals the reciprocal of that base raised to the positive exponent: a^(-n) equals 1 divided by a^n, for a not zero.
- Percent change formula
- Percent change equals the new value minus the old value, divided by the old value, then multiplied by one hundred; positive means increase.
- Slope formula
- For two points (x1,y1) and (x2,y2), slope m equals (y2-y1)/(x2-x1). It measures vertical change per horizontal change.
- Slope-intercept form
- The equation y = mx + b, where m is the slope and b is the y-intercept. It gives the line's steepness and where it crosses the y-axis.
- Point-slope form
- The equation y - y1 = m(x - x1), where m is slope and (x1,y1) is a point on the line; useful when a point and slope are known.
- Quadratic formula
- For ax^2 + bx + c = 0 with a not zero, x equals negative b plus or minus the square root of b squared minus 4ac, all divided by 2a.
- Discriminant
- The expression b^2 - 4ac in the quadratic formula. If positive there are two real roots; if zero one; if negative none real.
- Elimination method
- Solve a system by adding or subtracting equations to remove one variable, after multiplying equations if needed; then solve for the remaining variable.
- Absolute value equation
- An equation containing an absolute value. Rewrite it as two separate equations, one for the positive case and one for the negative case, then solve each.
- Function definition
- A relation in which each input value has exactly one output value. The vertical line test checks this on a graph.
- Domain and range
- Domain is the set of all possible input values of a function; range is the set of all possible output values.
- Average rate of change
- For a function f on the interval from a to b, it equals (f(b) - f(a)) divided by (b - a); the slope of the secant line.
- Vertical shift
- Adding a constant k outside a function, as in f(x) + k, moves the graph up by k units when k is positive and down when k is negative.
- Horizontal shift
- Replacing x with x - h in a function shifts the graph right by h units when h is positive, and left when h is negative.
- Inverse function
- A function that reverses another function. Find it by swapping x and y and solving for y; its graph reflects across the line y = x.
- Exponential function
- A function of the form f(x) = a times b^x, where a is not zero and b is positive and not one; b is the growth or decay factor.
- Pythagorean theorem
- In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs: a^2 + b^2 = c^2, where c is the hypotenuse.
- Distance formula
- The distance between points (x1,y1) and (x2,y2) equals the square root of (x2-x1)^2 plus (y2-y1)^2; derived from the Pythagorean theorem.
- Midpoint formula
- The midpoint of a segment with endpoints (x1,y1) and (x2,y2) is ((x1+x2)/2, (y1+y2)/2); it averages the x- and y-coordinates.
- Similar figures
- Figures with the same shape but not necessarily the same size. Corresponding angles are equal, corresponding side lengths are proportional, and areas scale by the square of the scale factor.
- Inscribed angle
- An angle whose vertex lies on a circle and whose sides are chords. Its measure is half the measure of its intercepted arc.
- Sector area
- The area of a pie-shaped part of a circle: (central angle/360) times pi times radius squared. The angle must be in degrees.
- Volume of a sphere
- The volume enclosed by a sphere equals four-thirds times pi times the cube of its radius: V = (4/3)pi r^3.
- Mean
- The arithmetic average of a data set: add all values and divide by the number of values. Outliers can pull the mean toward them.
- Interquartile range
- The difference between the third quartile and first quartile, Q3 minus Q1. It measures the spread of the middle half of a data set and resists outliers.
- Complement rule
- For an event A, the probability that A does not occur equals one minus the probability that A occurs: P(not A) = 1 - P(A).
- Conditional probability
- The probability of event A given that event B has occurred: P(A|B) equals P(A and B) divided by P(B), when P(B) is greater than zero.
- Independent events
- Two events are independent when the occurrence of one does not change the probability of the other; then P(A and B) equals P(A) times P(B).