Mathematics Exam Review

Flashcards for reviewing math exam questions on powers, roots, logarithms, algebraic operations, notable products, factorization, equations, systems, sets, inequalities, functions, matrices, and statistics.

Simplifying Powers (2^3 * 2^5)

Multiplying powers with the same base, add the exponents (2^(3+5) = 2^8)

Logarithm log10(1000)

The exponent to which the base (10) must be raised to produce the number (1000).

Square Root

A value that, when multiplied by itself, gives the original number.

Solving Radicals √8 + √16

Simplifying radicals

Simplifying (3x^2 + 2x - 5) + (x^2 - 4x + 1)

Combine like terms (3x^2 + x^2) + (2x - 4x) + (-5 + 1)

Multiplying (2x - 3)(x + 4)

Apply the distributive property (2x * x) + (2x * 4) + (-3 * x) + (-3 * 4)

Dividing (6x^3 - 9x^2) / 3x

Divide each term in the numerator by 3x (6x^3 / 3x) - (9x^2 / 3x)

Simplifying (x^2 - 9) / (x - 3)

Factor the numerator (x^2 - 9) as (x - 3)(x + 3), then cancel the (x-3) terms.

Expanding (x + 5)^2

Use the formula (x + a)^2 = x^2 + 2ax + a^2.

Factorizing x^2 - 9

Recognize the difference of squares pattern: a^2 - b^2 = (a - b)(a + b)

Factorizing 2x^2 - 8

Factor out the common factor of 2. Recognize the difference of squares.

Factorizing x^2 + 5x + 6

Find two numbers that multiply to 6 and add to 5.

Solving 3x - 7 = 14

Isolate x by adding 7 to both sides and then dividing by 3.

Solutions of x^2 - 5x + 6 = 0

Find two numbers that multiply to 6 and add to -5.

Solving the system 2x + y = 5, x - y = 1

Add the equations to eliminate y, then solve for x. Substitute x back into one of the equations to solve for y.

Solving x^2 + 3 = 7

Isolate the x^2 term and then take the square root of both sides.

A ∩ B where A = {1, 2, 3} and B = {3, 4, 5}

The intersection of sets A and B contains elements that are in both A and B.

Representing x ≥ -2

Represent all numbers greater than or equal to -2 on a number line.

Representing C = {x ∈ R | -3 < x ≤ 2}

Representing all real numbers x such that -3 < x ≤ 2.

Complement of A = {1, 2} in U = {1, 2, 3, 4}

The complement of A contains elements in U that are not in A.

Solving 4x - 3 > 9

Isolate x by adding 3 to both sides and then dividing by 4.

Solution of x^2 - 4 ≤ 0

Find the interval where x^2 - 4 is less than or equal to 0. Factor as (x-2)(x+2).

Solving (x+1) / (x-2) > 0

Analyze the signs of (x+1) and (x-2) to determine when the fraction is positive.

Solution of |x - 3| < 2

Solve for x when the distance between x and 3 is less than 2. |x-3| < 2 means -2 < x-3 < 2.

Slope of y = -2x + 5

The coefficient of x in the equation y = mx + b.

Vertex of y = x^2 - 6x + 8

Complete the square to find the vertex form of the quadratic.

If f(x) = 3x - 4, what is f(2)?

Substitute x = 2 into the function f(x) = 3x - 4.

Domain of f(x) = √x - 4

The expression inside the square root must be greater than or equal to zero.

Determinant of [[1, 2], [3, 4]]

Calculate (14) - (23).

B^2 where B = [[0, 1], [-1, 0]]

Multiply the matrix B by itself.

Sum of matrices [[2, -1], [0, 3]] + [[-1, 4], [5, 2]]

Add corresponding elements of the two matrices.

Product [[1, 2], [0, 1]] * [[3, 1], [2, 4]]

Calculate the dot product of the rows of the first matrix and the columns of the second matrix.

Mean of {2, 4, 6, 8, 10}

Sum of the numbers divided by the count of the numbers.

Median of {12, 3, 5, 8, 20} ordered

The middle value when the numbers are arranged in order.

Mode

The value that appears most frequently in a data set.