Digital SAT Advanced Math Cheat Sheet

Flashcards summarizing key concepts and formulas for the Digital SAT Advanced Math topics.

How do you simplify expressions like x^4 + 2x^2 + 1?

Look for hidden patterns: x^4 + 2x^2 + 1 can be expressed as (x^2 + 1)^2.

What does f(a)=b represent in function notation?

It represents the point (a, b) on the graph of the function.

What is the transformation for a function f(x) + c?

It represents a shift of the graph of the function up by c units.

What is the difference between linear and exponential growth?

Linear growth follows the formula y = mx + b, exhibiting a constant rate of change, while exponential growth follows y = a * b^x, with a multiplying rate.

How do you find the inverse of a function?

Swap x and y, then solve for y.

What must you do when solving rational equations?

Isolate radicals and then square them, and always check for extraneous solutions.

What should you define clearly when approaching word problems?

Define variables clearly and translate context into math.

What is the formula for the vertex of a parabola?

x = -b / (2a).

How can Desmos be used strategically for the SAT?

Graph quickly, confirm answers, solve systems, and check roots.

What does f(x + c) represent?

f(x + c) represents a horizontal translation of the function f(x) to the left by c units if c is positive, and to the right by c units if c is negative.

What does f(x - c) represent?

f(x - c) represents a horizontal translation of the function f(x) to the right by c units if c is positive, and to the left by c units if c is negative.

What does -f(x) do?

It reflects the graph of f(x) across the x-axis.

What operation do the words: sum, total, more than, combined, increased by, gain, together?

They indicate addition. x+y

Less than and More than reverse order of subtraction and addition: i.e. 2 less than x —> x-2, 2 more than x —> x+2

The terms 'less than' and 'more than' indicate the operations of subtraction and addition, respectively. For example, '2 less than x' translates to 'x - 2' and '2 more than x' translates to 'x + 2'.

What is the formula for the axis of symmetry of a parabola?

The axis of symmetry is given by the formula x = -b/2a which is derived from the standard form of a quadratic equation y = ax² + bx + c.

How does the discriminant affect the nature of roots?

The discriminant, calculated as b^2 - 4ac, determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

What does the formula -b/a represent?

The formula -b/a represents the sum of the roots of a quadratic equation.

How do you find the product of the roots using the coefficients?

The product of the roots is given by c/a in a quadratic equation of the form ax^2 + bx + c = 0.

What does the exponential growth formula y = a(b^x) imply?

In the formula y = a (b^x), a represents the initial value, b is the growth factor, and x is the exponent or time period.

What do the variables m and b represent in the linear formula y = mx + b?

In the linear equation y = mx + b, m represents the slope of the line, and b represents the y-intercept.