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United StatesMaths

Advanced Math

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you rewrite algebraic expressions into equivalent forms by factoring, expanding, and using exponent rules?

Equivalent expressions: factor and expand polynomials, simplify rational expressions, apply exponent and radical rules, and rewrite an expression to reveal a needed feature.
A focused answer to the Digital SAT Advanced Math skill of equivalent expressions: factoring and expanding, the laws of exponents, simplifying rational expressions, and rewriting an expression to reveal the feature a question asks for.
11 min answer →

How do you solve nonlinear equations in one variable, including quadratics, radicals, and exponential equations?

Nonlinear equations in one variable: solve quadratics by factoring, the quadratic formula and completing the square, and solve radical, rational and exponential equations, checking for extraneous solutions.
A focused answer to the Digital SAT Advanced Math skill of solving nonlinear equations in one variable: quadratics by factoring, formula and completing the square, plus radical and exponential equations and extraneous-solution checks.
11 min answer →

How do you recognise and interpret nonlinear functions such as exponential, polynomial, rational and radical functions?

Nonlinear functions: distinguish linear from exponential growth, interpret polynomial, rational, radical and exponential functions and their graphs, and read key features and end behaviour.
A focused answer to the Digital SAT Advanced Math skill of nonlinear functions: telling linear from exponential growth, interpreting exponential, polynomial, rational and radical functions and graphs, and reading their key features in context.
11 min answer →

How do the three forms of a quadratic reveal its vertex, zeros and intercept, and how do you read a parabola?

Quadratic functions and their graphs: use standard, factored and vertex form to read the y-intercept, the x-intercepts and the vertex, and connect the discriminant to the number of x-intercepts.
A focused answer to the Digital SAT Advanced Math skill of quadratic functions and graphs: the standard, factored and vertex forms, reading the vertex, axis of symmetry, zeros and y-intercept, and the discriminant's link to x-intercepts.
11 min answer →

How do you solve a system that pairs a linear equation with a nonlinear one, such as a line and a parabola?

Systems of equations in two variables with a nonlinear equation: solve a line-and-parabola system by substitution, interpret the number of intersection points, and use the discriminant to count solutions.
A focused answer to the Digital SAT Advanced Math skill of solving systems with a nonlinear equation: substituting a line into a parabola, finding intersection points, and using the discriminant to count how many solutions a system has.
11 min answer →