PSAT Algebra — setting it up and reading it back

Algebra and Advanced Math are most of the Math section, and on the PSAT they are rarely hard as algebra. The difficulty sits either side of the working: turning a described situation into an equation, and reading an equation back as a statement about the thing it models. These ten questions are built around those two moves.

Four of them start from a situation and ask for the equation or the number: a printing job with a flat fee and a rate per page, a cinema selling two kinds of ticket, a warehouse with a floor-space limit, a phone bill with a monthly charge and a per-minute rate. In each, the arithmetic takes seconds and the translation is the whole question — which is why the wrong answers are the specific translation errors, named in the explanation: the fee added where it should be subtracted, the rate multiplied where it should divide, the coefficients attached to the wrong variables.

Two are equivalent expressions. One of them, a factoring question, has three distractors that each survive a different partial check — one gets the constant term right and the middle term wrong, one is the answer of a student who divided by two and forgot to put it back — and the explanation expands all three so you can see what each actually is. The advice that follows from it is worth taking literally: multiplying your answer back out takes ten seconds and settles the question.

The rest cover the pieces that recur. What the constant in a linear model means when the model has units attached. Which form of a quadratic shows which feature — factored form gives the roots, and that is the whole of that question. Solving a quadratic by factoring. And telling an exponential process from a linear one, where the linear model is offered as a distractor because it is the commonest thing to reach for when something is described as growing.

Nothing here needs a calculator, and a calculator is allowed on the whole Math section anyway. Nothing here has a figure either, which the real test does; for anything that depends on reading a graph, use College Board's own practice.

Zestly is an independent study tool. It is not affiliated with College Board, which owns the PSAT/NMSQT, and it is not a test centre.

• Turn a described situation with a fixed charge and a rate into a linear equation, and solve it
• Set up and solve a system of two linear equations from a context, and answer for the quantity actually asked
• Say what the slope or the intercept of a linear model means in the units of the thing being modelled
• Express a real constraint as an inequality, with the right coefficients on the right variables
• Factor a quadratic completely, and check an answer by expanding it back
• Choose which form of a quadratic to use for a given feature — roots, vertex or intercept
• Recognise an exponential process from its description and reject the linear model

A phone plan costs 15 dollars a month plus 0.04 dollars for each minute of calls. One month's bill comes to 27 dollars. How many minutes of calls were made that month?