KellyMath Blog

You can solve many SSAT quadratics problems on the SSAT Upper Level with a substitution shortcut called Choose 1. This replaces factoring, FOILing, and the quadratic formula for a specific question type. It works on “polynomial equivalency” questions. These give you one form of an expression and ask which answer choice shows the same expression in a different form. Plug 1 into the original expression to get a “magic number.” Then plug 1 into each answer choice until one matches.

The same shortcut also handles related equivalency questions with a leading coefficient, more than one variable, or exponents higher than x². It doesn’t solve every kind of quadratic question, and knowing exactly where it applies is what makes it reliable.

The short answer: The ‘Choose 1’ strategy solves “polynomial equivalency” questions on the SSAT Upper Level. These give you one form of an expression and ask which answer choice is the same expression in a different form. Plug a number (usually 1) into the original expression to get a magic number. Then test each answer choice until one matches. This works because the SSAT is multiple choice.

It works on leading coefficients, multi-variable expressions, and higher-degree polynomials too, since none of those change the underlying question type. If two answer choices tie at your first number, or the value you’re solving for cancels out entirely, try a second number instead. This method doesn’t solve quadratic equations for their roots, since that’s a different question type entirely.

Which Quadratics Problems to Use ‘Choose 1’

The SSAT only includes one or two quadratic questions per test. But they span a wide range of formats: equivalent expressions, factored forms, graphs, and word problems. Traditional factoring can take students weeks to master, especially once leading coefficients and higher exponents get involved. That’s a lot of study time for a question type that shows up so rarely.

‘Choose 1’ eliminates the need to learn many of those skills. It works on most polynomial equivalency questions. These hand you a polynomial in one form (like \((2x+3)(x-5)\) or \(2x^2-7x-15\) and ask which answer choice shows it in a different form: factored versus expanded, or one arrangement versus another.

If a question instead asks you to solve a quadratic equation for its roots, or to identify a feature of its graph, Choose 1 doesn’t apply. Those are different question types with their own methods.

Chapter 17 of Kelly Campbell’s SSAT Upper Level prep book, Quadratics: The Easy Way, goes deeper into how to tackle all the quadratic questions you might encounter – while only using skills you already have.

The Choose 1 Shortcut, Step by Step

For any “which is equivalent,” “what is the factored form,” or “what is the expanded form” question, follow these steps.

1. Plug 1 into the original expression and simplify. That result is your magic number.
2. Then plug 1 into each answer choice and simplify those too. Whichever answer choice matches the magic number is correct.
3. If more than one answer choice matches, cross out any other answer choices. Repeat the process by plugging in 2 to the original expression and only the answer choices that remain.

Whichever one still matches is the answer.

Why Choose 1 Actually Works on the SSAT

This shortcut works for one reason only: the SSAT is multiple choice. On top of that, the test-makers seem to write 4 wrong answers that would fail to match the magic number you get from choosing 1, making it an easy shortcut that is not normally taught.

It’s good to remember that plugging one number into an expression and getting a matching result doesn’t actually prove two expressions are equivalent in the strict algebraic sense. A single matching value could theoretically be a coincidence. But a multiple choice question gives you limited options to test. In practice, testing one point is usually enough to eliminate four wrong answers.

On the rare occasion a distractor happens to match by coincidence too, testing a second number clears it up.

Applying Choose 1 Across Different Situations

The reason this shortcut is so useful is that it works beyond quadratics problems on the SSAT Upper Level, as long as the question is still matching one polynomial form to another. The three examples below show it working on situations that usually make students reach for a pencil to start factoring by hand. Only the first example is a true quadratic. The other two step into multi-variable and higher-degree polynomials, which the SSAT tests using the exact same equivalency setup, even though they’re technically a different category of expression.

When There’s a Leading Coefficient

A leading coefficient in front of x² doesn’t change the method at all.

Which of the following is equivalent to (2x − 3)(4x + 5)?

Plug in 1: \( (2 – 3)(4 + 5) = (-1)(9) = -9 \).

The magic number is -9.

Testing choice (D): \( 8 – 2 – 15 = -9 \). It matches, so the answer is (D).

When There Are Multiple Variables

Multi-variable expressions work the same way, with one adjustment. Avoid plugging in 1 for a variable with more than one exponent in the problem, since 1 raised to any power is still 1. That can make two different answer choices look identical when they aren’t. Use a different number, like 2, for at least one variable instead.

What is the factored form of 9a² − 16b⁴?

Plug in a = 2 and b = 1: \( 9(4) – 16(1) = 36 – 16 = 20 \).

The magic number is 20.

Testing choice (C): \( (6 + 4)(6 – 4) = (10)(2) = 20 \). It matches, and none of the other choices land on 20, so the answer is (C).

When the Exponents Go Higher Than x²

The same shortcut applies to cubic expressions and beyond. It never actually depends on the degree of the polynomial.

Which of the following is equivalent to (7x + 8)(x² + 5x − 4)?

Plug in 1: \( (7 + 8)(1 + 5 – 4) = (15)(2) = 30 \).

The magic number is 30.

Testing choice (B): \( 7 + 43 + 12 – 32 = 30 \). It matches, so the answer is (B).

Worked Sample Problem

Choose 1 also solves a related version of the same question type. Instead of matching a given expression to an equivalent one, you’re solving for the unknown value that makes two full polynomials identical for every x, then checking that value against the answer choices. It’s still an equivalency question at heart. This version has one extra wrinkle worth knowing before test day.

If the equation x² + b(x − 1) − 3 = x² + 4x − 7 is true for all values of x, what is the value of b?

Step 1: Try plugging in 1 for x first, the usual first move. \( 1 + b(1-1) – 3 = 1 + 4 – 7 \) \( 1 + b(0) – 3 = -2 \) \( -2 = -2 \)

This is true no matter what b is. The (x − 1) next to b became 0 at x = 1, which erased b from the equation entirely.

Step 2: Since 1 didn’t work, try a different number. Plug in 2 for x. \( 4 + b(2-1) – 3 = 4 + 8 – 7 \) \( 4 + b – 3 = 5 \) \( b + 1 = 5 \)

Step 3: Solve for b. \( b = 4 \)

The answer is (C) 4.

This example is worth slowing down on for one reason: the first number you try won’t always work. Whenever b is multiplied by an expression like (x − 1), watch for the number that makes that expression 0. Plugging that number in will erase b from the equation entirely. That’s not a mistake. It’s a signal to pick a different number and try again.

Common Mistakes to Avoid

The most common mistake is stopping after one number produces a tie between two answer choices. Test a second number to break the tie instead.

A close second is plugging in 1 when the problem specifies a range for the variable such as \(x>2\).

When solving for an unknown coefficient, watch for the number you chose canceling that coefficient out entirely. It’s a normal part of the process, not a dead end. It just means it’s time to try a different number.

It’s also important to note that this strategy may take more than a minute to solve. It is often better to circle this type of problem and come back to it at the end if you have time, once you have finished solving all the easier questions. You can read more about my top 5 SSAT Shortcuts and best practices for time management on the SSAT in my other posts.

Where This Fits Into SSAT Prep

Quadratics problems on the SSAT Upper Level show up rarely, but Choose 1 is worth learning well before test day. It replaces algebra that can otherwise take weeks to master. Hacking the SSAT Upper Level Math: Shortcuts & Strategies for Every Question Type covers this shortcut in full inside Chapter 17. It also covers quadratic graphs and real-world quadratic word problems.

For full SSAT Upper Level Math prep, the Complete Course walks through all 18 chapters – 545 pages covering nothing but SSAT Upper Level Math, written the way a tutor actually explains it, built from real experience working with 50+ SSAT students. If you’d like personalized help along with it, explore the book + tutoring packages. 

If you’re not sure where to start, Kelly offers a free SSAT Upper Level Math diagnostic on her homepage. Take the diagnostic and you’ll know within an hour exactly which topics need the most attention.

Frequently Asked Questions: Quadratics Problems on the SSAT Upper Level

Does Choose 1 work on every SSAT quadratics problem?

No. It only applies to polynomial equivalency questions, where the test gives one form of an expression. You’re asked which answer choice matches it in another form. It doesn’t solve a quadratic equation for its roots or answer questions about a quadratic’s graph. Those question types use different methods.

Why does plugging in just one number prove the right answer?

Strictly speaking, it doesn’t prove algebraic equivalence on its own. It works because the SSAT is multiple choice, and the wrong answer choices are built to fail at whatever number you test. Testing one number is usually enough to eliminate four incorrect choices. That’s what actually makes this a shortcut rather than a full proof.

Does the Choose 1 shortcut work with a leading coefficient or multiple variables?

Yes, as long as the question is still matching one polynomial form to another. The method doesn’t depend on the degree of the polynomial or how many variables it has. For multi-variable problems, it helps to avoid plugging in 1 for every variable, since that can cause two different answer choices to look identical by coincidence.

What do you do if plugging in 1 doesn’t give a clear answer?

Try a different number, usually 2, and repeat the process. This happens when two answer choices tie at x = 1, or when the number you chose makes the unknown value you’re solving for cancel out.