About this test · ~4 min read
What Practice Test 4 covers
Practice Test 4 is a word-problem gauntlet. It concentrates on systems of equations, nonlinear functions, three-dimensional volume, percentage change, and probability — the topics where the hard part is translating a paragraph into math. Expect fewer bare equations and more scenarios you must model yourself.
Difficulty level
Balanced-to-hard, with the challenge coming from setup rather than computation. The arithmetic is manageable; the translation is where points are won or lost.
Skills tested
- Modeling systems of equations from word problems
- Evaluating nonlinear and exponential functions
- Volume of prisms, cylinders, cones, and spheres
- Percent increase, decrease, and percent-of problems
- Multi-step probability
Who should take this test
Students whose pure algebra is reliable but who lose points turning words into equations. If your errors cluster in word problems, this is the test to grind.
Study tips
- Define your variables explicitly in writing before you compute — "let x = number of adult tickets" prevents half of all setup errors.
- For volume questions, identify the solid first and pull its formula from the reference sheet before plugging in numbers.
- Translate "percent of" as multiplication and "percent change" as (new − old)/old; keeping the two straight avoids the classic percentage trap.
Common mistakes
- Answering the wrong quantity — solving for x when the question asked for 2x or for y.
- Using diameter instead of radius in a cylinder or sphere volume formula.
- Applying a percent increase and decrease as if they cancel, when a 20% rise then 20% fall does not return to the start.
Worked example
For the equation x² − 6x + 9 = 0, how many distinct real solutions are there?
Count solutions with the discriminant, b² − 4ac, from ax² + bx + c = 0.
Here a = 1, b = −6, c = 9, so the discriminant is (−6)² − 4(1)(9) = 36 − 36 = 0.
A discriminant of exactly 0 means one repeated real solution.
Confirm by factoring: x² − 6x + 9 = (x − 3)², so x = 3 is a double root.
Answer: One distinct real solution (x = 3).
Frequently asked questions
Why does Practice Test 4 feel wordier than the others?
It is built around modeling — turning real-world scenarios into systems, functions, and percentages. The math itself is standard; the skill under test is translation, so expect denser reading.
How do I avoid answering the wrong quantity?
Underline exactly what the question asks for before you start, and after solving, reread that phrase. Many Test 4 traps give you a correct intermediate value as a wrong answer choice.
Which volume formulas should I have ready?
Prisms and cylinders use base area times height; cones and pyramids are one-third of that; spheres use (4/3)πr³. All appear on the reference sheet, but you must know to use the radius, not the diameter.
Do a 20% increase and a 20% decrease cancel out?
No — this is a favorite SAT trap. Increasing 100 by 20% gives 120, and decreasing 120 by 20% gives 96. Percent changes compound off different bases, so they do not undo each other.