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Drill by score band: 400–500 500–600 600–700 700–800

Score band 400-500 · Passport to Advanced Math

Exponential Functions and Exponent Rules drills for 400-500

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Targeted practice for students currently scoring in the 400-500 range, drilling exclusively on exponential functions and exponent rules.

What a 400-500 scorer needs from this topic

The 400 to 500 score band on SAT Math is the foundations band. Students scoring here are usually strong on arithmetic but losing easy points to careless setup, missed units, or an unfamiliar SAT phrasing of a familiar idea. Drilling the foundations questions here is the highest leverage thing you can do for your score, because every problem you convert from a guess to a confident solve moves you a measurable number of scaled points. Foundations questions in this band test one idea at a time, with friendly numbers and short stems. Treat them as warmups for the rest of the section: do them untimed first, write every step on paper, and check that your final value answers the actual question being asked, not the value of x.

For Exponential Functions and Exponent Rules specifically, students in the 400-500 band need to focus on the question patterns the College Board uses at this difficulty level. Apply exponent rules and interpret exponential growth. The questions below are pulled from the ScoreReady question bank and filtered to the 400-500 band based on difficulty calibration that matches publicly released College Board practice materials.

Drill these untimed first. Once you can produce a clean worked solution on paper for every question without notes, switch to timed mode and aim for under 75 seconds per question. That pace is roughly the average time per question on the actual SAT Math section, and it leaves time for the harder questions you will see at the end of each module.

Practice set

  1. 400-500 easy Applying Exponent Rules

    A bacteria population starts at 514 cells and multiplies by a factor of 2 every hour. How many cells are present after 2 hours?

    1. A 1028
    2. B 2056
    3. C 2057
    4. D 518
    Worked solution

    Answer: B — 2056

    Exponential growth: P(t) = P_0 × r^t = 514 × 2^2 = 514 × 4 = 2056 cells.

  2. 400-500 easy Exponential Growth and Decay Models

    A radioactive sample of mass 751 grams loses a factor of 3 every year. What is its mass after 3 years?

    1. A 84.44
    2. B 83.44
    3. C 742.00
    4. D 27.81
    Worked solution

    Answer: D — 27.81

    Exponential decay: m(t) = m_0 × (1/3)^t = 751 / 3^3 = 751 / 27 = 27.81 grams.

  3. 400-500 easy Fractional and Radical Exponents

    A bacteria population starts at 464 cells and multiplies by a factor of 5 every hour. How many cells are present after 1 hours?

    1. A 2321
    2. B 2320
    3. C 469
    4. D 464
    Worked solution

    Answer: B — 2320

    Exponential growth: P(t) = P_0 × r^t = 464 × 5^1 = 464 × 5 = 2320 cells.

  4. 400-500 easy Comparing Exponential and Linear Models

    A radioactive sample of mass 514 grams loses a factor of 10 every year. What is its mass after 4 years?

    1. A 474.00
    2. B 0.51
    3. C 0.05
    4. D 12.85
    Worked solution

    Answer: C — 0.05

    Exponential decay: m(t) = m_0 × (1/10)^t = 514 / 10^4 = 514 / 10000 = 0.05 grams.

  5. 400-500 easy Applying Exponent Rules

    A bacteria population starts at 265 cells and multiplies by a factor of 2 every hour. How many cells are present after 2 hours?

    1. A 269
    2. B 1060
    3. C 1061
    4. D 530
    Worked solution

    Answer: B — 1060

    Exponential growth: P(t) = P_0 × r^t = 265 × 2^2 = 265 × 4 = 1060 cells.

  6. 400-500 easy Exponential Growth and Decay Models

    A radioactive sample of mass 114 grams loses a factor of 3 every year. What is its mass after 2 years?

    1. A 108.00
    2. B 19.00
    3. C 12.67
    4. D 38.00
    Worked solution

    Answer: C — 12.67

    Exponential decay: m(t) = m_0 × (1/3)^t = 114 / 3^2 = 114 / 9 = 12.67 grams.

How to use these drills to climb a band

Climbing from one score band to the next requires a different study mix than climbing within a band. Within a band, you are mostly fixing careless errors and pattern-recognizing the question types you already understand. Climbing to the next band means adding new question types to your toolbox — patterns you currently recognize but cannot solve fluently. The 700–800 set in this drill is exactly that toolbox for students currently in the 600–700 range.

The single most reliable indicator that you are ready to move up a band is being able to explain a worked solution to someone else, in your own words, without referring to notes. Practice this with one classmate or one parent per week. The act of teaching exposes the gaps your timed solves did not.

Other 400-500 drills