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Score band 600-700 · Additional Topics in Math

Complex Numbers drills for 600-700

400500600700800

Targeted practice for students currently scoring in the 600-700 range, drilling exclusively on complex numbers.

What a 600-700 scorer needs from this topic

The 600 to 700 band is the largest plateau on the SAT Math section. Students stuck here are usually accurate on every easy question and most medium questions, but they lose four to six points to harder algebra and to one or two arithmetic slips per section. Breaking out of this band requires both a deeper toolbox and a faster execution speed on the questions you already know how to do. Strengthening-band drills target the harder question patterns: quadratic systems, exponential and rational manipulation, function composition, conditional probability, and the geometry questions that require an extra construction line you must add to the figure yourself.

For Complex Numbers specifically, students in the 600-700 band need to focus on the question patterns the College Board uses at this difficulty level. Add, multiply, and simplify complex number expressions. The questions below are pulled from the ScoreReady question bank and filtered to the 600-700 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. 600-700 medium Powers of i

    What is the product (-6 - 2i)(-1 + 6i) expressed in the form a + bi?

    1. A 6 + -12i
    2. B 19 - 34i
    3. C 18 + -33i
    4. D 18 - 34i
    Worked solution

    Answer: D — 18 - 34i

    Use FOIL and replace i^2 with -1. (-6 + -2i)(-1 + 6i) = 6 + -36i + 2i + -12i^2 = 6 + -34i + -12(-1) = 18 + -34i.

  2. 600-700 medium Adding and Subtracting Complex Numbers

    What is the product (1 - 4i)(-4 + 1i) expressed in the form a + bi?

    1. A 1 + 17i
    2. B 0 + 17i
    3. C -4 + -4i
    4. D 0 + 18i
    Worked solution

    Answer: B — 0 + 17i

    Use FOIL and replace i^2 with -1. (1 + -4i)(-4 + 1i) = -4 + 1i + 16i + -4i^2 = -4 + 17i + -4(-1) = 0 + 17i.

  3. 600-700 medium Multiplying Complex Numbers

    What is the product (1 - 6i)(-1 + 6i) expressed in the form a + bi?

    1. A 35 + 13i
    2. B 36 + 12i
    3. C 35 + 12i
    4. D -1 + -36i
    Worked solution

    Answer: C — 35 + 12i

    Use FOIL and replace i^2 with -1. (1 + -6i)(-1 + 6i) = -1 + 6i + 6i + -36i^2 = -1 + 12i + -36(-1) = 35 + 12i.

  4. 600-700 medium Complex Conjugates and Division

    What is the product (4 + 6i)(5 + 4i) expressed in the form a + bi?

    1. A -4 + 46i
    2. B -4 + 47i
    3. C -3 + 46i
    4. D 20 + 24i
    Worked solution

    Answer: A — -4 + 46i

    Use FOIL and replace i^2 with -1. (4 + 6i)(5 + 4i) = 20 + 16i + 30i + 24i^2 = 20 + 46i + 24(-1) = -4 + 46i.

  5. 600-700 medium Powers of i

    What is the product (2 - 1i)(1 + 5i) expressed in the form a + bi?

    1. A 8 + 9i
    2. B 2 + -5i
    3. C 7 + 10i
    4. D 7 + 9i
    Worked solution

    Answer: D — 7 + 9i

    Use FOIL and replace i^2 with -1. (2 + -1i)(1 + 5i) = 2 + 10i + -1i + -5i^2 = 2 + 9i + -5(-1) = 7 + 9i.

  6. 600-700 medium Adding and Subtracting Complex Numbers

    What is the product (-1 + 6i)(2 + 3i) expressed in the form a + bi?

    1. A -20 + 9i
    2. B -2 + 18i
    3. C -20 + 10i
    4. D -19 + 9i
    Worked solution

    Answer: A — -20 + 9i

    Use FOIL and replace i^2 with -1. (-1 + 6i)(2 + 3i) = -2 + -3i + 12i + 18i^2 = -2 + 9i + 18(-1) = -20 + 9i.

  7. 600-700 hard Multiplying Complex Numbers

    What is the product (1 - 1i)(-2 + 1i) expressed in the form a + bi?

    1. A -1 + 3i
    2. B -2 + -1i
    3. C -1 + 4i
    4. D 0 + 3i
    Worked solution

    Answer: A — -1 + 3i

    Use FOIL and replace i^2 with -1. (1 + -1i)(-2 + 1i) = -2 + 1i + 2i + -1i^2 = -2 + 3i + -1(-1) = -1 + 3i.

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 600-700 drills