D667 Precalculus, catalog number MATH 1040, is the four-CU course that covers functions, trigonometry, systems of equations, analytic geometry, and sequences and series in preparation for calculus. Its purpose is stated in its own description: preparation. Everything in it exists because calculus assumes it. That makes D667 a strange course to study for, because the real test of whether you passed it properly arrives one course later.
Precalculus is a fluency course, not a knowledge course
The content of precalculus is not conceptually hard. Almost every topic can be understood in an afternoon. The difficulty is that calculus does not want you to understand these things, it wants you to not have to think about them. When a derivative problem requires you to rewrite a radical as a fractional exponent, factor a quadratic and recall that the tangent of a right angle is undefined, any hesitation at those three points turns a five minute problem into a twenty minute problem, and there are forty of them.
That changes how you should study. Understanding is necessary and insufficient. What you are building is speed and reliability on a specific list of moves: factoring, expanding, simplifying rational expressions, converting between logarithmic and exponential forms, evaluating trigonometric functions at standard angles, solving systems, and recognising the shape of a function from its equation.
The practical consequence is that a study session which finishes with you nodding at a worked example has done nothing. A session which finishes with twenty problems solved on blank paper, timed, with the errors classified, has done the work. This is the single largest difference between students who move from precalculus into calculus comfortably and students who repeat the pattern of struggle one course later.
The trigonometry half deserves its own approach
Students usually arrive with the function and algebra material partly in place and the trigonometry entirely absent. That half needs a different method, because trigonometry is memory plus geometry rather than manipulation.
Build it from the unit circle outward rather than from a table of identities inward. If you can draw the circle, place the standard angles in all four quadrants, and read sine and cosine off the coordinates, then you never need to memorise a table, because the table becomes something you can reconstruct in thirty seconds. Tangent follows as a ratio. The signs in each quadrant follow from the coordinates rather than from a mnemonic.
Identities then split into two groups. A small set is worth memorising because they appear constantly: the Pythagorean identity and the definitions relating the six functions. The rest are derivable from those, and deriving one twice is faster to learn than memorising it once. Where the course also covers graphs of trigonometric functions, connect amplitude, period and shift to the equation rather than treating them as three separate rules, since every one of them is visible in the same expression.
Planning four competency units of preparation
Open your Course of Study first. WGU keeps assessment detail and the competency list there rather than in the public catalog, and how your version of the course is assessed decides how you should spend your weeks. Where a performance assessment exists, each scored aspect is judged on its own three-point scale and a score of 2 in each passes the task, with no compensation between aspects. Where the instrument is a proctored objective assessment, the preassessment is your planning tool.
A worked plan with numbers. Five content blocks: functions and their transformations, exponentials and logarithms, trigonometry, systems and analytic geometry, and sequences and series. Over seven weeks at ten hours a week that is seventy hours, or fourteen per block. Split each block as four hours learning, eight hours working problems, and two hours building a one-page reference sheet you write yourself. Then add a rule: no block is finished until you can complete a mixed set of twelve problems from it in under forty minutes without notes. Fluency has to be measured or it does not happen.
The mixed set matters more than the total count. Studying one topic at a time produces students who can solve any problem provided someone tells them which method to use. Calculus does not do that, and neither does a proctored exam.
How to lay out a precalculus solution
Where directions specify a format, follow it. Otherwise this layout makes the reasoning visible, which matters wherever work is submitted rather than answered on a screen.
| Line | What appears | Why it matters |
|---|---|---|
| Given | The function or system exactly as stated, before any rewriting | Transcription errors are the most common cause of a completely wrong solution |
| Goal | What is being found, in words | Prevents solving for the wrong quantity in a multi-part problem |
| Restrictions | Domain limits, excluded values, angle range | Extraneous solutions are created by the rewriting you are about to do |
| Transformation | Each algebraic move on its own line, with the rule named where it is not obvious | Makes a partially correct solution recoverable rather than invisible |
| Solution set | All solutions, then the ones the restrictions allow | Trigonometric equations have infinitely many, and the range decides which count |
| Verification | Substitution back into the original | Catches sign and squaring errors before an evaluator does |
| Interpretation | What the answer means where the problem had a context | Applied aspects are not satisfied by a numeric answer alone |
The restrictions line is the one to make automatic. Squaring both sides, multiplying by a variable expression and taking logarithms all create the possibility of answers that solve the new equation and not the old one. Writing the restrictions before the manipulation makes the check at the end mechanical.
Practice habits that build calculus-ready fluency
- Keep an error log with three columns: the problem, what went wrong, and the category. After two weeks the categories will show you that most of your errors are two or three specific moves, not general weakness.
- Redo problems you got wrong, from blank paper, three days later. Immediate correction teaches recognition. Delayed correction teaches recall.
- Time yourself. Fluency is a speed property, and untimed practice will not tell you whether you have it.
- Work mixed sets, not topic sets, from week three onward.
- Write out exact values rather than decimal approximations. Calculus works in exact forms, and a habit of decimals now produces trouble later.
- Sketch before solving. A rough graph of the function catches impossible answers faster than any algebraic check.
One extra habit pays for itself: after finishing a problem, write one sentence saying what technique it was really testing. This turns a pile of practice into a map of the course, and the map is what you revise from in the last week.
What Competent looks like in D667
WGU records outcomes as Competent or Not Competent, with no letter grades and no ordinary grade point average. Performance assessment work can be revised and resubmitted without penalty. Objective assessments are proctored and are yours alone to sit, which is where the boundary sits for support.
Precalculus work that passes cleanly tends to show:
- Restrictions stated before manipulation and applied at the end.
- Exact values kept, with decimals introduced only where the question asks for them.
- Every step legible and in order, so a reader never has to guess what happened between two lines.
- Trigonometric solutions given for the full range requested rather than the first one found.
- Answers interpreted where the problem had a context.
The rule on proctored assessments is absolute. We prepare only. We build the diagnostic, the drill plan, the worked examples and the timed practice, and we give you an honest readiness read. We do not sit or assist during any assessment and we never ask for portal credentials.
Six mistakes that cost time in D667
- Memorising a trigonometric table instead of the unit circle. Tables fall out of memory under pressure. A circle you can draw does not.
- Treating logarithm rules as arbitrary. Every one of them is an exponent rule in disguise, and seeing that once removes the need to memorise three.
- Skipping the graphing. A sketch takes twenty seconds and rules out whole categories of wrong answers.
- Practising only the topic just studied. Real assessments and real calculus problems arrive unlabelled.
- Accepting every solution a manipulation produces. Squaring and multiplying create extraneous roots. Verification is not optional.
- Rushing to calculus because precalculus feels understood. Understood and fluent are different states, and only the second one survives a calculus workload.
How support works on this course
Send your competency list, your preassessment result if you have taken it, and any task directions from your Course of Study. What comes back is a diagnostic identifying which of the five blocks is actually costing you, a drill plan with mixed sets and timing targets, worked examples that show the reasoning rather than just the answer, and where written work is required, a model solution laid out so every step is traceable.
WGU terms run six months at a flat rate, so what lowers your effective cost per course is how many you close per term. Precalculus is worth clearing early for a second reason as well: it sits directly in front of calculus, and arriving at that course with fluency rather than familiarity is what decides whether the next four CUs take six weeks or a whole term.
Questions students ask about D667
Is D667 the same as MATH 1040?
Can I skip precalculus and go straight to calculus?
How much trigonometry is in this course?
Precalculus in front of calculus and the weeks are short?
Send your competency list and preassessment result. You get a diagnostic, mixed-set drills with timing targets, and worked examples that show the reasoning.
Where D667 sits in WGU's programs
The July 2026 catalog places this code in 6 current WGU programs. Open a program page for the complete standard path and term positions. The live Degree Plan remains authoritative after transfer credit, substitutions, and mentor planning.
The assessments, one by one
The public catalog does not publish this course's PA/OA identity or task count. WGU Tutors publishes at most one PA manual per course and only from a WGU-controlled public rubric. Until that source exists, PA help begins from the student's real Course of Study and OA support remains preparation only.