Praxis Math 5165 study plan

Praxis Math 5165 · Give each week a clear focus.

8 weeks · About 6 hours per week

Week 1

Number and Quantity, Algebra, and Functions

Compute fluently with rational, radical, and exponential expressions with no calculator
Solve linear, quadratic, absolute-value, and radical equations, checking for extraneous roots
Translate multi-step rate, mixture, and work word problems into equations and solve them
Convert among fraction, decimal, and percent forms and apply ratio and proportion reasoning

30-item diagnostic scored and entered into an error tracker that names the cause of every miss; target 70% or higher correct

Week 2

Sketch and transform linear, quadratic, polynomial, exponential, and logarithmic functions
Determine domain and range for rational, radical, and logarithmic functions and their composites
Solve exponential and logarithmic equations and apply them to growth and decay contexts
Find inverse functions and verify them by composition
Interpret function notation and compute average rate of change from a graph or table

One-page parent-function and transformation reference sheet plus 25 solved practice items at 80% accuracy or better

Week 3

Compute and interpret mean, median, mode, range, variance, and standard deviation
Solve z-score and normal-distribution problems using the empirical rule and standard tables
Select and justify an appropriate data display for a given data set
Identify sampling methods and sources of bias in study designs

Data-analysis write-up summarizing three data sets with correct center, spread, and display, plus 15 practice items at 75% or better

Week 4

Apply addition, multiplication, complement, and conditional rules to compute probabilities
Distinguish permutation from combination situations and solve both types of counting problems
Compute expected value and interpret it in context
Test whether events are independent and justify the conclusion with a formula

Timed 40-item cumulative quiz covering Domains 1 and 3, scored at 65% or higher, with every missed item reworked in writing

Week 5

Evaluate limits algebraically and from graphs, including one-sided limits
Differentiate using power, product, quotient, and chain rules
Interpret the derivative as slope, instantaneous rate of change, and tangent-line slope
Solve optimization and related-rate problems
Interpret the definite integral as accumulated change and signed area

30-item calculus problem set on limits, derivatives, and applications scored at 75% or higher

Week 6

Compute perimeter, area, surface area, and volume for standard two- and three-dimensional figures
Apply similarity, congruence, and Pythagorean relationships to find missing measures
Solve coordinate geometry problems using distance, midpoint, slope, and equations of lines and circles
Apply transformations and use angle relationships for parallel lines and polygons

Geometry portfolio of 25 fully worked problems with labeled diagrams, at 80% correct or better

Week 7

Evaluate sine, cosine, and tangent of standard angles using the unit circle
Solve right and oblique triangles with trig ratios and the Law of Sines and Law of Cosines
Graph trig functions and identify amplitude, period, and phase shift
Verify and apply fundamental trigonometric identities
Convert between degrees and radians and compute arc length and sector area

30-item trigonometry assessment at 75% or better plus a correctly labeled unit circle reproduced from memory

Week 8

Complete two full-length timed practice tests under exam conditions
Classify every missed item by domain and by error type
Re-teach and re-test the two weakest subskills identified in the error log
Consolidate a single formula sheet covering area and volume, trig identities, derivative rules, and statistics formulas

Full-length practice test scored at 80% or higher, with a completed formula sheet and an error log showing every repeat-miss item resolved

Week 2: Score 80% or higher on a 20-item algebra and functions checkpoint before moving on to Domain 3

Week 4: Score 65% or higher on the timed 40-item Domain 1 and 3 cumulative quiz with a fully written error log

Week 6: Score 75% or higher on a 25-item geometry and trigonometry checkpoint taken untimed, then 70% timed

Week 8: Score 80% or higher on two consecutive full-length timed practice tests, with all three domains at 70% or above individually