Mathematics, Engineering Economics and Basic Engineering Sciences
Mathematics
The shape of the exam
This is the highest-yield domain for speed practice. The recurring topics are algebra and simultaneous equations, quadratic and polynomial behaviour, plane and spherical trigonometry, analytic geometry (lines, conics, distances), differential calculus (maxima-minima, related rates, curvature), integral calculus (areas, volumes, centroids, work), differential equations (separable, linear first-order, second-order with constant coefficients), matrices and determinants, complex numbers, probability and counting, and descriptive statistics including mean, median, standard deviation and the normal curve.
Where candidates lose points
Angle mode: calculator set in radians when the problem is in degrees destroys trig items - check before you commit. In conics, a rotated axis or a translation of origin changes the equation form. In integration, the most common failure is a missed constant of integration or a reversed limit that changes the sign of a centroid or work answer. In probability, decide whether order matters (permutation) or not (combination) before writing a formula, and remember that "at least one" is almost always easiest through the complement. In statistics, the sample standard deviation uses $n-1$, the population value uses $n$.
Worked example
Evaluate the definite integral:
$$\int_0^2 (3x^2 + 2x),dx = \left[x^3 + x^2\right]_0^2 = (8 + 4) - 0 = 12$$
Rule of thumb: for any area or centroid item, sketch the region and identify the upper and lower curve before integrating; the sketch catches sign errors that algebra will not.
Engineering Economics and Basic Engineering Sciences
The shape of the exam
Economics dominates the item count: time value of money (single payment, uniform series, gradient, capitalized cost), effective versus nominal interest, depreciation (straight line, sum-of-years-digits, declining balance, sinking fund), annual worth and present worth comparison of alternatives, rate of return, benefit-cost ratio, break-even analysis, and inflation. The basic sciences half covers statics (resultants, equilibrium, friction, trusses), dynamics (kinematics, work-energy, impulse-momentum), and introductory chemistry and physics.
Where candidates lose points
Nominal versus effective interest: an annual nominal rate compounded monthly must be converted with $i_{\text{eff}} = (1 + r/m)^m - 1$ before any annuity formula is applied. Annuity factors require the interest rate and the number of periods to match - a quarterly factor with an annual rate is wrong. In depreciation, salvage value appears in straight line and sinking fund but not in declining balance, which is a standard trap. In comparing alternatives, differing lives require either a common study period or comparison by annual worth; comparing present worths of unequal lives is invalid.
Worked example
Present worth of ₱10,000 received annually for 5 years at 10%:
$$P = A\frac{(1+i)^n - 1}{i(1+i)^n} = 10{,}000 \times \frac{1.61051 - 1}{0.1 \times 1.61051} \approx 37{,}908$$
Rule of thumb: money moves to the present by dividing by $(1+i)^n$ and to the future by multiplying - do this one cash flow at a time when the pattern is irregular.