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Sample FAST-NU Test Practice Questions

Try these sample questions to review concepts for the FAST-NU Test exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 92+ question experience with AI tutoring.

1Evaluate the limit: lim_{x -> 0} (sin(5x)) / (3x).
A.5/3
B.3/5
C.0
D.5/15
Explanation: Using the standard trigonometric limit lim_{u -> 0} (sin u)/u = 1, we rewrite the expression as (5/3) * lim_{x -> 0} (sin(5x)/(5x)) = (5/3) * 1 = 5/3. Alternatively, applying L'Hôpital's Rule yields lim_{x -> 0} (5 cos(5x))/3 = 5/3.
2What is the value of lim_{x -> 0} (1 - cos(x)) / x^2?
A.1/2
B.1
C.0
D.Undefined
Explanation: Using the half-angle identity 1 - cos(x) = 2 sin^2(x/2), the expression becomes 2 sin^2(x/2) / x^2 = 2 * (1/4) * [sin(x/2)/(x/2)]^2, which evaluates to 1/2 as x approaches 0. L'Hôpital's Rule also gives sin(x)/(2x) -> 1/2.
3Determine the domain of the real-valued function f(x) = √(9 - x^2).
A.[-3, 3]
B.(-∞, -3] U [3, ∞)
C.(-3, 3)
D.[0, 3]
Explanation: For the square root to yield real values, the radicand must satisfy 9 - x^2 >= 0. Factoring gives (3 - x)(3 + x) >= 0, which corresponds to the closed interval [-3, 3].
4If f(x) = (2x + 1) / (x - 3) for x ≠ 3, find the formula for its inverse function f⁻¹(x).
A.(3x + 1) / (x - 2)
B.(3x - 1) / (x + 2)
C.(x - 3) / (2x + 1)
D.(2x - 1) / (x + 3)
Explanation: Setting y = (2x + 1)/(x - 3), cross-multiplying gives y(x - 3) = 2x + 1 => xy - 3y = 2x + 1. Rearranging terms: xy - 2x = 3y + 1 => x(y - 2) = 3y + 1 => x = (3y + 1)/(y - 2). Thus, f⁻¹(x) = (3x + 1)/(x - 2).
5Evaluate lim_{x -> ∞} (3x^2 + 5x - 2) / (2x^2 - 7x + 1).
A.3/2
B.∞
C.0
D.-2
Explanation: For a rational function as x approaches infinity, divide numerator and denominator by the highest power of x, which is x^2. This gives (3 + 5/x - 2/x^2) / (2 - 7/x + 1/x^2). As x -> ∞, terms with x in the denominator tend to 0, leaving 3/2.
6What is the derivative of y = ln(sec(x) + tan(x)) with respect to x?
A.sec(x)
B.tan(x)
C.sec^2(x)
D.sec(x) tan(x)
Explanation: Using the chain rule, dy/dx = (1 / (sec(x) + tan(x))) * d/dx(sec(x) + tan(x)) = (sec(x) tan(x) + sec^2(x)) / (sec(x) + tan(x)). Factoring sec(x) from the numerator gives sec(x)(tan(x) + sec(x)) / (sec(x) + tan(x)) = sec(x).
7If y = sin(x^2), find dy/dx.
A.2x cos(x^2)
B.cos(x^2)
C.2x sin(x)
D.-2x cos(x^2)
Explanation: Apply the chain rule to the outer sine function and the inner square function. The derivative is cos(x^2) times 2x, giving 2x cos(x^2).
8Evaluate d/dx [arctan(2x)].
A.2 / (1 + 4x^2)
B.1 / (1 + 4x^2)
C.2 / (1 + 2x^2)
D.1 / (1 + x^2)
Explanation: The standard derivative formula is d/dx [arctan(u)] = (1 / (1 + u^2)) * du/dx. Here u = 2x and du/dx = 2, yielding 2 / (1 + (2x)^2) = 2 / (1 + 4x^2).
9Find the slope of the tangent line to the curve y = x^3 - 3x + 2 at x = 2.
A.9
B.4
C.6
D.12
Explanation: The slope of the tangent line is given by the first derivative dy/dx = 3x^2 - 3. Evaluating at x = 2 gives dy/dx|_{x=2} = 3(2)^2 - 3 = 3(4) - 3 = 12 - 3 = 9.
10For what value of x does the function f(x) = 2x^3 - 9x^2 + 12x + 5 achieve its local minimum?
A.x = 2
B.x = 1
C.x = 3
D.x = 0
Explanation: First, find critical points: f'(x) = 6x^2 - 18x + 12 = 6(x^2 - 3x + 2) = 6(x - 1)(x - 2) = 0, so x = 1 and x = 2. Compute the second derivative: f''(x) = 12x - 18. At x = 1, f''(1) = -6 < 0 (local maximum). At x = 2, f''(2) = 6 > 0 (local minimum). Hence, the local minimum occurs at x = 2.

About the FAST-NU Test Exam

Independent English-language practice by OpenExamPrep focuses on engineering/computing. Engineering requires SSC/HSSC 60% with the specified subjects; computing requires SSC 60%, HSSC 50% and mathematics. Pre-medical computing applicants must have passed additional mathematics or be awaiting its result. This is an English-language MCQ study adaptation of selected skills, not an official translation, format simulation or substitute for the business essay. The reviewed sources did not explicitly confirm every test delivery language or a mandatory undergraduate oral, practical or case-study test component.

Exam sponsor: National University of Computer and Emerging Sciences (FAST-NUCES). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Engineering/computing CBT: advanced mathematics 50%, basic mathematics 20%, analytical/IQ 20%, English 10%. Business: basic mathematics 50%, analytical/IQ 25%, English 10%, essay 15%. Separate section timers, negative marking and no calculators; the reviewed pattern page does not specify the penalty amount.

Time Limit

Approximately 2–3 hours according to the application instructions; follow the appointment and section timers.

Passing Score

Program/campus merit cutoffs. Engineering aggregate: test 33%, HSSC 50%, SSC 17%; computing/business: test 50%, HSSC 40%, SSC 10%.

Exam / Certification Fees

Confirm the current application/test amount on the official voucher; a 2026 amount was not independently confirmed.

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Official sources

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

50% engineering/computing

Advanced Mathematics

Algebra, functions, calculus, matrices, vectors and trigonometry.

20% engineering/computing

Basic Mathematics

Arithmetic, percentages, ratios, rates and probability.

20% engineering/computing

Analytical Skills and IQ

Sequences, deduction, arrangements and analogies.

10% engineering/computing

English

Vocabulary, grammar and reading.

Preparing for the FAST-NU Test Exam

What You Need to Know

  • Passing score: Program/campus merit cutoffs. Engineering aggregate: test 33%, HSSC 50%, SSC 17%; computing/business: test 50%, HSSC 40%, SSC 10%.
  • Assessment: Engineering/computing CBT: advanced mathematics 50%, basic mathematics 20%, analytical/IQ 20%, English 10%. Business: basic mathematics 50%, analytical/IQ 25%, English 10%, essay 15%. Separate section timers, negative marking and no calculators; the reviewed pattern page does not specify the penalty amount.
  • Time limit: Approximately 2–3 hours according to the application instructions; follow the appointment and section timers.
  • Exam / certification fees: Confirm the current application/test amount on the official voucher; a 2026 amount was not independently confirmed. Official sources

Using Our Practice Resources

  • Work through all 92 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

FAST-NU Test: Suggested Study Strategy

1Practise mathematics without a calculator.
2Use separate timed blocks for each section.
3Check current program eligibility and scoring instructions.

Frequently Asked Questions

Does FAST apply negative marking?

Yes. Follow current test instructions for the penalty; the official pattern page reviewed does not publish its numerical amount.

Does this cover the business test?

Only some shared skills. Business has different weights and a 15% essay component requiring separate writing practice.