Free Practice Questions for IUP ITS

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Key Facts: IUP ITS Exam

90 min

Total CBT Duration (60 min TPA + 30 min Math)

ITS IUP Official Admission Guidelines

2 Parts

Written Test Components (Academic Potential + Mathematics)

ITS Tes SMITS Page

IDR 1M / USD 100

Application Fee (Indonesian / International)

ITS IUP Admission Schedule

English

Medium of Examination & Instruction

ITS IUP Curriculum Guidelines

Mandatory

Admissions Interview Component

ITS IUP Selection Route

IUP ITS entrance for Batches 2 and 3 requires an online English-medium CBT (60-minute Academic Potential plus 30-minute Mathematics) and a mandatory online interview. The application fee is IDR 1,000,000 for Indonesian applicants or USD 100 for non-Indonesian applicants. This independent bank studies the academic-test skills and does not simulate the interview.

Sample IUP ITS Practice Questions

Try these sample questions to review concepts for the IUP ITS exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1If alpha and beta are the real roots of the quadratic equation 3x^2 - 12x + 5 = 0, what is the value of alpha^2 + beta^2?

A.34/3

B.38/3

C.44/3

D.14

Explanation: By Vieta's formulas, the sum of roots is alpha + beta = -(-12)/3 = 4 and the product of roots is alpha * beta = 5/3. Expanding the algebraic identity gives alpha^2 + beta^2 = (alpha + beta)^2 - 2(alpha * beta) = 4^2 - 2(5/3) = 16 - 10/3 = 38/3.

2What is the complete solution set for the rational inequality (3x - 2) / (x + 4) <= 2?

A.-4 < x <= 10

B.-4 <= x <= 10

C.x < -4 or x >= 10

D.x <= -4 or x > 10

Explanation: Subtracting 2 from both sides yields (3x - 2)/(x + 4) - 2(x + 4)/(x + 4) <= 0, which simplifies to (x - 10)/(x + 4) <= 0. The critical values are x = -4 and x = 10; testing test intervals shows the expression is negative or zero between -4 and 10. Because x = -4 produces a zero denominator, it must be excluded, giving the half-open interval -4 < x <= 10.

3What is the real solution to the logarithmic equation log_3(x - 2) + log_3(x + 4) = 3?

A.-7

B.7

C.5

D.-7 and 5

Explanation: Applying the product rule of logarithms yields log_3((x - 2)(x + 4)) = 3, which converts to the algebraic equation (x - 2)(x + 4) = 3^3 = 27. Expanding and rearranging gives x^2 + 2x - 35 = 0, which factors into (x + 7)(x - 5) = 0, giving candidate roots x = -7 and x = 5. Since logarithmic arguments must be strictly positive (x - 2 > 0 requires x > 2), x = -7 is extraneous, leaving x = 5 as the unique valid solution.

4When the polynomial P(x) = 2x^3 - kx^2 + 4x - 6 is divided by (x - 2), the remainder is 14. What is the value of the constant k?

A.-1

B.2

C.3

D.1

Explanation: According to the Polynomial Remainder Theorem, dividing P(x) by (x - 2) leaves a remainder equal to P(2). Setting P(2) = 14 gives 2(2)^3 - k(2)^2 + 4(2) - 6 = 14, which evaluates to 16 - 4k + 8 - 6 = 14. Simplifying gives 18 - 4k = 14, leading to 4k = 4, so k = 1.

5Given the functions f(x) = 2x + 5 and g(x) = (x - 3) / 4, what is the value of (f o g)^(-1)(7)?

A.7

B.5

C.9

D.4

Explanation: The expression (f o g)^(-1)(7) represents the input x such that f(g(x)) = 7. Setting f(g(x)) = 2*g(x) + 5 = 7 gives 2*g(x) = 2, so g(x) = 1. Substituting g(x) = (x - 3)/4 = 1 yields x - 3 = 4, which gives x = 7.

6What is the sum of the real roots of the exponential equation 4^x - 5(2^x) + 4 = 0?

A.5

B.2

C.4

D.1

Explanation: Let u = 2^x, so 4^x = (2^x)^2 = u^2. The equation transforms into the quadratic u^2 - 5u + 4 = 0, which factors as (u - 1)(u - 4) = 0, yielding u = 1 and u = 4. Returning to x gives 2^x = 1 (so x = 0) and 2^x = 4 (so x = 2). The sum of the roots is 0 + 2 = 2.

7The 4th term of an arithmetic sequence is 19 and the 9th term is 44. What is the sum of the first 15 terms of this sequence?

A.540

B.615

C.585

D.570

Explanation: In an arithmetic sequence, a_n = a + (n - 1)d. We have a + 3d = 19 and a + 8d = 44. Subtracting the two equations gives 5d = 25, so the common difference is d = 5, which means the first term is a = 19 - 3(5) = 4. The sum of the first 15 terms is S_15 = (15/2)(2a + 14d) = (15/2)(2*4 + 14*5) = (15/2)(8 + 70) = (15/2)(78) = 15 * 39 = 585.

8An infinite geometric series has a first term of 12 and a common ratio of -1/3. What is its sum to infinity?

A.18

B.9

C.8

D.36

Explanation: For an infinite geometric progression with |r| < 1, the sum to infinity is given by S = a / (1 - r). Substituting a = 12 and r = -1/3 gives S = 12 / (1 - (-1/3)) = 12 / (4/3) = 12 * (3/4) = 9.

9Matrix A is defined as [[2, x], [4, x + 3]]. For what value of x is matrix A singular (non-invertible)?

A.-3

B.6

C.2

D.3

Explanation: A square matrix is singular if and only if its determinant equals zero. For matrix A = [[2, x], [4, x + 3]], det(A) = 2(x + 3) - 4(x) = 2x + 6 - 4x = 6 - 2x. Setting det(A) = 0 yields 6 - 2x = 0, so 2x = 6, which gives x = 3.

10For what real value of m does the system of linear equations 2x + 3y = 7 and 4x + my = 15 have no solution?

A.6

B.-6

C.3

D.12

Explanation: A system of two linear equations in two variables has no solution when the lines are parallel and distinct. This requires the ratio of the coefficients of x and y to be equal, while differing from the ratio of the constant terms: 2/4 = 3/m != 7/15. Solving 1/2 = 3/m yields m = 6. Since 7/15 != 1/2, the system is inconsistent and has no solution.

About the IUP ITS Exam

The International Undergraduate Programme (IUP) at Institut Teknologi Sepuluh Nopember (ITS) is an English-medium undergraduate route. Admission for Batches 2 and 3 includes the online English-medium Academic Test SMITS (a 60-minute Academic Potential test and a 30-minute Mathematics test) alongside a mandatory online admissions interview. Batches 1 and 4 use academic-record and interview selection without this written test. This independent practice bank covers the Batch 2/3 written-test areas; it does not simulate the separate interview.

Exam sponsor: Institut Teknologi Sepuluh Nopember (ITS). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Computer-based test (CBT) delivered entirely in English: Academic Potential (60 minutes covering verbal, logical, spatial, and quantitative reasoning) and Mathematics (30 minutes covering advanced high school math), followed by a mandatory separate online interview.

Time Limit

90 minutes (60 minutes Academic Potential + 30 minutes Mathematics)

Passing Score

Program-specific competitive selection based on academic test scores, academic records, and mandatory admissions interview; no universal numeric cut-off is published

Exam / Certification Fees

IDR 1,000,000 (Indonesian applicants) / USD 100 (non-Indonesian applicants)

Exam sponsor website

Reported exam pass rate: Not published; admissions are competitive based on departmental intake quotas. ITS does not publish a universal numeric pass mark or admissions rate for the IUP track. 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.

35 questions (35% of bank)

Mathematics

High school pre-calculus and calculus: algebra, functions, logarithms, trigonometry, differential and integral calculus, analytical coordinate geometry, and vectors.

25 questions (25% of bank)

Academic Potential — Quantitative Reasoning

Arithmetic operations, numerical and alphanumeric sequences, word problems, percentages, ratios, rate and work problems, and data interpretation.

20 questions (20% of bank)

Academic Potential — Logical & Analytical Reasoning

Deductive syllogisms, conditionality (modus ponens, modus tollens), sequencing, linear and circular seating arrangements, and grouping logic.

20 questions (20% of bank)

Academic Potential — Verbal & Spatial Reasoning

English verbal analogies, critical reading comprehension, context vocabulary, and 2D/3D spatial rotations, paper folding, and cube net transformations.

Preparing for the IUP ITS Exam

What You Need to Know

Passing score: Program-specific competitive selection based on academic test scores, academic records, and mandatory admissions interview; no universal numeric cut-off is published
Assessment: Computer-based test (CBT) delivered entirely in English: Academic Potential (60 minutes covering verbal, logical, spatial, and quantitative reasoning) and Mathematics (30 minutes covering advanced high school math), followed by a mandatory separate online interview.
Time limit: 90 minutes (60 minutes Academic Potential + 30 minutes Mathematics)
Exam / certification fees: IDR 1,000,000 (Indonesian applicants) / USD 100 (non-Indonesian applicants) Official sources

Using Our Practice Resources

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IUP ITS: Suggested Study Strategy

1Prioritize speed and precision in Mathematics: with only 30 minutes allocated to the Mathematics section, focus on rapid algebraic manipulation, calculus derivatives, and trigonometric identities.

2Work out quantitative word problems methodically: set up concise algebraic expressions for work-rate, mixture, and percentage problems before computing numerical values.

3Diagram logic puzzles immediately: sketch linear arrangements or grouping grids on scratch paper to identify constrained positions before answering deductive reasoning items.

4Sharpen spatial visualisation skills: practice identifying faces on unfolded cube nets and visualising 90-degree and 180-degree 3D rotations.

5Review academic reading and verbal analogies: pay attention to nuances in logical relationships (cause-effect, tool-function, category-member) and critical comprehension inferences.

Frequently Asked Questions

What is the IUP ITS entrance selection process?

The International Undergraduate Programme (IUP) at ITS conducts admissions across several batches. For Batches 2 and 3, candidates must take the online English-medium Academic Test SMITS (consisting of Academic Potential and Mathematics) and undergo a mandatory online admissions interview. Batches 1 and 4 evaluate candidates via school academic records, certificates, and interviews without requiring the written academic test.

What subjects are tested on the IUP ITS Academic Test?

The written academic test consists of two main sections: Academic Potential (60 minutes), covering verbal, logical, spatial, and quantitative reasoning; and Mathematics (30 minutes), covering high-school level algebra, functions, trigonometry, coordinate geometry, vectors, and calculus.

What is the language of the IUP ITS Academic Test?

All questions and instructions on the IUP ITS Academic Test are delivered entirely in English, reflecting the English-medium curriculum of the International Undergraduate Programme.

How much is the registration fee for IUP ITS?

The application fee for IUP ITS is IDR 1,000,000 for Indonesian applicants or USD 100 for non-Indonesian (international) applicants. Fees are paid through designated banking channels and are non-refundable.

Does this question bank include preparation for the admissions interview?

No. This question bank focuses exclusively on the written Academic Test (Academic Potential and Mathematics) for Batches 2 and 3. The admissions interview is a mandatory, separately administered oral evaluation conducted online by ITS faculty members assessing motivation, communication, and academic readiness.

Is there a fixed passing score for IUP ITS?

ITS does not publish a universal numeric passing score. Final admission offers are determined competitively by each department's admissions committee based on the candidate's composite performance across the academic test, academic records, English certification, and interview.