Free Practice Questions for Bagrut Mathematics (3/4/5 Units)

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Key Facts: Bagrut Mathematics (3/4/5 Units) Exam

55 / 100

Minimum passing grade required on each Bagrut module and composite subject grade

Israel Ministry of Education (משרד החינוך) Examination Regulations

3, 4, or 5 Units

Study unit tiers (יחידות לימוד), with 4 and 5 units required for STEM university admissions

Council for Higher Education (מל"ג) & Ministry of Education

2 to 3.5 Hours

Exam duration per questionnaire (e.g. Questionnaire 581 is 3.5 hours, 582 is 2 hours)

Ministry of Education Division of Examinations (אגף הבחינות)

Moed Bet (מועד ב)

National retake opportunity in July where the higher of the two summer scores is awarded

Ministry of Education Bagrut Administration Portal

No fee

Nominal fee for external examinees; free for regular enrolled high school students

Ministry of Education External Examinee Division Guidelines

Questionnaires 481/482 & 581/582

Standard modular questionnaire numbers for 4-unit and 5-unit matriculation tracks

National Mathematics Curriculum Guidelines (מפמ"ר מתמטיקה)

Scientific Calculator

Permitted exam aid along with the official Ministry-provided formula sheet

Ministry of Education Approved Exam Aids Circular

English MCQ Adaptation

Independent study resource by OpenExamPrep, not the official Hebrew written paper

OpenExamPrep Practice Bank Disclosure

Independent practice for the Israel Bagrut Mathematics exam by OpenExamPrep: 100 English MCQs across algebra, sequences, analytic geometry, trigonometry, vectors, calculus, and probability for students preparing for Israeli 3, 4, and 5-unit matriculation modules.

Sample Bagrut Mathematics (3/4/5 Units) Practice Questions

Try these sample questions to review concepts for the Bagrut Mathematics (3/4/5 Units) exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1In an arithmetic sequence, the first term is a_1 = 7 and the common difference is d = 4. What is the 15th term, a_15?

A.59

B.63

C.67

D.71

Explanation: In an arithmetic sequence, the general n-th term formula is a_n = a_1 + (n - 1)d. Substituting a_1 = 7, d = 4, and n = 15 gives a_15 = 7 + (15 - 1) · 4 = 7 + 14 · 4 = 7 + 56 = 63.

2An arithmetic sequence has first term a_1 = 3 and common difference d = 5. What is the sum of the first 10 terms, S_10?

A.255

B.240

C.270

D.510

Explanation: The sum of the first n terms of an arithmetic sequence is given by S_n = (n / 2) · [2a_1 + (n - 1)d]. Substituting n = 10, a_1 = 3, and d = 5 gives S_10 = (10 / 2) · [2(3) + (10 - 1) · 5] = 5 · [6 + 45] = 5 · 51 = 255.

3In a geometric sequence, the first term is a_1 = 5 and the common ratio is q = 3. What is the 5th term, a_5?

A.135

B.405

C.1215

D.75

Explanation: The n-th term of a geometric sequence is given by a_n = a_1 · q^(n - 1). For n = 5, a_5 = 5 · 3^(5 - 1) = 5 · 3^4 = 5 · 81 = 405.

4An infinite geometric progression has first term a_1 = 12 and common ratio q = 1/3. What is the sum S of this infinite sequence?

A.16

B.18

C.24

D.36

Explanation: For an infinite geometric progression where |q| < 1, the sum of all terms is given by S = a_1 / (1 - q). Here, S = 12 / (1 - 1/3) = 12 / (2/3) = 12 · (3/2) = 18.

5What is the equation of the straight line passing through the point (2, 5) with a slope of m = 3?

A.y = 3x - 1

B.y = 3x + 1

C.y = 3x - 11

D.y = 3x + 7

Explanation: Using the point-slope form y - y_1 = m(x - x_1), substitute m = 3 and (x_1, y_1) = (2, 5): y - 5 = 3(x - 2) => y - 5 = 3x - 6 => y = 3x - 1.

6What are the coordinates of the center and the length of the radius for the circle defined by (x - 4)^2 + (y + 3)^2 = 49?

A.Center (-4, 3), radius 7

B.Center (4, -3), radius 49

C.Center (4, -3), radius 7

D.Center (-4, -3), radius 7

Explanation: The standard equation of a circle is (x - a)^2 + (y - b)^2 = R^2, where (a, b) is the center and R is the radius. Comparing (x - 4)^2 + (y - (-3))^2 = 7^2, the center is (4, -3) and the radius is R = sqrt(49) = 7.

7In an arithmetic sequence, the 4th term is a_4 = 19 and the 9th term is a_9 = 44. What are the first term a_1 and the common difference d?

A.a_1 = 4, d = 5

B.a_1 = 3, d = 5

C.a_1 = 4, d = 6

D.a_1 = 5, d = 4

Explanation: The difference between the terms is a_9 - a_4 = (9 - 4)d = 5d. Thus 44 - 19 = 25 => 5d = 25 => d = 5. To find a_1: a_4 = a_1 + 3d => 19 = a_1 + 3(5) => 19 = a_1 + 15 => a_1 = 4.

8In a geometric sequence of positive real numbers, the 2nd term is a_2 = 12 and the 5th term is a_5 = 324. What is the sum of the first 4 terms, S_4?

A.120

B.160

C.180

D.320

Explanation: In a geometric sequence, a_5 / a_2 = (a_1 · q^4) / (a_1 · q) = q^3. Therefore, q^3 = 324 / 12 = 27, which gives q = 3 (since terms are positive). Then a_1 = a_2 / q = 12 / 3 = 4. The sum of the first 4 terms is S_4 = a_1 · (q^4 - 1) / (q - 1) = 4 · (3^4 - 1) / (3 - 1) = 4 · (81 - 1) / 2 = 4 · 80 / 2 = 160. Alternatively, S_4 = 4 + 12 + 36 + 108 = 160.

9What is the equation of the line that is perpendicular to the line 2x - 6y + 9 = 0 and passes through the point (1, -4)?

A.y = -3x - 1

B.y = 3x - 7

C.y = -1/3 x - 11/3

D.y = -3x + 1

Explanation: Rewrite the given line in slope-intercept form: 6y = 2x + 9 => y = (1/3)x + 3/2. The slope of the given line is m_1 = 1/3. For a perpendicular line, the slope m_2 satisfies m_1 · m_2 = -1, so m_2 = -3. Using the point (1, -4): y - (-4) = -3(x - 1) => y + 4 = -3x + 3 => y = -3x - 1.

10Find all intersection points between the circle x^2 + y^2 = 25 and the straight line y = x + 1.

A.(3, 4) and (-4, -3)

B.(4, 3) and (-3, -4)

C.(3, 4) and (-3, -2)

D.(0, 1) and (-1, 0)

Explanation: Substitute y = x + 1 into the circle equation: x^2 + (x + 1)^2 = 25 => x^2 + x^2 + 2x + 1 = 25 => 2x^2 + 2x - 24 = 0. Divide by 2: x^2 + x - 12 = 0. Factoring gives (x + 4)(x - 3) = 0, so x = 3 or x = -4. For x = 3, y = 3 + 1 = 4, giving (3, 4). For x = -4, y = -4 + 1 = -3, giving (-4, -3).

About the Bagrut Mathematics (3/4/5 Units) Exam

The Israel Bagrut Matriculation Examination in Mathematics (בחינת בגרות במתמטיקה) is the national school-leaving and university-qualifying examination administered by the Israeli Ministry of Education (משרד החינוך). Mathematics is a mandatory core subject for the Te'udat Bagrut (matriculation certificate) and is offered at three levels of intensity: 3 Units (basic qualification), 4 Units (rigorous college-preparatory), and 5 Units (intensive advanced STEM preparatory level). The examinations are written modular assessments taken primarily in grades 11 and 12 across winter (Moed Alef) and summer (Moed Alef and Moed Bet) test dates. Each level requires passing two modular questionnaires: 4-unit candidates sit Questionnaires 481 and 482, while 5-unit candidates sit Questionnaires 581 and 582. The exam papers require multi-step proofs, analytic calculations, and algebraic derivations across algebra, analytic geometry, trigonometry, stereometry, 3D vectors, complex numbers, differential and integral calculus, and probability. This practice bank provides an English-language multiple-choice adaptation authored by OpenExamPrep to help students drill essential calculations, verify formula applications, and master core concepts.

Exam sponsor: Israel Ministry of Education (משרד החינוך). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

The Israeli Bagrut in Mathematics is stratified into three curriculum tracks, each assessed by two external written papers under the Ministry of Education's current questionnaire series. 5 units: sheelon 035571 (3 hours 45 minutes, 60% of the subject grade) and sheelon 035572 (2.5 hours, 40%); these replaced the retired sheelon 035581 and 035582. 4 units: sheelon 035471 (3.5 hours, 65%) and sheelon 035472 (2 hours, 35%), replacing 035481 and 035482. 3 units: sheelon 035371 (2 hours 15 minutes, 35%) and sheelon 035372 (2 hours 15 minutes, 40%), replacing 035381 and 035382, with sheelon 035172 (1.5 hours) and the internal assessment sheelon 035173 supplying the remaining 25%. The first 5-unit paper covers algebra, sequences, growth and decay, probability, and differential and integral calculus; the second covers analytic geometry, vectors, trigonometry in space (stereometry), complex numbers, and exponential and logarithmic functions. Candidates answer a chosen subset of multi-part constructed-response problems using a non-graphing calculator and the official Ministry formula sheet (daf nusha'ot). This resource provides independent practice for the Israel Bagrut Mathematics exam by OpenExamPrep.

Time Limit

Modular. 5 units: sheelon 035571 (3 hours 45 minutes) and sheelon 035572 (2.5 hours), 6.25 hours in total. 4 units: sheelon 035471 (3.5 hours) and sheelon 035472 (2 hours), 5.5 hours in total. 3 units: sheelon 035371 and 035372 (2 hours 15 minutes each).

Passing Score

55 out of 100 (minimum passing mark on each module and overall composite subject grade)

Exam / Certification Fees

No exam fee. The Israel Ministry of Education charges nothing to register for or sit a Bagrut examination, for school (internal) students and external (extern) candidates alike; only late registration through the MARBAG flexible examination centre (mrkz bchinh gmish) carries a per-unit charge.

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.

20%

Algebra, Sequences, and Analytic Geometry

Arithmetic and geometric sequences, sum formulas, recursive sequences, lines, circles, parabolas, and intersection points in the Cartesian plane.

20%

Trigonometry and Vectors

Trigonometric identities, angle-sum formulas, sine and cosine laws, 2D coordinate vectors, 3D spatial vectors, dot product, and vector equations of lines and planes.

30%

Differential Calculus

Derivatives of polynomials, rational functions, radical expressions, exponential and logarithmic functions; tangents, extrema, asymptotes, and optimization word problems.

15%

Integral Calculus

Standard antiderivatives, substitution, definite integrals, area between two curves, area under the x-axis, volume of solids of revolution, and accumulation problems.

15%

Probability and Statistics

Combinatorics, multi-stage events, conditional probability, tree diagrams, Bayes' theorem, and Bernoulli trials (binomial distribution).

Preparing for the Bagrut Mathematics (3/4/5 Units) Exam

What You Need to Know

Passing score: 55 out of 100 (minimum passing mark on each module and overall composite subject grade)
Assessment: The Israeli Bagrut in Mathematics is stratified into three curriculum tracks, each assessed by two external written papers under the Ministry of Education's current questionnaire series. 5 units: sheelon 035571 (3 hours 45 minutes, 60% of the subject grade) and sheelon 035572 (2.5 hours, 40%); these replaced the retired sheelon 035581 and 035582. 4 units: sheelon 035471 (3.5 hours, 65%) and sheelon 035472 (2 hours, 35%), replacing 035481 and 035482. 3 units: sheelon 035371 (2 hours 15 minutes, 35%) and sheelon 035372 (2 hours 15 minutes, 40%), replacing 035381 and 035382, with sheelon 035172 (1.5 hours) and the internal assessment sheelon 035173 supplying the remaining 25%. The first 5-unit paper covers algebra, sequences, growth and decay, probability, and differential and integral calculus; the second covers analytic geometry, vectors, trigonometry in space (stereometry), complex numbers, and exponential and logarithmic functions. Candidates answer a chosen subset of multi-part constructed-response problems using a non-graphing calculator and the official Ministry formula sheet (daf nusha'ot). This resource provides independent practice for the Israel Bagrut Mathematics exam by OpenExamPrep.
Time limit: Modular. 5 units: sheelon 035571 (3 hours 45 minutes) and sheelon 035572 (2.5 hours), 6.25 hours in total. 4 units: sheelon 035471 (3.5 hours) and sheelon 035472 (2 hours), 5.5 hours in total. 3 units: sheelon 035371 and 035372 (2 hours 15 minutes each).
Exam / certification fees: No exam fee. The Israel Ministry of Education charges nothing to register for or sit a Bagrut examination, for school (internal) students and external (extern) candidates alike; only late registration through the MARBAG flexible examination centre (mrkz bchinh gmish) carries a per-unit charge. Official sources

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Bagrut Mathematics (3/4/5 Units): Suggested Study Strategy

1Master the official Ministry formula sheet (דף נוסחאות): know exactly which formulas are provided and practice deriving intermediate results without relying on external tables.

2Pay strict attention to the domain of definition (תחום הגדרה) before performing calculus operations on rational, square root, or logarithmic functions to avoid extraneous solutions.

3Work backward from the derivative's sign chart (טבלת סימנים) to sketch curves accurately, identifying vertical and horizontal asymptotes, extrema, and inflection points.

4In analytic geometry and vectors, sketch clear diagrams before writing coordinate equations; verify perpendicularity with the dot product (u · v = 0) and check slope relationships (m1 · m2 = -1).

5For probability word problems, construct complete probability tree diagrams with branch labels to correctly apply Bayes' formula and conditional probability P(A|B) = P(A ∩ B) / P(B).

6Practice full written solutions from past Ministry of Education questionnaires (שאלונים) under strict timed conditions to build stamina for 2-hour and 3.5-hour papers.

7Review the specific question options carefully in this practice bank: each distractor reflects a classic algebraic sign error, missed chain-rule factor, or incorrect integration constant.

Frequently Asked Questions

What is the structure of the Israel Bagrut Mathematics exam?

The examination is modular and tiered into 3, 4, and 5 study units (יחידות לימוד / יח"ל). Four-unit students take Questionnaires 481 (first paper, 3.5 hours) and 482 (second paper, 2 hours). Five-unit students take Questionnaires 581 (first paper, 3.5 hours) and 582 (second paper, 2 hours). Three-unit students complete Questionnaires 381 and 382. Each paper contains multi-part constructed-response questions with student-selected choices.

What is the passing score for Bagrut Mathematics?

The passing grade is 55 out of 100 on both the individual questionnaire modules and the final weighted subject score. For internal high school students, the final grade combines the external Bagrut exam score with the school-awarded annual grade (ציון שנתי / מגן).

What calculators and reference sheets are allowed during the Bagrut?

Students are permitted to use standard scientific calculators approved by the Ministry of Education (graphing capabilities are restricted depending on the specific module and regulation). An official formula sheet (דף נוסחאות) provided by the Ministry of Education is distributed with the exam paper.

What is Moed Bet (מועד ב) and who is eligible to take it?

Moed Bet is a second chance examination session held in July for the summer administration in mathematics and English. Any student who sat Moed Alef (or missed it) can take Moed Bet to improve their score. The higher of the two examination grades is taken as the final exam score.

What fees are associated with the Bagrut Mathematics examination?

There is no exam fee. The Israel Ministry of Education charges nothing to register for or sit a Bagrut examination, and this applies equally to enrolled school (internal) students, graduates re-sitting to improve a grade (nivchanei mishneh) and external (extern) candidates. The Ministry's official regulations for external examinees confirm that both opening an examinee file and registering for papers are free of charge. The only charges the Ministry publishes are for late registration through the MARBAG flexible examination centre and for obtaining a photocopy of an answer booklet when appealing a grade.

How does this OpenExamPrep question bank relate to the official exam?

This resource represents independent practice for the Israel Bagrut Mathematics exam by OpenExamPrep. While the official Ministry of Education examinations consist of written multi-step free-response questions in Hebrew (and Arabic), this bank provides an English-language multiple-choice adaptation designed to build calculation accuracy and conceptual mastery.

Free Practice Questions for Bagrut Mathematics (3/4/5 Units)

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