100+ Free EGE Math (Base) Practice Questions

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Question 1

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Express the variable a from the formula S = a x b, where b is not zero.

a = S + b

a = b / S

a = S / b

a = S x b

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Key Facts: EGE Math (Base) Exam

21 short-answer tasks in 180 minutes, maximum 21 primary points; you need at least 7 points to pass, with results converted to a school grade of 2-5.

Sample EGE Math (Base) Practice Questions

Try these sample questions to test your EGE Math (Base) exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A notebook costs 38 rubles. What is the largest number of such notebooks you can buy with 300 rubles?

A.6

B.8

C.7

D.9

Explanation: Divide 300 by 38: 300 / 38 = 7.89. Since you can only buy a whole number of notebooks and cannot exceed the money you have, you round DOWN to 7. This is a classic Task 1 'how many can you buy' problem where rounding by sense means taking the floor.

2A store sells a shirt for 1200 rubles. During a sale, the price is reduced by 25%. What is the sale price?

A.975 rubles

B.900 rubles

C.850 rubles

D.1175 rubles

Explanation: A 25% discount means you pay 75% of the original price. 1200 x 0.75 = 900 rubles. Equivalently, 25% of 1200 is 300, so 1200 - 300 = 900.

3Calculate: 0.6 x 0.5 + 0.7.

A.0.65

B.0.37

C.1.3

D.1.0

Explanation: Follow order of operations: multiplication before addition. 0.6 x 0.5 = 0.30, then 0.30 + 0.7 = 1.0. Decimal multiplication: multiply 6 x 5 = 30 and place two decimal places.

4The mass of one tablet of a medicine is 20 mg. How many grams of the active ingredient are in 250 tablets?

A.50 g

B.5 g

C.0.5 g

D.500 g

Explanation: Total mass = 20 mg x 250 = 5000 mg. Convert to grams: 1 g = 1000 mg, so 5000 mg = 5 g. Unit conversion is a core Task 2 skill on the Base exam.

5Find the value of the expression (2/3) + (1/6).

A.3/9

B.5/6

C.1/2

D.3/6

Explanation: Bring to a common denominator of 6: 2/3 = 4/6. Then 4/6 + 1/6 = 5/6. The fraction 5/6 is already in lowest terms.

6A car travels 540 km using 45 liters of fuel. How many liters are needed to travel 360 km at the same rate?

A.24 liters

B.36 liters

C.30 liters

D.27 liters

Explanation: Fuel consumption is 45 / 540 = 1/12 liter per km. For 360 km: 360 x (1/12) = 30 liters. This is a direct-proportion (proportionality) Task 2 problem.

7Round the number 7.348 to the nearest tenth.

A.7.4

B.7.3

C.7.35

D.7.0

Explanation: The tenths digit is 3, and the next digit is 4, which is less than 5, so we round down and keep 7.3. Standard rounding rules apply.

8Find the value of the expression 2^5 - 2^3.

A.4

B.16

C.24

D.32

Explanation: Compute the powers separately: 2^5 = 32 and 2^3 = 8. Then 32 - 8 = 24. Powers of two are common on the Base computation tasks.

9A worker is paid 250 rubles per hour for the first 8 hours and 375 rubles per hour for each additional hour. How much does the worker earn for a 10-hour shift?

A.2000 rubles

B.2500 rubles

C.3750 rubles

D.2750 rubles

Explanation: First 8 hours: 8 x 250 = 2000 rubles. Additional 2 hours: 2 x 375 = 750 rubles. Total = 2000 + 750 = 2750 rubles. This is a two-rate practical Task 1 problem.

10Express the variable a from the formula S = a x b, where b is not zero.

A.a = S x b

B.a = b / S

C.a = S / b

D.a = S + b

Explanation: To isolate a in S = a x b, divide both sides by b: a = S / b. Rearranging formulas is a Task 4 skill on the Base exam.

About the EGE Math (Base) Exam

The EGE Mathematics Base Level (Математика базового уровня) is one of two mathematics options in Russia's Unified State Exam; students choose Base OR Profile. The Base exam consists of 21 short-answer tasks of basic difficulty, each worth 1 primary point, for a maximum of 21 points over a 180-minute sitting. It tests practical, applied mathematics needed for graduation rather than for technical-university admission: arithmetic and computations, percentages and proportions, real-life word problems, basic algebra and equations, reading functions and graphs, planimetry and solid geometry, and elementary probability. Unlike most EGE subjects, the Base level result is reported as a 5-point school grade rather than a 100-point scale, and universities do not accept it for admission. A student must score at least 7 primary points to pass and receive the school leaving certificate.

Questions

100 scored questions

Time Limit

180 minutes (3 hours)

Passing Score

Minimum 7 of 21 primary points to pass; primary points are converted to a 5-point school grade (2-5), with 3 the minimum passing grade.

Exam Fee

No fee for eligible school graduates in the main exam period (state-funded). (Rosobrnadzor / Federal Institute of Pedagogical Measurements (FIPI))

EGE Math (Base) Exam Content Outline

30%

Numbers and Computations

Arithmetic, fractions, decimals, percentages, proportions, powers, roots, rounding, units and quantities.

22%

Geometry (Planimetry & Stereometry)

Area, perimeter, volume, angles, the Pythagorean theorem, and properties of plane and solid figures.

16%

Practical Word Problems

Real-life applications: bills, discounts, motion, work rate, finance, scale, and reading tables/charts.

13%

Algebra and Equations

Linear and simple quadratic/exponential equations, inequalities, formula manipulation, and simplifying expressions.

11%

Probability and Statistics

Classical and complementary probability, independent events, averages, and chart interpretation.

Functions and Graphs

Reading graphs, linear functions, slope, function values, roots, and coordinate points.

How to Pass the EGE Math (Base) Exam

What You Need to Know

Passing score: Minimum 7 of 21 primary points to pass; primary points are converted to a 5-point school grade (2-5), with 3 the minimum passing grade.
Exam length: 100 questions
Time limit: 180 minutes (3 hours)
Exam fee: No fee for eligible school graduates in the main exam period (state-funded).

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

EGE Math (Base) Study Tips from Top Performers

1Master mental arithmetic with percentages, fractions, and proportions, since these appear throughout the practical word problems.

2Memorize the core formulas allowed on the exam: areas and volumes, the Pythagorean theorem, and basic probability rules.

3Practice reading values from graphs, tables, and charts accurately, watching signs and units carefully.

4Work through complete 21-task variants under the 180-minute time limit to build pace and accuracy.

5Always check your final answer by substituting back or estimating, since each task is worth a full point and is graded only on the final answer.

Frequently Asked Questions

How many tasks are on the EGE Mathematics Base Level exam?

There are 21 short-answer tasks of basic difficulty, each worth 1 primary point, for a maximum of 21 primary points. The answer to each task is a whole number, a finite decimal, or a sequence of digits.

What score do I need to pass?

You need at least 7 of the 21 primary points to pass and receive your school certificate. Results are reported on a 5-point school grade scale (2-5), where 3 is the minimum passing grade.

How long is the exam?

The EGE Mathematics Base Level lasts 180 minutes (3 hours).

Can I use the Base level result to enter university?

No. Russian universities do not accept the Base level result for admission. Students who plan to apply to technical or mathematics-heavy programs take the Profile level instead.

Who administers the exam?

The EGE is administered nationally by Rosobrnadzor, with exam content (KIM) developed by FIPI, the Federal Institute of Pedagogical Measurements.

Is there an essay or extended-response part?

No. The Base level has a single part of 21 short-answer tasks; there is no extended written or essay section, unlike the Profile level.

100+ Free EGE Math (Base) Practice Questions

Russia EGE - Mathematics (Base Level)