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Quizzes > High School Quizzes > Mathematics

Simulacro ICFES Practice Quiz

Sharpen skills with real exam simulation challenges

Difficulty: Moderate
Grade: Grade 11
Study OutcomesCheat Sheet
Colorful paper art promoting Reto ICFES, an interactive quiz for high school students.

Solve for x: 2x + 3 = 7.
2
3
1
4
Subtracting 3 from both sides gives 2x = 4, and dividing by 2 results in x = 2. This is a basic example of solving a linear equation.
What is the perimeter of a rectangle with a length of 5 units and a width of 3 units?
16 units
15 units
11 units
8 units
The perimeter of a rectangle is calculated as 2*(length + width). Here, 2*(5 + 3) equals 16 units.
Identify the subject in the sentence: 'The quick brown fox jumps over the lazy dog.'
the lazy dog
jumps
The quick brown fox
over
The subject of a sentence is the noun or noun phrase performing the action. In this sentence, 'The quick brown fox' is the subject that performs the action 'jumps'.
Which of the following sentences is punctuated correctly?
It is too late to go home.
Its' too late, to go home.
It's too late, to go home.
Its too late to go home.
Option C is punctuated correctly with proper spelling and no unnecessary commas. The sentence clearly and correctly conveys its meaning.
In a sentence, a synonym is a word that:
rhymes with another word.
sounds similar to another word.
is spelled similarly to another word.
has a similar meaning to another word.
A synonym is defined as a word that has the same or nearly the same meaning as another word. This basic concept is essential in vocabulary and language studies.
Solve the quadratic equation: x² - 5x + 6 = 0.
x = 1 and x = 6
x = -2 and x = -3
x = 2 and x = -3
x = 2 and x = 3
The quadratic factors as (x - 2)(x - 3) = 0, yielding x = 2 or x = 3. This is a standard method for solving quadratic equations by factoring.
Factorize the expression: x² - 9.
(x - 9)(x + 1)
(x - 9)(x - 1)
x(x - 9)
(x - 3)(x + 3)
x² - 9 is a difference of squares and factors neatly into (x - 3)(x + 3). Recognizing this pattern is key in algebraic factorization.
Given f(x) = 3x - 4, what is the value of f(5)?
11
14
16
15
By substituting 5 into the function, we calculate f(5) = 3(5) - 4 = 15 - 4, which equals 11. This is a direct application of function evaluation.
Solve the system of equations: x + y = 6 and x - y = 2.
x = 3, y = 3
x = 2, y = 4
x = 4, y = 2
x = 5, y = 1
Adding the equations gives 2x = 8, so x = 4. Substituting x = 4 into one of the equations yields y = 2, which satisfies both equations.
Read the following sentence: 'Despite the heavy rain, the match continued uninterrupted.' What best describes the role of the phrase 'Despite the heavy rain'?
It describes the outcome of the event.
It shows contrast, highlighting that the match continued despite adverse conditions.
It provides the reason for the match.
It emphasizes the intensity of the rain.
The phrase 'Despite the heavy rain' introduces a contrast between the unfavorable weather and the continuation of the match. It indicates that the match persisted even under adverse circumstances.
Choose the sentence that is grammatically correct.
Each of the students have finished their assignment.
None of the books is available now.
Neither of the answers are correct.
Every student was given a clear assignment.
Option C demonstrates proper subject-verb agreement and clear structure. It avoids the common errors of pluralization and verb mismatch found in the other options.
If a fair six-sided die is rolled once, what is the probability of rolling a number greater than 4?
2/3
1/6
1/2
1/3
There are 6 equally likely outcomes, and only the outcomes 5 and 6 are greater than 4. Thus, the probability is 2/6, which simplifies to 1/3.
In similar triangles, corresponding angles are equal. Which of the following statements is true?
The ratios of corresponding sides are equal.
Similar triangles have proportional altitudes only.
The sums of the interior angles of similar triangles are different.
The areas of similar triangles are equal.
One of the key properties of similar triangles is that their corresponding sides are proportional, making option B the correct answer. This proportionality is essential in many geometric proofs.
In literature, a metaphor is best described as:
A humorous or sarcastic remark.
A direct comparison using 'like' or 'as'.
A figure of speech that describes one thing as if it were another.
An exaggerated statement not meant to be taken literally.
A metaphor asserts that one thing is another, offering a direct comparison without using 'like' or 'as'. This enriches language by providing deeper meaning through symbolic representation.
If a car travels 150 kilometers in 3 hours, what is its average speed in km/h?
60 km/h
50 km/h
55 km/h
45 km/h
Average speed is determined by dividing total distance by total time. In this case, 150 km divided by 3 hours equals 50 km/h.
Solve for x: 3(x - 2)² = 12.
x = 1 or x = 3
x = 2 ± √12
x = 0 or x = 4
x = 2 or x = -2
Dividing both sides by 3 gives (x - 2)² = 4. Taking the square root of both sides leads to x - 2 = ±2, so x = 0 or x = 4. This is a standard method for solving quadratic equations presented in squared form.
In a right triangle, if one acute angle is 30° and the hypotenuse measures 10 units, what is the length of the side opposite the 30° angle?
8.66 units
10 units
5 units
√10 units
In a 30-60-90 right triangle, the side opposite the 30° angle is exactly half the length of the hypotenuse. Thus, with a 10 unit hypotenuse, the side length is 5 units.
Solve for x: ln(x) = 3.
x = 3
x = e³
x = ln(3)
x = 1/3
The equation ln(x) = 3 means that x is the exponential of 3, because the natural logarithm is the inverse function of the exponential function. Therefore, x = e³.
Analyze the following excerpt and determine the predominant literary tone: 'In the midst of chaos, there lies a silent order, a calm that surpasses the clamor of the storm.'
Ironic
Optimistic
Reflective
Melancholic
The excerpt invites contemplation by contrasting chaos with an underlying calm, suggesting a reflective tone. It is not overtly optimistic or ironic, but instead encourages deep thought.
Given the system of equations: 2x + 3y = 12 and 4x - y = 5, solve for x and y.
x = 27/14, y = 19/7
x = 2, y = 2
x = 3, y = 1
x = 27/14, y = 5/7
By rearranging the second equation to y = 4x - 5 and substituting into the first, the system simplifies to 14x = 27, resulting in x = 27/14. Substituting back gives y = 19/7, which satisfies both equations.
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Study Outcomes

  1. Understand core mathematical concepts essential for exam success.
  2. Analyze language comprehension and grammar challenges.
  3. Apply problem-solving techniques under simulated test conditions.
  4. Evaluate performance results for targeted exam preparation.
  5. Synthesize study strategies from interactive practice exercises.

Simulacro ICFES Practice Test Cheat Sheet

  1. Master the Order of Operations (PEMDAS) - Don't let tricky equations chaos your brain! Always start with Parentheses, then tackle Exponents, followed by Multiplication and Division (left to right), and finish with Addition and Subtraction (left to right). With enough practice, you'll breeze through any multi”step problem like a math ninja. Brainscape Flashcards
  2. Understand Divisibility Rules - Speed up your number crunching by knowing simple shortcuts: a number is divisible by 3 if its digits add up to a multiple of 3, and by 9 if the digit sum is a multiple of 9. These little tricks save time and chemical brain cells during contests and exams. Soon you'll spot divisible numbers in a single glance! Brainscape Flashcards
  3. Learn Exponent Properties - Power up your simplifying skills with rules like a^m × a^n = a^(m+n) and (a^m)^n = a^(m×n). These properties help you condense giant expressions into sleek, manageable forms. Practice these until they become your superpower for tackling algebra equations. Brainscape Flashcards
  4. Memorize Area & Perimeter Formulas - From rectangles to triangles, knowing that Area = base×height or ½×base×height, and Perimeter = sum of sides, is key. Geometry problems fall apart without these staples, so quiz yourself until they're second nature. Soon you'll be sketching shapes and calculating measurements in your sleep! Scribd Basic Geometry Formulas
  5. Convert Between Fractions, Decimals & Percentages - Flip, stretch, or shrink numbers by moving decimal points or multiplying by 100 to switch formats. For example, 0.75×100 becomes 75%, while 3/8 → 0.375 → 37.5%. Mastering these conversions makes data interpretation and real”world calculations a breeze. Knowunity ICFES Math Prep
  6. Apply the Pythagorean Theorem - In any right triangle, a² + b² = c², where c is the hypotenuse. This timeless relationship lets you find missing sides quickly and check if triangles are right-angled. Practice on different examples until this formula jumps off the page into your memory. Scribd Pythagorean Guide
  7. Use the Quadratic Formula - For ax² + bx + c = 0, the roots come from x = (−b ± √(b²−4ac))❄(2a). This one”and”done tool solves any quadratic without guessing factors. Keep this formula on your mental speed dial and watch quadratics surrender instantly. Knowunity Quadratic Toolkit
  8. Grasp Functions & Their Behavior - Understand domain, range, and the shapes of linear, quadratic, and exponential functions to predict how graphs behave. Recognizing a function's pattern helps you solve equations and model real”life scenarios like population growth. Visual practice will cement these concepts for test day. Pearson Study Guide
  9. Master Basic Probability - Calculate the chance of single events (like rolling a 3 on a die is 1/6) and combine probabilities for multiple events. Understanding independent versus dependent events gives you an edge in statistics questions. Turn randomness into a strategic advantage with a bit of practice. Pearson Probability Basics
  10. Build Problem”Solving Strategies - Break complex problems into bite”sized steps, spot patterns, and apply logical reasoning to conquer even the toughest questions. Developing these critical”thinking muscles makes you a more confident test taker and a sharper thinker overall. Practice these strategies in mock tests to see your score skyrocket. Knowunity Strategy Guide
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