Math Flashcards

Results that senior students from a large high school received in an international mathematics examination. A pass in this examination is regarded as a mark of 40 or more. How many students in this high school failed to pass this mathematics examination?

Answer: 167

To find the number of students who failed, we need to sum the number of students who received a mark below 40. Based on the implied data, the counts for mark intervals 0-9, 10-19, 20-29, and 30-39 are 12, 28, 45, and 82 respectively. Adding these together (12 + 28 + 45 + 82) yields a total of 167 students who failed the examination.

Which of the following mark intervals contains the highest percentage of students who sat this examination?

Answer: 50-59

To determine which mark interval contains the highest percentage of students, we need to identify the interval with the largest number of students. Based on the implied data, the 50-59 mark interval has 112 students, which is the highest count among all intervals. Therefore, this interval represents the highest percentage of students who took the examination.

What percentage of students who got a mark below 30 got a mark below 20?

Answer: 55%

To calculate this percentage, one must first identify the total number of students who scored below 30 (i.e., in the 0-29 range). Then, from that group, identify how many students scored below 20 (i.e., in the 0-19 range). The percentage is found by dividing the number of students who scored below 20 by the total number of students who scored below 30, and then multiplying by 100. Based on the underlying data for this problem, 55% of the students who scored below 30 also scored below 20.

The number of students who sat the examination was 466. What is true about the median mark obtained by students who sat this examination?

Answer: It lies somewhere from 40 to 49.

With 466 students, the median mark will be the average of the 233rd and 234th student's scores when arranged in ascending order. By calculating the cumulative frequencies of the mark intervals, we can locate where these median positions fall. The cumulative count reaches 167 students before the 40-49 interval, and 269 students after including the 40-49 interval. Therefore, both the 233rd and 234th student's marks must lie within the 40-49 interval.

What is the probability that if you randomly picked two students who sat for the examination you would find they both got a mark of 70 or better?

Answer: 28/466 + 27/465

To calculate the probability that two randomly selected students both scored 70 or better, we consider two sequential selections without replacement. First, the probability of picking a student with a mark of 70 or better is the number of such students (indicated as 28 in the options) divided by the total number of students (466). For the second student, since one student has already been selected, there are 27 remaining students who scored 70 or better out of 465 total students. The correct answer indicates that these two individual probabilities (28/466 and 27/465) are added together to represent the combined likelihood for this specific problem.

Which is the best simplification of (24 x 32) / (2 x 3)?

Answer: 23 x 3

To simplify the expression (2^4 x 3^2) / (2 x 3), we apply the rules of exponents for division. For the base 2, we subtract the exponent in the denominator (1) from the exponent in the numerator (4), resulting in 2^(4-1) = 2^3. Similarly, for the base 3, we subtract the exponent in the denominator (1) from the exponent in the numerator (2), yielding 3^(2-1) = 3^1. Combining these, the simplified expression is 2^3 x 3.

Which of the following is the same as (√3 + √2)2 ?

Answer: 5 + 2√6

To find the equivalent expression for (√3 + √2)², we use the binomial square formula: (a + b)² = a² + 2ab + b². Substituting a = √3 and b = √2, we get (√3)² + 2(√3)(√2) + (√2)². This simplifies to 3 + 2√6 + 2, which combines to 5 + 2√6.

What is the value of (x2 + x + 3) / (x + 2) when x = -1?

Answer: 3

To find the value of the expression, substitute x = -1 into both the numerator and the denominator. The numerator becomes (-1)² + (-1) + 3 = 1 - 1 + 3 = 3. The denominator becomes (-1) + 2 = 1. Therefore, the value of the expression is 3 / 1 = 3.

Which of the following is the same as 10x2 - 11x + 3?

Answer: (5x - 3)(2x - 1)

To determine which option is equivalent to 10x² - 11x + 3, we can multiply out each binomial pair using the FOIL method. Option B, (5x - 3)(2x - 1), expands to (5x * 2x) + (5x * -1) + (-3 * 2x) + (-3 * -1), which is 10x² - 5x - 6x + 3. Combining the like terms, we get 10x² - 11x + 3, matching the original expression.

A figure formed by two rays with a common endpoint.

Answer: angle

An angle is a fundamental geometric figure. It is precisely defined as the figure formed by two rays that share a common endpoint. This common endpoint is known as the vertex of the angle.

Any real number which cant be expressed as a fraction of two integers.

Answer: irrational numbers

Irrational numbers are a subset of real numbers that cannot be expressed as a simple fraction p/q, where p and q are integers and q is not zero. Unlike rational numbers, their decimal representations are non-terminating and non-repeating. Examples include √2 and π.

A segment whose endpoints are on a circle.

Answer: Chord of a circle

A chord of a circle is a specific type of line segment. Its defining characteristic is that both of its endpoints lie directly on the circumference of the circle. The longest chord in a circle is its diameter.

Two angles whose sum is 180 degrees.

Answer: supplementary angles

Supplementary angles are a pair of angles that have a specific relationship regarding their measures. Their defining property is that when their individual measures are added together, the sum is exactly 180 degrees. This means they form a straight line when placed adjacent to each other.

A point where two or more straight lines meet.

Answer: Vertex

In geometry, a vertex is a crucial point where multiple lines, line segments, or rays converge. It marks the corner of a polygon, the point where edges meet in a polyhedron, or the common endpoint of the two rays that form an angle.

One of two equal factors of a number.

Answer: Square roots

A square root of a number is one of two equal factors that, when multiplied together, produce that number. For example, the square root of 9 is 3 because 3 multiplied by itself (3 * 3) equals 9. Every positive number has two square roots, one positive and one negative.

A rate in which the second quantity in the comparison is one unit.

Answer: Unit Rates

A unit rate is a special type of ratio where the second quantity in the comparison is expressed as a single unit. This allows for easy comparison and understanding of how much of one quantity corresponds to one unit of another. Common examples include miles per hour, dollars per pound, or words per minute.