Mathematics Test Jss 1

The given expression is a quadratic equation in the form of ax^2 + bx + c. To find the factors, we need to factorize the equation. By using the product-sum method or trial and error, we can determine that the factors of 8x^2 - 13x + 5 are (8x - 5) and (x - 1).

The equation 5/8 = -(-5/-8) is true because when we simplify the right side of the equation, we get -(-5/-8) = -(5/8) = -5/8. Therefore, the left side of the equation is equal to the right side, making the equation true.

The prime factorization of 6 is 2 * 3. This means that 6 can be expressed as the product of the prime numbers 2 and 3.

In a plane, lines are said to be concurrent if they intersect at the same point. The correct answer is "Three or More" because when three or more lines intersect at a single point, they are considered to be concurrent.

The given expression is (8-4)-9. First, we solve the subtraction inside the parentheses: 8-4 = 4. Then, we subtract 9 from 4, which gives us -5. Therefore, the correct answer is -5.

The difference between a mathematical equation and a mathematical expression lies in the presence of the equal sign. An equation includes an equal sign, indicating that two expressions are equal to each other. On the other hand, an expression does not have an equal sign and represents a mathematical statement without asserting equality.

The statement "All fractions are rational" is false because there are fractions that are not rational, such as irrational numbers like π or √2. Rational numbers can be expressed as a ratio of two integers, whereas fractions like π cannot be written in the form of a ratio. Therefore, not all fractions are rational.

An angle is formed by two rays with the same endpoint. The rays are called the sides of the angle and the common endpoint is called the vertex. The angle is the space between the two rays, which can be measured in degrees. Angles are used to describe the amount of turn or rotation between two lines or surfaces. They are an important concept in geometry and are used in various fields such as engineering, architecture, and physics.

The given equation, 9 × (1 × 4) = (9 × 1) × 4, demonstrates the property of associativity in multiplication. This property states that the grouping of numbers being multiplied does not affect the final product. In this case, regardless of whether we multiply 1 and 4 first or 9 and 1 first, the end result will be the same.

Based on the given data, out of the recent 10 vases produced, 2 were chipped and 8 were not. This means that 20% of the vases produced were chipped. Therefore, if we apply the same percentage to the next 20 vases, we would expect 4 of them to be chipped.

When two lines intersect, the angles that are opposite each other are called vertical angles. Vertical angles are congruent, meaning they have the same measure. Therefore, the correct answer is vertical angles.

A point is a basic geometric entity that has no dimension. It is represented by a dot and does not have any length, width, or height. It is considered to be a location in space and is used to define other geometric objects such as lines, planes, and angles. Unlike lines, planes, and angles, which have measurable dimensions, a point is considered to be dimensionless. Therefore, the statement "It has no dimension" is a characteristic that specifically applies to a point.

The set {1, 2, 3, 4, 5} is not a subset of set A = {1, 4, 9, 16, 25} because it contains elements that are not present in set A. Set A only contains the squares of the numbers 1 to 5, so any set that includes numbers other than 1, 4, 9, 16, or 25 cannot be a subset of set A.

A plane is a flat surface that extends infinitely in all directions. It has no thickness or boundaries. It can be thought of as a two-dimensional surface that goes on forever. Unlike a line or line segment, which are one-dimensional, a plane has length and width. Therefore, the correct answer is plane.

Adjacent angles are two angles that share a common vertex and a common side, but do not overlap. In other words, they are side by side and do not intersect.

Jan started with 25 model airplanes. This year, she has 32% more, which is 0.32 * 25 = 8 model airplanes. So, she has a total of 25 + 8 = 33 model airplanes. After giving 6 to her brother, she has 33 - 6 = 27 model airplanes remaining.

The electric consumption can be calculated by multiplying the power rating (65 W) by the time it is used (3 hours) and converting it to kilowatt-hours. So, 65 W x 3 hours = 195 Wh. Since 1 kilowatt-hour (kWh) is equal to 1000 watt-hours (Wh), we divide 195 Wh by 1000 to get the consumption in kWh, which is 0.195 kWh.

A line is a collection of points that extends infinitely in opposite directions. It does not have any endpoints and continues indefinitely. A line can be thought of as a straight path that goes on forever in both directions.

The given answer "Collinear" is correct because collinear points are points that lie on the same line. In this case, the question asks if the points are on the same line, and "Collinear" is the term that specifically refers to points on the same line. Therefore, the points mentioned in the question are collinear.

When the sum of the measures of two angles is 90 degrees, they are called complementary angles. Complementary angles are two angles that add up to form a right angle. In this case, since the sum of the measures of the two angles is 90 degrees, they are complementary angles.

The absolute value of a number is its distance from zero on the number line. In this case, |-9| is asking for the distance of -9 from zero. Since -9 is 9 units away from zero in the negative direction, the absolute value of -9 is 9.

Skew lines are lines that do not lie on the same plane and do not intersect. Therefore, it is correct to say that these two lines do not lie on a plane.

The sequence is formed by adding the previous three terms. Starting with 1, 1, 2, the next term is obtained by adding 1 + 2 + 4 = 7. Similarly, the next term is obtained by adding 2 + 4 + 7 = 13, and so on. Therefore, the next three terms in the sequence are obtained by adding 4 + 7 + 13 = 24, 7 + 13 + 24 = 44, and 13 + 24 + 44 = 81. Hence, the correct answer is 44, 81, 149.

In the expansion of (x + y + 3)2, all the terms will be obtained by multiplying the terms in the binomial (x + y + 3) twice. The term 6xy is not present in the expansion because it cannot be obtained by multiplying any combination of the terms in the binomial. The terms in the expansion will be x^2, xy, 3x, y^2, 3y, and 9.

Adjacent angles are formed by intersecting lines that are supplementary and are next to each other. Adjacent angles share a common vertex and a common side. In this case, since the intersecting lines are supplementary (add up to 180 degrees) and are next to each other, the correct answer is adjacent angle.

An adjacent angle is defined as an angle that shares a common side and a common vertex with another angle. This means that the two angles are right next to each other and share a common point and a common line segment. Adjacent angles are commonly found in geometric figures and can be used to determine relationships between angles in a shape.

The International System of Units or SI is internationally recognized and widely used by nearly all countries in the world. It is a decimal-based system of measurement that provides a standardized way to measure various physical quantities such as length, mass, time, and temperature. The SI system is used in fields such as science, engineering, and industry, ensuring consistency and uniformity in measurements across different countries and disciplines.

When angles form a linear pair, it means they are adjacent (share a common vertex and side) and their non-common sides form a straight line. In this case, the angles are supplementary, meaning their measures add up to 180 degrees. Therefore, the correct statement is that they are adjacent and supplementary.

The given representation (-4) corresponds to the pattern (+)(-)(+)(-)(-)(-)(-)(-). This pattern indicates that there are 4 negative signs (-) alternating with 4 positive signs (+).

Vertical angles are formed by intersecting lines that are on the diagonals and have the same measure. Vertical angles are opposite angles formed by the intersection of two lines. They are congruent, meaning they have the same measure. In other words, if one angle measures x degrees, then the other angle will also measure x degrees. Therefore, vertical angle is the correct answer.

A collinear line refers to a set of points that lie on the same straight line. In the given figure, the points are arranged in a straight line, indicating that they are collinear. Therefore, the correct answer is "Collinear line".

If lnl = 8, it means that the absolute value of n is 8. Therefore, n can be either -8 or 8, as both of these values have an absolute value of 8. So, both option a (-8) and option c (8) can replace n.

The given question is asking for the angle shown below. The correct answer is "Adjacent angle." An adjacent angle is an angle that shares a common side with another angle and has a common vertex. In this case, the angle shown below is adjacent to another angle, as they share a common side and vertex.

The surface area of a rectangular box can be found by adding up the areas of all its sides. In this case, the aquarium has six sides: a bottom, a top, a front, a back, a left side, and a right side. The area of each side can be found by multiplying the length by the width. The bottom and top have the same dimensions, so their areas are the same. The front and back also have the same dimensions, as do the left and right sides. Thus, the surface area of the aquarium is equal to twice the sum of the areas of the bottom, front, and left side. By plugging in the given dimensions, we find that the surface area is 9400 cm2.

The given series does not follow a typical mathematical pattern. However, upon closer observation, we can see that each number in the series is obtained by multiplying the previous number by the sum of its digits and then adding 1. For example, 1 * (1+0) + 1 = 2, 2 * (2+0) + 1 = 6, and so on. Applying the same pattern to the last number in the series, 1806 * (1+8+0+6) + 1 = 3263442. Therefore, the next number in the series is 3263442.

The cardinality of a set refers to the number of elements in the set. The empty set, also known as the null set, is a set that contains no elements. Therefore, the cardinality of the empty set is 0, as there are no elements to count.

The set of natural numbers is an infinite set because it includes all positive whole numbers starting from 1 and continuing indefinitely. It does not have an endpoint or a largest number, so it goes on forever. In contrast, the empty set has no elements and is finite, while the universal set contains all possible elements but can still be finite if it has a specific limit or endpoint.

The equation (5)(3+4)=(5)(3)+(5)(4) demonstrates the distributive property. This property states that when multiplying a number by a sum of two or more numbers, you can distribute the multiplication to each term inside the parentheses. In this equation, the number 5 is being multiplied by the sum (3+4), and according to the distributive property, we can multiply 5 by each term inside the parentheses separately. This results in (5)(3) + (5)(4), which shows the distributive property in action.

Vertical angles are formed when two lines intersect. They are opposite angles that share the same vertex but do not have to be next to each other. The sum of the measures of vertical angles is always equal to 180 degrees. Therefore, the correct answer is "Opposite angles formed by intersecting lines."

The expression 5(x - y) represents "five times the difference of x and y." This can be understood by breaking down the expression: 5 multiplied by (x - y). Since (x - y) represents the difference between x and y, multiplying it by 5 gives us "five times the difference of x and y."

The mean is not the correct answer because it is the average of all the data points and does not necessarily divide the data set into two equal halves. The mode is not the correct answer either because it represents the value that appears most frequently in the data set and does not divide the data set into two halves. The range is not the correct answer because it is the difference between the maximum and minimum values in the data set and does not divide the data set into two halves. The correct answer is the median because it is the middle value in the data set when arranged in ascending or descending order, dividing the data set into two equal halves.

The equation 1 = 3 - 2x is not equivalent to 3 + 2x = 1 because the terms are arranged in a different order. In the original equation, the constant term (1) is on the right side, while in the given equation, it is on the left side. Additionally, the coefficients of x have opposite signs in the two equations.

Collinear points are points that lie on the same line. If a line can be drawn through a set of points, it means that those points are collinear. Coplanar points, on the other hand, lie in the same plane, but not necessarily on the same line. Vertical points refer to points that lie on the same vertical line. Noncollinear points are points that do not lie on the same line. Therefore, the correct answer is Collinear.

The given answer lists the different parts of a polygon, which include vertices, sides, angles, and diagonals. A vertex is a point where two or more sides of a polygon meet. Sides are the line segments that form the boundaries of a polygon. Angles are formed at each vertex when two sides meet. Diagonals are line segments that connect non-adjacent vertices of a polygon. Therefore, the answer correctly identifies the various components of a polygon.

The equation x^3 - x = 0 can be factored as x(x^2 - 1) = 0. This implies that either x = 0 or x^2 - 1 = 0. Solving the second equation, we get x = 1 or x = -1. Therefore, all of the given options (-1, 0, 1) are solutions to the equation x^3 - x = 0.

The degree of a polynomial is determined by the highest power of the variable in the polynomial. In this case, the highest power of the variable "y" is 5, therefore the degree of the polynomial x^3 - 9x^2y + 7xy^2 + y^5 is 5.

A dodecagon is a polygon with 12 sides. To find the number of diagonals that can be drawn in a dodecagon, we can use the formula n(n-3)/2, where n is the number of sides. Plugging in 12 for n, we get 12(12-3)/2 = 12(9)/2 = 108/2 = 54. Therefore, the correct answer is 54.