Arithmetic Problems and Concepts

The average speed of an object is the total distance traveled divided by the total time taken.

A scalene triangle is a triangle where all three sides have different lengths.

The volume of a cuboid is calculated by multiplying its length, width, and height.

The area of a rectangle is calculated by multiplying its length and width.

A percentage is a way of representing a fraction out of 100.

The ratio of 6:5 can be expressed as 24:20 because both parts of the ratio are multiplied by 4.

14^3 means 14 multiplied by itself three times.

To convert imperial gallons to liters, you multiply by 4.546.

The process of removing roots from the denominator of a fraction.

A cylinder's volume is the space it occupies, calculated by multiplying the area of its base (πr²) by its height (h).

The curved surface area of a cylinder is the area of its side, excluding the top and bottom circles. It's calculated by multiplying the circumference (2πr) by its height (h).

The square root of a number is a value that, when multiplied by itself, equals that number. A positive number always has two square roots: one positive and one negative.

The cube root of a number is a value that, when multiplied by itself three times, results in the original number. A negative number has only one real cube root, which is also negative.

The square of a number, also known as the number squared, is the result of multiplying the number by itself. The square of a number is always positive.

The process of finding the cube of a number involves multiplying a number by itself three times. The cube of a number can be positive, negative, or zero, depending on the original number.

The value of a fraction is the same as the value of its equivalent decimal.

A percentage is a way of expressing a part of a whole as a fraction out of 100. To convert a fraction to a percentage, multiply by 100%.

To find the speed of a driven gear, multiply the speed of the driving gear by the ratio of the number of teeth on the driving gear to the number of teeth on the driven gear.

The piston displacement of a master cylinder is the volume of fluid it can displace when the piston moves through its entire stroke. It's calculated by multiplying the area of the piston face by the piston stroke.

The curved surface area of a right cone is the area of its slanted surface, excluding the base. It's calculated by multiplying half the circumference of the base by the slant height.

An equation is solved by isolating the variable on one side of the equation. This is done by performing the same operation on both sides of the equation until the variable is alone.

To make a variable the subject of a formula, you need to manipulate the formula so that the variable is isolated on one side of the equation.

The product of two binomials can be found by expanding them using the distributive property: FOIL (First, Outer, Inner, Last).

An angle measuring less than 90 degrees.

A straight line segment that connects two points on a circle's circumference.

A quadrilateral with two pairs of adjacent sides equal and diagonals intersecting at right angles. Not all sides are equal.

The y-value where the line crosses the y-axis. In the equation 4y = 2x + 8, the y-intercept is 2.

The rate at which a line rises or falls. It's calculated by dividing the change in y-values by the change in x-values.

A number that has a decimal part but no whole-number part.

The logarithm of a number to a given base is the exponent to which the base must be raised to produce that number. In this case, it's the power you raise 6 to get 3. It's not a simple whole number, but rather a mathematical value needing calculation.

An equation where the highest power of the variable is 2.

The logarithm of 1000 to the base 10 is 3, because 10 raised to the power of 3 equals 1000. (10 * 10 * 10 = 1000).

The logarithm of the product of two numbers is equal to the sum of the logarithms of those numbers.

The logarithm of the quotient of two numbers is equal to the difference of the logarithms of those numbers.

The circumference of a circle is calculated by multiplying the diameter by pi (π).

A triangle with two equal sides and two equal angles.

To evaluate an algebraic expression, substitute the given values for the variables and then simplify using order of operations (PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).

When multiplying exponents with the same base, add the powers together. (x^m * x^n = x^(m+n)).

To factorise an expression, rewrite it as a product of simpler expressions (usually two factors).

To solve for x in an equation, isolate x on one side of the equation by performing equivalent operations on both sides.

To make a variable the subject of an equation, rearrange the equation by isolating that variable on one side, using inverse operations.

To simplify an algebraic expression, combine like terms and apply the distributive property (to remove brackets).

Expanding brackets means multiplying each term inside one bracket by each term inside the other bracket.

To remove brackets and simplify, square each term inside the brackets and multiply the results.