BASIC ALGEBRA Some variable expressions may be simplified. The expression above can be simplified by collecting like terms. Like terms can be collected or grouped together, while unlike terms cannot. For example 2x 2 - 3y - z + 5y + 6 contains both like and unlike terms. In the expression, 3y and 5y are like terms because both have the same variable part: y. The like terms are collected by adding their coefficients together taking into consideration their signs in the expression. Thus, we add together -3y + 5y and get +2y. Therefore: 2x 2 - 3y - z + 5y +6 = 2x 2 - z + 2y +6

BASIC ALGEBRA To isolate x, we multiply both sides by the coefficient that is dividing x. For example, if a = 2 and c = 5: x / a = c x / 2 = 5 (2) x / 2 = 5 (2) x = 10

BASIC ALGEBRA If a = 2, b = 5, and c = 19 in the equation ax + b = c, we can solve for x. ax + b = c Substituting: 2x + 5 = 19 Subtract 5 from each side: 2x = x = 14 Divide each side by 2 2x / 2 = 14 / 2 x = 7

BASIC ALGEBRA Given the equation, x = 2a + 5, solve for x when a = 8. x = 2a + 5 Substituting: x = 2 x Simplifying: x = x 2 = 25 Take the square root of both sides: x 2 = 25 Simplify: x = 5 Therefore the solution is x = 5.

TRIANGLE A triangle is a three sided figure. Three angles are formed by the intersection of the sides. In a triangle, the total of the three angles is always equal to 180º no matter what the shape of the triangle or how large it is. An important triangle is the right angle triangle or as it is often called the right triangle. The right triangle gets its name from the fact that one angle is a 90 o or right angle. The sum of the other two angles contained is equal to 90º. The side opposite to the 90º angle is called the hypotenuse. Triangles that have two sides equal are called isosceles triangles. In the isosceles triangle the angles opposite the equal sides are equal.

TRIANGLE

CIRCLE A circle is a plane figure made up of a curved line which is always equidistant from a point called the center. A straight line drawn from one point on the circle to another and passing through the center is called the diameter. The radius of a circle is a straight line drawn from the center to the edge. The length of the diameter of a circle is always 2x the length of the radius.

CIRCLE

PERIMETER OF GEOMETRIC FIGURES

AREA OF GEOMETRIC FIGURES

Work WORK = FORCE x DISTANCE WORK = Newtons x meters WORK = Nm (Joules) The units of work are Newton meters or Nm. Nm are also called Joules. In the SI system, work is most often expressed in Joules. A Joule is a relatively small unit in industry so kilojoules (kJ) or megajoules (MJ) may be used instead. Kilojoules are determined by dividing Joules by 1000 and megajoules are determined by dividing Joules by 1,000,000.

POWER Power is defined as the rate of doing work. When the same amount of work is done in a shorter period of time, greater power is required. The units for time are seconds and the units for work are Nm or Joules (J).

ENERGY Energy is the ability to do work. There are many forms of energy. Heat is a form of energy that can be produced by combustion. The sun and nuclear power plants provide us with energy which is transformed into electrical energy. Electrical energy can be transformed into heat or mechanical energy as in an electric motor to do mechanical work. Energy can be neither created nor destroyed. It can and often is transformed from one form to another to do the work.

POTENTIAL ENERGY Potential energy is the energy that a body possesses by virtue of its position. A body that is suspended in the air above the ground has the potential to do work on the ground or any point below it. A brick that is suspended at a height has the ability to do work if dropped on the object that it hits. This will be immediately apparent if the object the brick works on, is your toe. The potential energy a body possesses is related to the mass of the object and the height the mass is above some reference point. The potential energy of the body exists because of its mass and its height above a point. POTENTIAL ENERGY (PE) = MASS(kg) x 9.81 (N/kg) x HEIGHT(m)

KINETIC ENERGY Kinetic Energy is energy that a body possesses by virtue of its motion. A car possesses energy when it is traveling down the highway. The kinetic energy of the car will vary directly with its velocity squared. If the car crashes into a tree the car demonstrates an ability to do work. The damage to the car and tree are evidence of the work done by the car on itself and whatever it hits.

LEVERS AS SIMPLE MACHINES Simple machines are devices that enable us to multiply our ability to exert forces. Simple machines are used to make the complex machines. A lever consists of a rigid bar that is arranged so that it will pivot about a point (fulcrum) so that a resistance or load can be overcome by a force or effort. One of the major reasons for using a lever is so a large load can be lifted with relatively small effort. EFFORT x EFFORT DISTANCE = LOAD x LOAD DISTANCE L / E = D E / D L

Mechanical Advantage mechanical advantage (MA) is the factor by which a mechanism multiplies the force put into it. The ratio of the load lifted to the effort applied is the advantage we obtain from using the machine. This is called the Mechanical Advantage. The ideal mechanical advantage is the mechanical advantage of an ideal machine. It is usually calculated using physics principles because there is no ideal machine. It is 'theoretical.‘ideal machine The IMA of a machine can be found with the following formula: – Where –DE equals the –DR equals the resistance distanceresistance distance

SIMPLE MACHINES - EFFICIENCY The efficiency of a simple machine is: