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• FETMaths

This module and collection are included inLens: Siyavula: Mathematics (Gr. 10-12)
By: Siyavula

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Summary and exercises

Equations and inequalities: Summary and exercises

• A linear equation is an equation where the power of the variable(letter, e.g. xx) is 1(one). A linear equation has at most one solution
• A quadratic equation is an equation where the power of the variable is at most 2. A quadratic equation has at most two solutions
• Exponential equations generally have the unknown variable as the power. The general form of an exponential equation is: ka(x+p)=mka(x+p)=m
• A linear inequality is similar to a linear equation and has the power of the variable equal to 1. When you divide or multiply both sides of an inequality by any number with a minus sign, the direction of the inequality changes. You can solve linear inequalities using the same methods used for linear equations
• When two unknown variables need to be solved for, two equations are required and these equations are known as simultaneous equations. There are two ways to solve linear simultaneous equations: graphical solutions and algebraic solutions. To solve graphically you draw the graph of each equation and the solution will be the co-ordinates of the point of intersection. To solve algebraically you solve equation one, for variable one and then substitute that solution into equation two and solve for variable two.
• Literal equations are equations where you have several letters (variables) and you rearrange the equation to find the solution in terms of one letter (variable)
• Mathematical modelling is where we take a problem and we write a set of equations that represent the problem mathematically. The solution of the equations then gives the solution to the problem.

End of Chapter Exercises

1. What are the roots of the quadratic equation x2-3x+2=0x2-3x+2=0

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2. What are the solutions to the equation x2+x=6x2+x=6

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3. In the equation y=2x2-5x-18y=2x2-5x-18, which is a value of xx when y=0y=0

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4. Manuel has 5 more CDs than Pedro has. Bob has twice as many CDs as Manuel has. Altogether the boys have 63 CDs. Find how many CDs each person has.

5. Seven-eighths of a certain number is 5 more than one-third of the number. Find the number.

6. A man runs to a telephone and back in 15 minutes. His speed on the way to the telephone is 5 m/s and his speed on the way back is 4 m/s. Find the distance to the telephone.

7. Solve the inequality and then answer the questions: x3-14>14-x4x3-14>14-x4
1. If xâˆˆRxâˆˆR, write the solution in interval notation.
2. if xâˆˆZxâˆˆZ and x<51x<51, write the solution as a set of integers.

8. Solve for aa: 1-a2-2-a3>11-a2-2-a3>1

9. Solve for xx: x-1=42xx-1=42x

10. Solve for xx and yy: 7x+3y=137x+3y=13 and 2x-3y=-42x-3y=-4


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Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

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| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks