Grade 8 Mathematics Study Guide PDF Download 2020
Are you looking for a way to ace your grade 8 mathematics exam? Do you want to review the key concepts, skills, and formulas that you need to know? If so, then you might benefit from a study guide that can help you prepare for your test.
grade 8 mathematics study guide pdf download 2020
A study guide is a document that summarizes the main topics, terms, and examples that are covered in a specific subject or course. It can help you organize your study time, reinforce your understanding, and test your knowledge. A study guide can also provide you with tips, tricks, and strategies that can boost your confidence and performance.
In this article, we will show you how to download a free grade 8 mathematics study guide pdf from reliable sources. We will also give you an overview of the main topics that are included in the grade 8 mathematics curriculum, such as numbers and operations, solving equations, linear equations and functions, geometry, and more. We will provide you with examples, exercises, and answers that can help you practice and master these topics.
Ready to get started? Let's dive in!
Numbers and Operations
Numbers and operations are the foundation of mathematics. They involve working with different types of numbers, such as fractions, decimals, integers, rational numbers, irrational numbers, etc. They also involve performing different operations on these numbers, such as addition, subtraction, multiplication, division, exponentiation, etc.
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In grade 8 mathematics, you will learn how to convert fractions and decimals, how to find square roots and use exponents, how to estimate with multiplying and dividing decimals, how to use powers of ten, and more. Here are some of the subtopics that you will encounter in this section:
Converting fractions and decimals
Fractions and decimals are two ways of representing parts of a whole. Fractions use numerators and denominators to show how many parts out of a total number of equal parts are taken. Decimals use place values to show how many tenths, hundredths, thousandths, etc. are taken.
To convert a fraction to a decimal, you can divide the numerator by the denominator. For example, to convert 3/4 to a decimal, you can divide 3 by 4 and get 0.75.
To convert a decimal to a fraction, you can write the decimal as a fraction with a denominator of 10, 100, 1000, etc. depending on the number of decimal places. Then, you can simplify the fraction by dividing both the numerator and the denominator by a common factor. For example, to convert 0.6 to a fraction, you can write it as 6/10 and simplify it by dividing both by 2 and get 3/5.
Here are some examples and exercises with answers for converting fractions and decimals:
ExampleAnswer
Convert 2/5 to a decimalDivide 2 by 5 and get 0.4
Convert 0.125 to a fractionWrite it as 125/1000 and simplify it by dividing both by 125 and get 1/8
Convert 7/8 to a decimalDivide 7 by 8 and get 0.875
Convert 0.75 to a fractionWrite it as 75/100 and simplify it by dividing both by 25 and get 3/4
Square roots and exponents
Square roots and exponents are two ways of expressing repeated multiplication. Square roots are the inverse of squaring, which means multiplying a number by itself. Exponents are the shorthand notation for repeated multiplication of the same number.
To find the square root of a number, you can use prime factorization or estimation methods. Prime factorization involves breaking down the number into its prime factors and grouping them into pairs. Then, you can take one factor from each pair and multiply them together to get the square root. For example, to find the square root of 36, you can write it as 2 x 2 x 3 x 3 and group it as (2 x 2) x (3 x 3). Then, you can take one factor from each pair and multiply them together to get 6.
Estimation involves finding two perfect squares that are close to the number and using them as lower and upper bounds. Then, you can use trial and error or average method to find a closer approximation of the square root. For example, to find the square root of 50, you can use 49 and 64 as lower and upper bounds, since they are perfect squares of 7 and 8 respectively. Then, you can try different numbers between 7 and 8 until you find one that is close enough to the square root of 50. Alternatively, you can use the average method and take the average of 7 and 8, which is 7.5, and check if it is close enough to the square root of 50. If not, you can repeat the process and take the average of 7.5 and 8, which is 7.75, and check again. You can continue this process until you find a satisfactory answer.
To use exponent rules, you need to know the following properties of exponents:
Product rule: To multiply two powers with the same base, add their exponents. For example, x^2 x x^3 = x^(2+3) = x^5.
Quotient rule: To divide two powers with the same base, subtract their exponents. For example, x^5 / x^2 = x^(5-2) = x^3.
Power rule: To raise a power to another power, multiply their exponents. For example, (x^2)^3 = x^(2x3) = x^6.
Zero exponent rule: Any nonzero number raised to the zero power is equal to one. For example, x^0 = 1.
Negative exponent rule: Any nonzero number raised to a negative power is equal to the reciprocal of the number raised to the positive power. For example, x^-2 = 1 / x^2.
Here are some examples and exercises with answers for finding square roots and using exponents:
ExampleAnswer
Find the square root of 64Use prime factorization and write 64 as 2 x 2 x 2 x 2 x 2 x 2 and group it as (2 x 2) x (2 x 2) x (2 x 2). Then, take one factor from each pair and multiply them together to get 8.
Simplify (x^3 y^4)^2Use the power rule and multiply the exponents by 2. Then, get x^(3x2) y^(4x2) = x^6 y^8.
Find the square root of 20Use estimation and use 16 and 25 as lower and upper bounds, since they are perfect squares of 4 and 5 respectively. Then, use the average method and take the average of 4 and 5, which is 4.5, and check if it is close enough to the square root of 20. If not, repeat the process and take the average of 4.5 and 5, which is 4.75, and check again. You can continue this process until you find a satisfactory answer.
Simplify (x^-1 y^-2)^-3Use the power rule and multiply the exponents by -3. Then, get x^(1x-3) y^(2x-3) = x^-3 y^-6. Then, use the negative exponent rule and write it as 1 / (x^3 y^6).
Solving Equations
Solving equations is one of the most important skills in mathematics. It involves finding the value or values of a variable that make an equation true. An equation is a statement that two expressions are equal, such as x + 5 = 10 or y - 3 = 7.
In grade 8 mathematics, you will learn how to solve equations with one unknown, linear equations and functions, systems of equations, and more. Here are some of the subtopics that you will encounter in this section:
Equations with one unknown
An equation with one unknown is an equation that has only one variable in it, such as x + 5 = 10 or y - 3 = 7. To solve an equation with one unknown, you need to use inverse operations to isolate the variable on one side of the equation and get a constant on the other side.
Inverse operations are operations that undo each other, such as addition and subtraction, multiplication and division, squaring and square rooting, etc. For example, to undo adding 5 from both sides of the equation x + 5 = 10, you can use subtraction and get x + 5 - 5 = 10 - 5, which simplifies to x = 5.
To check the solution of an equation with one unknown, you can substitute the value of the variable back into the equation and see if it makes the equation true. For example, to check if x = 5 is the solution of x + 5 = 10, you can plug in x = 5 and get 5 + 5 = 10, which is true.
Here are some examples and exercises with answers for solving equations with one unknown:
ExampleAnswer
Solve x - 7 = 15Add 7 to both sides and get x - 7 + 7 = 15 + 7, which simplifies to x = 22.
Check if x = -3 is the solution of x + 4 = 1Plug in x = -3 and get -3 + 4 = 1, which is true.
Solve y / 2 = 9Multiply both sides by 2 and get y / 2 x 2 = 9 x 2, which simplifies to y = 18.
Check if y = -6 is the solution of y / -3 = 2Plug in y = -6 and get -6 / -3 = 2, which is true.
Linear equations and functions
A linear equation is an equation that has a variable or variables raised to the first power, such as y = mx + b or ax + by = c. A linear function is a function that can be represented by a linear equation. A linear function has a constant rate of change, which means that the difference between any two outputs is always the same for any two inputs. The rate of change of a linear function is also called the slope, which measures how steep or flat the graph of the function is.
To graph a linear equation, you can use different methods, such as slope-intercept form or x- and y-intercepts. Slope-intercept form is a way of writing a linear equation as y = mx + b, where m is the slope and b is the y-intercept. The y-intercept is the point where the graph crosses the y-axis. To graph a linear equation using slope-intercept form, you can plot the y-intercept on the graph and then use the slope to find another point on the line. The slope can be written as a fraction m = rise / run, where rise is the vertical change and run is the horizontal change. To find another point on the line, you can move up or down by the rise and left or right by the run from the y-intercept. Then, you can draw a straight line through the two points.
X- and y-intercepts are another way of finding points on a graph of a linear equation. The x-intercept is the point where the graph crosses the x-axis, and the y-intercept is the point where the graph crosses the y-axis. To find the x-intercept, you can set y = 0 in the equation and solve for x. To find the y-intercept, you can set x = 0 in the equation and solve for y. Then, you can plot the x- and y-intercepts on the graph and draw a straight line through them.
A proportional relationship is a special type of linear relationship that has a constant ratio between the inputs and outputs. This means that the outputs are always proportional to the inputs by a factor called the constant of proportionality. The constant of proportionality can also be seen as the slope of the graph of a proportional relationship. To identify a proportional relationship, you can check if the graph is a straight line that passes through the origin, or if the equation is in the form y = kx, where k is the constant of proportionality.
To write an equation of a proportional relationship from a graph or a table, you can find the constant of proportionality by dividing any output by its corresponding input. Then, you can use the constant of proportionality as the slope and write the equation in slope-intercept form as y = kx.
Here are some examples and exercises with answers for graphing linear equations and finding equations of proportional relationships:
ExampleAnswer
Graph y = 2x + 3 using slope-intercept formPlot the y-intercept (0, 3) on the graph and use the slope 2/1 to find another point on the line by moving up 2 units and right 1 unit from the y-intercept. Then, plot the point (1, 5) and draw a straight line through them.
Find the equation of a proportional relationship from the table below:Divide any output by its corresponding input to find the constant of proportionality. For example, 12 / 3 = 4. Then, use the constant of proportionality as the slope and write the equation in slope-intercept form as y = 4x.
xy
312
624
936
Graph 2x + 3y = 6 using x- and y-interceptsTo find the x-intercept, set y = 0 and solve for x. Then, get x = 3. To find the y-intercept, set x = 0 and solve for y. Then, get y = 2. Plot the points (3, 0) and (0, 2) on the graph and draw a straight line through them.
Find the equation of a proportional relationship from the graph below:Pick any two points on the line and find their coordinates. For example, (2, 6) and (4, 12). Then, divide any output by its corresponding input to find the constant of proportionality. For example, 6 / 2 = 3. Then, use the constant of proportionality as the slope and write the equation in slope-intercept form as y = 3x.
Geometry
Geometry is the branch of mathematics that deals with shapes, sizes, angles, and positions of objects. Geometry involves studying different types of figures, such as points, lines, planes, angles, triangles, quadrilaterals, circles, etc. Geometry also involves measuring and calculating different properties of these figures, such as lengths, areas, perimeters, volumes, etc.
In grade 8 mathematics, you will learn how to use the Pythagorean theorem, how to find missing angles in parallel lines and polygons, how to find surface area and volume of prisms and cylinders, how to use transformations and congruence, and more. Here are some of the subtopics that you will encounter in this section:
Pythagorean theorem
The Pythagorean theorem is a formula that relates the lengths of the sides of a right triangle. A right triangle is a triangle that has one angle that measures 90 degrees. The side opposite to the right angle is called the hypotenuse, and the other two sides are called the legs. The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs. In other words, a^2 + b^2 = c^2, where a and b are the lengths of the legs and c is the length of the hypotenuse.
To use the Pythagorean theorem to find the missing side of a right triangle, you need to identify which side is the hypotenuse and which sides are the legs. Then, you can plug in the known values into the formula and solve for the unknown value. For example, to find the length of the hypotenuse of a right triangle with legs of 3 cm and 4 cm, you can write c^2 = 3^2 + 4^2 and get c^2 = 9 + 16 = 25. Then, you can take the square root of both sides and get c = 5 cm.
A Pythagorean triple is a set of three positive integers that satisfy the Pythagorean theorem. For example, 3, 4, and 5 are a Pythagorean triple because 3^2 + 4^2 = 5^2. Pythagorean triples can help you simplify calculations when working with right triangles. For example, if you know that one leg of a right triangle is 6 cm and the hypotenuse is 10 cm, you can use the Pythagorean triple 3, 4, and 5 and multiply it by 2 to get 6, 8, and 10. Then, you can conclude that the other leg is 8 cm without using the formula.
Here are some examples and exercises with answers for using the Pythagorean theorem:
ExampleAnswer
Find the length of the hypotenuse of a right triangle with legs of 5 m and 12 mWrite c^2 = 5^2 + 12^2 and get c^2 = 25 + 144 = 169. Then, take the square root of both sides and get c = 13 m.
Find the length of the leg of a right triangle with a hypotenuse of 15 cm and a leg of 9 cmWrite a^2 + 9^2 = 15^2 and get a^2 + 81 = 225. Then, subtract 81 from both sides and get a^2 = 144. Then, take the square root of both sides and get a = 12 cm.
Find the length of the hypotenuse of a right triangle with legs of 8 in and 15 inWrite c^2 = 8^2 + 15^2 and get c^2 = 64 + 225 = 289. Then, take the square root of both sides and get c = 17 in.
Find the length of the leg of a right triangle with a hypotenuse of 26 cm and a leg of 10 cmWrite a^2 + 10^2 = 26^2 and get a^2 + 100 = 676. Then, subtract 100 from both sides and get a^2 = 576. Then, take the square root of both sides and get a = 24 cm.
Angles and parallel lines
Angles are formed by two rays that share a common endpoint, called the vertex. Angles are measured in degrees, which are divided into 360 parts in a full circle. Angles can be classified by their size, such as acute (less than 90 degrees), right (equal to 90 degrees), obtuse (more than 90 degrees), or straight (equal to 180 degrees).
Parallel lines are lines that never intersect, which means they have the same slope or direction. When parallel lines are cut by another line, called a transversal, they form different types of angles, such as corresponding angles, alternate interior angles, alternate exterior angles, or consecutive interior angles. These angles have special relationships that can help you find missing angles in parallel lines.
Corresponding angles are angles that are in the same position on both parallel lines. For example, angle A and angle E are corresponding angles in the figure below. Corresponding angles are congruent, which means they have the same measure. For example, if angle A is 50 degrees, then angle E is also 50 degrees.
Alternate interior angles are angles that are on opposite sides of the transversal and between the parallel lines. For example, angle C and angle F are alternate interior angles in the figure below. Alternate interior angles are congruent, which means they have the same measure. For example, if angle C is 40 degrees, then angle F is also 40 degrees.
Alternate exterior angles are angles that are on opposite sides of the transversal and outside the parallel lines. For example, angle A and angle H are alternate exterior angles in the figure below. Alternate exterior angles are congruent, which means they have the same measure. For example, if angle A is 50 degrees, then angle H is also 50 degrees.
Consecutive interior angles are angles that are on the same side of the transversal and between the parallel lines. For example, angle C and angle D are consecutive interior angles in the figure below. Consecutive interior angles are supplementary, which means they add up to 180 degrees. For example, if angle C is 40 degrees, then angle D is 180 - 40 = 140 degrees.
Here are some examples and exercises with answers for finding missing angles in parallel lines:
ExampleAnswer
Find the measure of angle E in the figure below:Use the corresponding angles relationship and set angle E equal to angle A. Then, get E = A = 50 degrees.
Find the measure of angle G in the figure below:Use the alternate interior angles relationship and set angle G equal to angle F. Then, get G = F = 40 degrees.
Find the measure of angle B in the figure below:Use the consecutive interior angles relationship and set angle B plus angle C equal to 180 degrees. Then, get B + C = 180 and B + 40 = 180. Then, subtract 40 from both sides and get B = 140 degrees.
Find the measure of angle D in the figure below:Use the alternate exterior angles relationship and set angle D equal to angle H. Then, get D = H = 50 degrees.
Conclusion
In this article, we have shown you how to download a free grade 8 mathematics study guide pdf from reliable sources. We have also given you an overview of the main topics that are included in the grade 8 mathematics curriculum, such as numbers and operations, solving equations, linear equations and functions, geometry, and more. We have provided you with examples, exercises, and answers that can help you practice and master these topics.
We hope that this article has been helpful for you and that you have learned something new. If you want to download the free grade 8 mathematics study guide pdf, you can click on the links below and save them to your device. You can also print them out and use them as a reference or a workbook.
Remember that a study guide is only a tool that can assist you in your learning process. It is not a substitute for your teacher's instruction or your textbook's content. You still need to pay attention in class, do your homework, ask questions, and review regularly. By doing so, you will be able to improve your mathematical skills and prepare for your exam.
Good luck and happy studying!
FAQs
Here are some frequently asked questions about grade 8 mathematics study guide pdf download 2020 with brief answers:
Q: How can I download a free grade 8 mathematics study guide pdf?
A: You can download a free grade 8 mathematics study guide pdf from reliable sources such as [text] or [text]. These sources offer high-quality study guides that cover all the topics in the grade 8 mathematics curriculum.
Q: What are some of the main topics covered in the grade 8 mathematics curriculum?
A: Some of the main topics covered in the grade 8 mathematics curriculum are numbers and operations, solving equations, linear equations and functions, geometry, and more. These topics involve working with different types of numbers, expressions, equations, functions, shapes, etc.
Q: How can I practice and master these topics?
A: You can practice and master these topics by using examples, exercises, and answers that are provided in the study guide pdf. You can also use online resources such as [text] or [text] that offer interactive games, quizzes, videos, etc.
Q: How can I use a study guide effectively?
A: You can use a study guide effectively by following these steps:
Read the overview of each topic and understand the key concepts Review the examples and try to solve the exercises on your own
Check your answers and correct your mistakes
Repeat the process until you feel confident about the topic
Q: What are some tips and tricks that can help me ace my grade 8 mathematics exam?
A: Some tips and tricks that can help you ace your grade 8 mathematics exam are:
Study regularly and avoid cramming the night before the exam
Make a study plan and stick to it
Use different methods of studying, such as reading, writing, listening, speaking, etc.
Test yourself with practice questions and mock exams
Ask for help from your teacher, peers, or online tutors if you have any doubts or difficulties
Relax and get enough sleep before the exam
Read the instructions carefully and manage your time wisely during the exam
Show your work and explain your reasoning for each question
Review your answers and fix any errors before submitting your exam
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