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### How to Get Percent of Discount

**Offer Details: **A toy is on sale for 40% **off**. If the original price was $40, what is the new sales price? Solution : Marked price = $40. Discount percent = 40%. Discount amount = 40% of 40 = (40/100) ⋅ 40 = 16. By subtracting the discount amount from marked price, we may get the sale price. Sale price = 40 - 16 = $24. Example 4 :

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### ROUNDING OFF NUMBERS

**Offer Details: **About "Rounding **off** numbers" Rounding **off** numbers : In our daily life we need to know approximate values or measurements. David bought a Lap Top for $499.85. When he wants to convey this amount to others, he simply says that he has bought it for $500. This is the approximate value which is given in hundreds only. Daniel buys a pair of slippers for $19.99.

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### Rewriting Percent Expressions

**Offer Details: **A discount store marks down all of its holiday merchandise by 20% **off** the regular selling price. Find the discounted price of decorations that regularly sell for $16 and $23. Solution : Step 1 : Use a bar model. Draw a bar for the regular price P. Then draw a …

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### Calculating Markups and Markdowns

**Offer Details: **A discount store marks down all of its holiday merchandise by 20% **off** the regular selling price. Find the discounted price of decorations that regularly sell for $16 and $23. Solution : Step 1 : Use a bar model. Draw a bar for the regular price P. Then draw a …

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### Rewriting Percent Expressions Worksheet

**Offer Details: **A discount store marks down all of its holiday merchandise by 20% **off** the regular selling price. Find the discounted price of decorations that regularly sell for $16 and $23. Solution : Step 1 : Use a bar model. Draw a bar for the regular price P. Then draw a …

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### ROUNDING OFF NUMBERS WORKSHEETS

**Offer Details: **Round **off** the following numbers to the nearest integer: 15) 288.29. 16) 3998.37. 17) 4856.795. 18) 4999.96. 19) 1.99. 20) 1.0012. Rounding **off** numbers worksheets - Solution. 1) Consider multiples of 10 before and after 521. ( i.e. 520 and 530 ) We find that 521 is nearer to 520 than to 530. It has been illustrated in the picture given below.

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### Area and Perimeter Word Problems

**Offer Details: **AREA AND PERIMETER WORD PROBLEMS. Problem 1 : The length of a rectangle is 4 less than 3 times its width. If its perimeter is 32 cm, then find the area of the rectangle. Solution : Let x be the width of the rectangle. Then, its length is (3x - …

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### How to Find Maximum and Minimum Value of a Function

**Offer Details: **The value of the function at a maximum point is called the maximum value of the function and the value of the function at a minimum point is called the minimum value of the function. Differentiate the given function. let f'(x) = 0 and find critical numbers; Then find the second derivative f''(x). Apply those critical numbers in the second derivative.

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### Percentage Change Word Problems

**Offer Details: **Joanne bought a doll at a 10 percent discount **off** the original price of $105.82. However, she had to pay a sales tax of x% on the discounted price. If the total amount she paid for the doll was $100, what is the value of x ? (A) 2 (B) 3 (C) 4 (D) 5. Solution : Original price of doll = $105.82

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### Percentage Problems on Sat

**Offer Details: **Lily buys a doll at a 10 percent discount **off** the original price of $105.82. However she has to pay a sales tax of x% on the discounted price. If the total amount she pays for the doll is $100, then find the value of x. Solution : The price of the doll after 10% discount : = (100 - 10)% ⋅ 105.82 = 90 % ⋅ 105.82 = 0.9 ⋅ 105.82 = $95.238

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### PROBABILITY FOR ROLLING 2 DICE

**Offer Details: **Since there are 36 outcomes in total when two dice are** rolled,** we have n(S) = 36. Practice Problems. Problem 1 : A dice is rolled twice. What is the probability of getting a …

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### How to identify function from graph

**Offer Details: **Step 2 : We have to check whether the vertical line drawn on the graph intersects the graph in at most one point. Step 3 : In the above graph, the vertical line intersects the graph in at most one point, then the given graph represents a function.

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### Identifying Functions from Mapping Diagrams

**Offer Details: **IDENTIFYING FUNCTIONS FROM MAPPING DIAGRAMS. A function assigns only output to each input. The value that is put into a function is the input. The result is the output. A mapping diagram can be used to represent a relationship between input values and output values. A mapping diagram represents a function if each input value is paired with only

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### How to Determine If a Function is Continuous on a Graph

**Offer Details: **About "How to Determine If a Function is Continuous on a Graph" How to Determine If a Function is Continuous on a Graph : Here we are going to see how to …

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### Set Builder Notation

**Offer Details: **Set builder notation is a notation for describing a set by indicating the properties that its members must satisfy. Reading Notation : ‘|’or ‘:’ such that. A = {x : x is a letter in the word dictionary} We read it as. “A is the set of all x such that x is a letter in the word dictionary”. Examples : (i) N = {x : x is a natural number}

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### Decimal Representation of Rational Numbers

**Offer Details: **Let us express 7/16 in** decimal form.** Then 7/16 = 0.4375. In this example, we observe that the remainder becomes zero after a few steps. Also the** decimal** expansion of 7/16 terminates. Similarly, using long division method we can express the following rational numbers in** decimal form** as. 1/2 = 0.5. 7/5 = 1.5.

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### Markup and Markdown Word Problems Worksheet

**Offer Details: **2) A product is originally priced at $55 is marked 25% **off**. What is the sale price? 3) A product is marked down 15%; the sale price is $127.46. What was the original price? 4) A sells to B an item at 15% profit. B sells the same item to C at 20% profit. If C pays $1656 for it. What is the price at which A bought the item?

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### How to Find the Minimum or Maximum Value of a Function in

**Offer Details: **Since it is positive, the parabola is open upward. So it will minimum value. (a) Write f (x) in the form k (x + t) 2 + r. (b) Find the value of x where f (x) attains its minimum value or its maximum value. (c) Find the vertex of the graph of **f**. By comparing it with vertex form, we get the value of k .

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### Differentiation from First Principles

**Offer Details: **If you have any feedback about our math content, please mail us : v4formath@gmail.com. We always appreciate your feedback. You can also visit the following web pages on different stuff in …

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### How to Determine an Exponential Function From a Table of

**Offer Details: **Solution : The domain values are at regular intervals of 10. Let’s see if there is a common factor among the range values. Since the domain values are at regular intervals and the range values have a common factor, the data are probably exponential. The equation for the data may involve (1/2)x. Exponential equation of the given data is (1/2)x.

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### How to Check if the Function is One to One From its Graph

**Offer Details: **Solution : Let us draw the line y = 1 and y = 3. The line y = 1 intersects the graph of **f** in one point, and the line y = 3 intersects the graph in zero points. Furthermore, we can see from the figure that each horizontal line will intersect the graph in at most one point. Hence f is a one-to-one function. After having gone through the stuff

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**Offer Details: **bulbs cost 25 cents and you get 20% **off** if you purchase 50 or more of the same color and 30% **off** if you purchase 60 or more of one color, how much does Dana need to spend? Show your work. (a) She needs 75 blue, 66 yellow 49 green and 43 red. $51.20 (b) She needs 66 blue, 75 yellow 49 green and 43 red. $51.20

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### Writing Linear Equations From a Table

**Offer Details: **Step 1 : Notice that the change in cost is the same for each increase of 100 minutes. So, the relationship is linear. Step 2 : Choose any two points in the form (x, y), from the table to find the slope : For example, let us choose (100, 14) and (200, 20). Use the slope formula. m = (y2 - y1) / (x2 - x1) Substitute :

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### Math Dictionary-O

**Offer Details: **Opposite rays Opposite rays are two rays that start from a common point and go **off** in the opposite directions. Opposite transformation A transformation that changes the orientation of the figure. Example: Reflection is an opposite transformation. Order Sequence of number arranged either in ascending or descending array.

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### Finding Increasing or Decreasing Intervals

**Offer Details: **Procedure to find where the function is increasing or decreasing : Find the first derivative. Then set f' (x) = 0. Put solutions on the number line. Separate the intervals. Choose random value from the interval and check them in the first derivative. If f (x) > 0, then the function is increasing in that particular interval.

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### Translations Using Vectors Worksheet

**Offer Details: **The storm pushes the boat **off** course to point C, as shown below. a. Write the component forms of the two vectors shown in the diagram. b. The final destination is 8 miles east and 4.5 miles north of the starting point. Write the component form of the vector that describes the path the boat can follow to arrive at its destination.

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### Definite Integrals of Odd and Even Functions

**Offer Details: **If you have any feedback about our math content, please mail us : v4formath@gmail.com. We always appreciate your feedback. You can also visit the following web pages on different stuff in …

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### Identifying Functions From Tables

**Offer Details: **IDENTIFYING FUNCTIONS FROM TABLES. A function assigns only output to each input. The value that is put into a function is the input. The result is the output. Relationships between input values and output values can also be represented using tables. The values in the first column are the input values. The values in the second column are the

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### How to Find a Limit Using a Table

**Offer Details: **Question 1 : Complete the table using calculator and use the result to estimate the limit. lim x->2 (x - 2)/ (x 2 - x - 2) Solution : Instead of applying the values of x directly in the given function, we may simplify the function and apply the values of x one by one given in the table. lim x->2 (x - …

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### Word Problems on Profit and Loss

**Offer Details: **Problem 1 : Cindy bought 50 pens for $100. She then sold each pen for $2.50. Find the profit or loss percentage. Solution : Cost price of 50 pens = $100. Cost price of 1 pen = 100/50 = $2. Selling price of 1 pen = $2.50. Because the selling price of 1 …

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### Calculating Markups and Markdowns Worksheet

**Offer Details: **2) A discount store marks down all of its holiday merchandise by 20% **off** the regular selling price. Find the discounted price of decorations that regularly sell for $16 and $23. 3) On selling 20 units of an item, the profit is equal to cost price of 5 units. Find the mark mark up rate. 4) Difference between the cost price of two products is $10.

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### Write Inequalities from Graphs

**Offer Details: **If the graph contains the solid line, then we have to use one of the signs ≤ or ≥. Example 5 : Write the inequality for the graph given below. Solution : From the above graph, first let us find the slope and y-intercept. Rise = -3 and Run = 1. Slope = -3 / 1 = …

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### Word problems on Percentage 4

**Offer Details: **A product is originally priced at $55 is marked 25% **off**. What is the sale price? Solution : Selling price (S.P) = (100 - M)% ⋅ L.P -----(1) Here, L.P = $55, M = 25 Substitute the above values in (1). (1)-----> S.P = (100 - 25)% ⋅ 55 S.P = 75% ⋅ 55. S.P = 0.75 ⋅ 55. S.P = 41.25

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### REFLECTION THROUGH Y AXIS

**Offer Details: **A reflection can be done through y-axis by folding or flipping an object over the y axis. The original object is called the pre-image, and the reflection is called the image. If the pre-image is labeled as ABC, then t he image is labeled using a prime symbol, such as A'B'C'. An object and its reflection have the same shape and size, but the figures face in opposite directions.

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### Finding function values from a graph worksheet

**Offer Details: **Finding function values from a graph worksheet : Here we are going to see some practice questions on finding values from graph. If a point (x, y) is on a function f, then f(x) = y. In other words, y is the output of **f** when the input is x. Let us see an example problem to understand how to find the values of the function from the graphs.

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### Math Quiz for Grade 3

**Offer Details: **MATH QUIZ FOR GRADE 3. Study the arrows below. Which is the shortest arrow ? Sam has 18 marbles. John has 7 marbles less than him.How many marbles does John have? What is the missing number ? The picture graph shows the number of dolls these 5 girls have. Who has less dolls. Which pair of numbers makes 13 ?

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### Proportional and Nonproportional Situations Using an Equation

**Offer Details: **PROPORTIONAL AND NONPROPORTIONAL SITUATIONS USING AN EQUATION. If a relationship is nonlinear, it is non-proportional. If it is linear, it may be either proportional or non-proportional. When the graph of the linear relationship contains the origin, the relationship is proportional. Linear equations can be written in the form y = mx + b.

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### Finding Maximum and Minimum Value of Quadratic Function

**Offer Details: **FINDING MAXIMUM AND MINIMUM VALUE OF QUADRATIC FUNCTION. The vertex of a parabola is the point where the line of symmetry of the parabola intersects the parabola. Let f be a quadratic function with standard form. y = a (x - h) 2 + k. the maximum and minimum value of **f** occurs at x = h. In order to find the maximum or minimum value of quadratic

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### Markup and Markdown Word Problems Answers

**Offer Details: **A product is originally priced at $55 is marked 25% **off**. What is the sale price? Solution : Selling price (S.P) = (100 - m)% ⋅ L.P -----(1) Here, L.P = $55, m = 25 Substitute 55 for L.P and 25 for m in (1). (1)-----> S.P = (100 - 25)% ⋅ 55 S.P = 75% ⋅ 55. S.P = 0.75 ⋅ 55. S.P = 41.25

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### HOW TO EXPRESS A GIVEN SURD TO SIMPLEST FORM

**Offer Details: **The following steps will be useful to reduce the given surd to its simplest form. Step 1 : Find factors of the number inside the given radical. Step 2 : Based on the order of the radical, we have to group them as pairs and factor out. Step 3 : In case we already have terms outside the radical, we have to multiply them by the factor taken out

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### Writing Rational Numbers as Decimals

**Offer Details: **A rational number is a number that can be written as a ratio of two integers a and b, where b is not zero. For example, 4/ 7 is a rational number, as is 0.37 because it can be written as the fraction. Example 1 : Write the rational number -5/16 as a decimal.

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### Math Terms Start with o

**Offer Details: **Opposite rays are two rays that start from a common point and go **off** in the opposite directions. Opposite Transformation : A transformation that changes the orientation of the figure. Example: Reflection is an opposite transformation. Order of Operation :

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### 4th grade- 10th set

**Offer Details: **counted their brownies to see how many were left then went **off** to the library. When they returned, they found half of the brownies were missing! Kim said “Now we have only 12 brownies to bring to the party. That won’t be enough for all of our friends”. How many brownies did Kim and Ben bake at first? (a) 30 brownies (c) 40 brownies

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### Practice Questions on Divisibility Rules

**Offer Details: **Solution : Divisibility rule for 3 : If the sum of all the digits of the given number is divisible by 3, then we decide that the given number is also divisible by 3. Let "x" be the unknown, then. = (5 + 1 + 7 + x + 3 + 2 + 4) / 3. = (22 + x) / 3. If x = 2, then 22 + x will become 24 and it is divisible by 3. Hence the smallest whole number for

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### Terminal Points on the Unit Circle

**Offer Details: **Suppose t is a real number. Let’s mark **off** a distance t along the unit circle, starting at the point (1, 0) and moving in a counterclockwise direction, if t is positive or in a clockwise direction, if t is negative. In this way we arrive at a point P(x, y) on the unit circle.

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