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Questions and Answers
In the matchstick pattern for the letter 'N', if 2 matchsticks are needed to form the vertical lines, and one matchstick for the diagonal, what is the algebraic expression for the number of matchsticks required to make 'x' number of 'N's?
In the matchstick pattern for the letter 'N', if 2 matchsticks are needed to form the vertical lines, and one matchstick for the diagonal, what is the algebraic expression for the number of matchsticks required to make 'x' number of 'N's?
- $x + 3$
- $3 + x$
- $3x$ (correct)
- $2x + 1$
Which rule accurately describes the progression in the number pattern: 250, 130, 70, 40, 25?
Which rule accurately describes the progression in the number pattern: 250, 130, 70, 40, 25?
- Divide by 2 and subtract 5.
- Divide the previous number by 2 and add 5. (correct)
- Multiply by 2 and subtract 370.
- Subtract 120 and add 10.
What does the equation $\frac{m}{7} - 12 = 23$ represent?
What does the equation $\frac{m}{7} - 12 = 23$ represent?
- One-seventh of a number is 12 less than 23. (correct)
- Seven times a number is 12 less than 23.
- Seven times a number is 12 more than 23.
- One-seventh of a number is 12 more than 23.
If $\frac{100a}{2} = 500$, what is the value of 'a'?
If $\frac{100a}{2} = 500$, what is the value of 'a'?
If Reema has $12a$ flowers and Ria has 6 more flowers than Reema, how many flowers does Ria have?
If Reema has $12a$ flowers and Ria has 6 more flowers than Reema, how many flowers does Ria have?
Rahul spends $y$ daily and saves $z$ per week. What is his income for three weeks?
Rahul spends $y$ daily and saves $z$ per week. What is his income for three weeks?
What is the 15th odd number in the sequence of odd numbers derived using the formula $2n - 1$?
What is the 15th odd number in the sequence of odd numbers derived using the formula $2n - 1$?
Akash has $t$ toffees. His brother Amit has 6 toffees less than Akash. How many toffees do they have together?
Akash has $t$ toffees. His brother Amit has 6 toffees less than Akash. How many toffees do they have together?
Sandeep was $p$ years old 18 years ago. If $p = 13$, how old is Sandeep now?
Sandeep was $p$ years old 18 years ago. If $p = 13$, how old is Sandeep now?
Consider a pattern of pentagons formed using matchsticks. If $n$ represents the number of pentagons, which expression accurately calculates the total number of matchsticks required?
Consider a pattern of pentagons formed using matchsticks. If $n$ represents the number of pentagons, which expression accurately calculates the total number of matchsticks required?
Using the formula for the $n^{th}$ odd number ($2n - 1$), determine which odd number in the sequence is equal to 45.
Using the formula for the $n^{th}$ odd number ($2n - 1$), determine which odd number in the sequence is equal to 45.
A pattern consists of repeating a unit made of matchsticks. The smallest unit has 6 uncommon matchsticks and 2 common matchsticks. What is the general formula for the total number of matchsticks required for $n$ units?
A pattern consists of repeating a unit made of matchsticks. The smallest unit has 6 uncommon matchsticks and 2 common matchsticks. What is the general formula for the total number of matchsticks required for $n$ units?
A sequence of figures is created using matchsticks. The first figure requires 7 matchsticks, and each subsequent figure requires 5 additional matchsticks. Determine the number of matchsticks needed to create the 10th figure in the sequence.
A sequence of figures is created using matchsticks. The first figure requires 7 matchsticks, and each subsequent figure requires 5 additional matchsticks. Determine the number of matchsticks needed to create the 10th figure in the sequence.
Which of the following expressions represents the total number of pencils Anwar has, if he puts them into x
boxes holding 15 pencils each, with 3 pencils left over?
Which of the following expressions represents the total number of pencils Anwar has, if he puts them into x
boxes holding 15 pencils each, with 3 pencils left over?
If Jyoti's current age is represented by $x$, which expression represents Mira's age 4 years ago, given that Mira is 3 years older than Jyoti?
If Jyoti's current age is represented by $x$, which expression represents Mira's age 4 years ago, given that Mira is 3 years older than Jyoti?
Ali's age is represented by $x$. Lucky is 4 times as old as Ali. What expression represents Lucky's age 6 years from now?
Ali's age is represented by $x$. Lucky is 4 times as old as Ali. What expression represents Lucky's age 6 years from now?
In a school, $x$ students are divided into 3 equal groups for a cricket tournament. If 4 cricketers are added to each group, which expression represents the number of cricketers in each group now?
In a school, $x$ students are divided into 3 equal groups for a cricket tournament. If 4 cricketers are added to each group, which expression represents the number of cricketers in each group now?
Pooja's present age is $y$ years. Which expression correctly represents her mother's age, if her mother is 5 years older than twice Pooja's age?
Pooja's present age is $y$ years. Which expression correctly represents her mother's age, if her mother is 5 years older than twice Pooja's age?
Sakshi is $x$ years old. Her uncle is $(3x - 4)$ years old. Which of the following statements accurately reflects this relationship?
Sakshi is $x$ years old. Her uncle is $(3x - 4)$ years old. Which of the following statements accurately reflects this relationship?
The cost of a shampoo bottle is $c$. The cost of a detergent pack is $(2c + 3)$. What does this algebraic expression tell us in ordinary language?
The cost of a shampoo bottle is $c$. The cost of a detergent pack is $(2c + 3)$. What does this algebraic expression tell us in ordinary language?
Flashcards
Formula for nth odd number
Formula for nth odd number
The nth odd number can be found by multiplying n by 2 and subtracting 1.
Matchsticks for one inverted C
Matchsticks for one inverted C
One inverted 'C' requires three matchsticks.
Total Matchsticks for 'n' inverted C
Total Matchsticks for 'n' inverted C
For 'n' inverted Cs, you need 2n + 1 matchsticks.
Matchstick Pattern Generalization
Matchstick Pattern Generalization
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Matchsticks in repeated pentagons
Matchsticks in repeated pentagons
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Repeated pentagons
Repeated pentagons
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Repeated pattern
Repeated pattern
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General formula.
General formula.
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Solution of an equation
Solution of an equation
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Trial and error method
Trial and error method
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Algebraic equation
Algebraic equation
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Balancing equations
Balancing equations
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General rule
General rule
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Variable
Variable
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Equation
Equation
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Translating word problems
Translating word problems
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What is an equation?
What is an equation?
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What is LHS?
What is LHS?
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What is RHS?
What is RHS?
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Expressions like 3y > 9. Equations?
Expressions like 3y > 9. Equations?
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Jaya's age after 10 years?
Jaya's age after 10 years?
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Jyoti's age 4 years ago?
Jyoti's age 4 years ago?
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If Ali is x, Lucky's age 6 years from now
If Ali is x, Lucky's age 6 years from now
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Expression for cricketers in each group.
Expression for cricketers in each group.
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Study Notes
Algebraic Expressions Basics
- Algebra uses letters and symbols to represent unknown numbers.
- These letters, called variables, can take on different values.
- Arithmetic is the branch of mathematics that deals with numbers having fixed values and basic operations.
Algebraic Expressions
- Algebraic expressions combine variables and constants connected by mathematical operations.
- Examples of algebraic expressions include
2x + 9
. a + 5
means '5 added to a,' '5 more than a,' or 'a increased by 5.'a - 5
means '5 subtracted from a,' '5 taken away from a,' or 'a decreased by 5.'5a
represents 5 multiplied by a, or 5 times a.a/5
represents a divided by 5 or one-fifth of a.- To evaluate an algebraic expression, substitute a given value for the variable.
Commutative and Distributive Properties
- The commutative property allows changing the order of numbers in multiplication (e.g.,
2 x 5 = 5 x 2
, orx * y = y * x
). - The distributive property can be written as
x * (y + z) = x * y + x * z
.
Even and Odd Numbers
- Numbers in the times table of 2 are even numbers, expressible as
2n
. - Odd numbers are expressible as
2n - 1
.
Matchstick Patterns
- Patterns can be generalized to find the number of matchsticks needed to make 'n' inverted C's:
2n + 1
- The total number of matchsticks in a repeated unit pattern can be generalized.
- You use: uncommon matchsticks + (number of units) + common matchsticks.
Equations
- An equation is a statement of equality between two expressions.
- The left-hand side (LHS) must equal the right-hand side (RHS).
- If LHS does not equal RHS, it is not an equation.
Solving Equations
- A 'solution' or 'root' satisfies an equation.
- The trial and error method involves substituting values to find the solution.
- Balancing an equation means performing the same operation on both sides.
Practical Applications
- Algebra can represent real-world scenarios.
- For example, the cost of
b
packs of biscuits at ₹10 each is10b
.
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