SUMMARY: This chapter introduces students to algebraic expressions, including their components and basic operations. KEY TOPICS: terms, coefficients, variables, constants, like terms, unlike terms, addition of algebraic expressions, subtraction of algebraic expressions, formation of expressions, simplification of expressions
Which of the following is a constant in the expression 5x + 3y - 7?
A5
B3y
C-7
Dx
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Correct answer: Option 3 — -7
Q21 Mark
Identify the like terms in the expression 4a + 3b + 2a - 5b.
A4a and 2a
B3b and -5b
C4a and 3b
D2a and 3b
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Correct answer: Option 1 — 4a and 2a
Q31 Mark
What is the coefficient of the term 7xy in the expression 5x + 7xy - 3y?
A5
B7
Cxy
D0
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Correct answer: Option 2 — 7
Q41 Mark
Simplify the expression: 3x + 4y - 2x + 5y.
Ax + 9y
B5x + 9y
Cx + y
D5x + 4y
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Correct answer: Option 1 — x + 9y
Q51 Mark
If you subtract the expression 2x - 3 from 5x + 4, what is the resulting expression?
A3x + 7
B3x - 7
C7x + 1
D7x - 1
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Correct answer: Option 1 — 3x + 7
Short Answer Questions5 questions
Q63 Marks
Define an algebraic expression and give an example.
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An algebraic expression is a combination of numbers, variables, and operations. For example, 3x + 5 is an algebraic expression where 3 is the coefficient, x is the variable, and 5 is a constant.
Q73 Marks
What are like terms? Provide an example.
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Like terms are terms that have the same variable raised to the same power. For example, 2x and 5x are like terms because they both contain the variable x raised to the first power.
Q83 Marks
Explain the difference between coefficients and constants in an algebraic expression.
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Coefficients are the numerical factors that multiply the variables in an expression, while constants are the fixed values that do not change. For example, in the expression 4x + 7, 4 is the coefficient and 7 is the constant.
Q93 Marks
How do you simplify the expression 3a + 5a - 2a?
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To simplify the expression, combine the like terms. 3a + 5a - 2a = (3 + 5 - 2)a = 6a. Thus, the simplified expression is 6a.
Q103 Marks
Subtract the algebraic expression (4x + 3y - 5) from (2x - y + 7). What is the result?
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To subtract the expressions, change the signs of the second expression and then combine like terms: (2x - y + 7) - (4x + 3y - 5) = 2x - y + 7 - 4x - 3y + 5 = -2x - 4y + 12.
Long Answer Questions5 questions
Q116 Marks
Define an algebraic expression and explain its components with examples. What are the differences between terms, coefficients, variables, and constants?
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An algebraic expression is a mathematical phrase that can contain numbers, variables, and operators. The components of an algebraic expression include terms, coefficients, variables, and constants. A term is a single mathematical expression, which can be a number (constant), a variable, or a product of numbers and variables. For example, in the expression 3x + 5, '3x' is a term where '3' is the coefficient and 'x' is the variable. The number '5' is a constant term. Coefficients are the numerical factors of the variables in the terms, while constants are fixed values that do not change.
Q126 Marks
Simplify the expression 4x + 3y - 2x + 5y. Show your working and explain how you combined like terms.
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To simplify the expression 4x + 3y - 2x + 5y, we first identify the like terms. The like terms for 'x' are 4x and -2x, and for 'y' are 3y and 5y. Combining the like terms, we get (4x - 2x) + (3y + 5y) = 2x + 8y. Thus, the simplified expression is 2x + 8y. We combined like terms by adding or subtracting their coefficients while keeping the variable part unchanged.
Q136 Marks
Form an algebraic expression for the following situation: A rectangle has a length that is 3 times its width. If the width is represented by 'w', write the expression for the perimeter of the rectangle and simplify it.
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Let the width of the rectangle be represented by 'w'. According to the problem, the length is 3 times the width, so the length can be expressed as '3w'. The formula for the perimeter (P) of a rectangle is given by P = 2(length + width). Substituting the values, we get P = 2(3w + w) = 2(4w) = 8w. Therefore, the algebraic expression for the perimeter of the rectangle is 8w.
Q146 Marks
Subtract the expression (5a + 3b - 2c) from (2a - 4b + 6c). Show your working and explain how you handled the subtraction of the algebraic expressions.
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To subtract the expression (5a + 3b - 2c) from (2a - 4b + 6c), we rewrite the operation as (2a - 4b + 6c) - (5a + 3b - 2c). Distributing the negative sign gives us 2a - 4b + 6c - 5a - 3b + 2c. Now, we combine like terms: (2a - 5a) + (-4b - 3b) + (6c + 2c) = -3a - 7b + 8c. Thus, the result of the subtraction is -3a - 7b + 8c.
Q156 Marks
Explain the process of simplifying the expression 2(x + 3) + 4(2x - 1). Show all steps and provide the final simplified expression.
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To simplify the expression 2(x + 3) + 4(2x - 1), we start by applying the distributive property. First, we distribute 2 into (x + 3) to get 2x + 6. Next, we distribute 4 into (2x - 1) to get 8x - 4. Now, we combine these results: 2x + 6 + 8x - 4. Combining like terms, we have (2x + 8x) + (6 - 4) = 10x + 2. Therefore, the final simplified expression is 10x + 2.
Assertion–Reason Questions5 questions
Q161 Mark
Assertion (A): The expression 3x + 5y is an algebraic expression.
Reason (R): Algebraic expressions consist of terms that include variables and constants.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q171 Mark
Assertion (A): Like terms can be added together to simplify an expression.
Reason (R): Like terms have the same variable raised to the same power.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q181 Mark
Assertion (A): The expression 4a + 3b - 2a + 5b can be simplified to 2a + 8b.
Reason (R): Combining like terms involves adding the coefficients of the same variable.
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Correct answer: Option 2 —
Both A and R are true, but R is not the correct explanation of A.
Q191 Mark
Assertion (A): The term '5' in the expression 2x + 5 is a coefficient.
Reason (R): '5' is a constant term in the expression.
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Correct answer: Option 3 —
A is true, but R is false.
Q201 Mark
Assertion (A): The expression 7xy - 3x + 2y is a polynomial.
Reason (R): Polynomials can have multiple terms with non-negative integer exponents.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Statement-Based Questions5 questions
Q211 Mark
Statement 1: The term '5x' has a coefficient of 5 and a variable of x.
Statement 2: The term '7' is a variable.
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Correct answer: Option 2 —
Only Statement 1 is true.
Q221 Mark
Statement 1: Like terms can be added or subtracted to simplify an expression.
Statement 2: Unlike terms can be combined to form a single term.
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Correct answer: Option 3 —
Only Statement 2 is true.
Q231 Mark
Statement 1: The expression '3a + 2b - 5a' can be simplified to '-2a + 2b'.
Statement 2: The expression '4x + 3y - 2x + 5' can be simplified to '2x + 3y + 5'.
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Correct answer: Option 1 —
Both statements are true.
Q241 Mark
Statement 1: A constant term is a term that does not contain any variables.
Statement 2: The expression '2xy + 3x - 4y' has three terms.
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Correct answer: Option 1 —
Both statements are true.
Q251 Mark
Statement 1: The expression 'x + 2x' simplifies to '3x'.
Statement 2: The expression '5y - 3y + 2' simplifies to '2y + 2'.
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Correct answer: Option 4 —
Both statements are false.
