Introduction To Algebra

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टीचर्स के लिए: Introduction To Algebra (Maths [CIE], Core) के लिए इस्तेमाल के लिए तैयार लेसन स्लाइड्स, रिवीज़न नोट्स, डायग्राम — इन्हें अपने लेसन में इस्तेमाल करें, या टॉपिक को एक इंटरैक्टिव क्लास एक्टिविटी की तरह चलाएं जिसे आपके स्टूडेंट्स लाइव गेम की तरह खेलें।

लेसन नोट्स

Algebraic Notation

Algebra uses letters (variables) to represent general or unknown numbers.
Algebraic notation writes calculations using letters: e.g., `a + b`, `ab` means `a × b`, `a/b` means `a ÷ b`.
Multiplication is implied: `3ab` means `3 × a × b`.
Order of operations applies: brackets, powers, then multiplication/division, then addition/subtraction.
Powers and roots are written as with numbers: `a²` means `a × a`, `√a` means square root of `a`.
Brackets work as with numbers: `3(a + b)` means `3 × (a + b)`.

Algebraic Vocabulary

A term is a variable, a number (constant), or a product of numbers and variables (e.g., `5x`, `4xy`).
The number in front of a variable is the coefficient (e.g., coefficient of `x` in `6x` is 6).
A factor divides a term exactly; e.g., factors of `3x` are 1, 3, x, 3x.
An expression has no equals sign (e.g., `2x + 5y`).
An equation has an equals sign and can be solved (e.g., `2x = 10`).
A formula is a rule linking quantities (e.g., `w = mg`); substituting values turns it into an equation.

Substitution

Substitution replaces letters in a formula with given numbers.
Always use brackets around negative numbers when substituting (e.g., `x = -3` → `x² = (-3)² = 9`).
Follow order of operations: brackets, powers, multiplication/division, addition/subtraction.
Substitution can produce an equation to solve for an unknown variable.
Example: If `P = 2l + 2w`, `P = 20`, `w = 4`, then `20 = 2l + 8` → `l = 6`.

Collecting Like Terms

Like terms have exactly the same variables and powers (e.g., `2x` and `3x`; `5xy` and `-7xy`).
Unlike terms have different variables or powers (e.g., `2x` and `3y`; `4x²` and `6x`).
To collect like terms, add or subtract their coefficients.
Keep the sign with its term; `2x - 3y` is the same as `2x + (-3y)`.
Simplify: `8a - 5b - 6a + 4b` → `(8a - 6a) + (-5b + 4b)` → `2a - b`.
Do not leave `1x` or `-1x`; write `x` or `-x`.

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साइन अप करें — फ्री लॉग इन

प्रैक्टिस सवाल

फ्री प्रीव्यू — 57 में से 8 सवाल। सभी देखने के लिए साइन अप करें।

1.Which of the following is an expression?
Easy
- A2x + 5 = 4
- B7x - 9
- Cx = vt - w
- D3 + 4 = 7
2.Which of the following is an equation?
Easy
- A2x + 5
- B7x - 9
- C2x + 5 = 4
- Dx = vt - w
3.Simplify: 6a - 3b + 2a - 4b
Medium
- A8a - 7b
- B8a + 7b
- C4a - 7b
- D8a - b
4.Simplify: 4x + 3y + 2x - 8y
Medium
- A6x - 5y
- B6x + 5y
- C2x - 5y
- D6x - 11y
5.W = 3a + 5c. Find the value of W when a = 6 and c = 2.
Easy
- A28
- B23
- C48
- D36
6.Simplify: 3c - 5d - c + 2d
Medium
- A2c - 3d
- B2c - 7d
- C4c - 3d
- D2c + 3d
7.Simplify: 5w + 3h - 7w + 8h
Medium
- A-2w + 11h
- B2w + 11h
- C-2w - 5h
- D12w + 11h
8.Simplify: 5c - d - 3d - 2c
Medium
- A3c - 4d
- B3c + 4d
- C7c - 4d
- D3c - 2d

और सवाल

9.Simplify: 5t + 4t - 2t
Easy
- A7t
- B11t
- C3t
- Dt
10.Simplify: 8a + 3b - 2a + b
Medium
- A6a + 4b
- B10a + 4b
- C6a + 2b
- D6a - 4b
11.A = 1/4 b c². Calculate the value of A when b = 3 and c = 6.
Medium
- A27
- B9
- C54
- D12
12.T = 3a² / b. Find the value of T when a = 4 and b = 5.
Medium
- A9.6
- B48
- C12
- D4.8
13.Kyra has a faulty thermometer. It always shows the temperature as 2°C higher than the actual temperature. The temperature on the thermometer is T °C. Write an expression, in terms of T, for the actual temperature.
Medium
- AT - 2
- BT + 2
- C2 - T
- DT/2
14.Calculate the value of 4x² + xy when x = 3 and y = -2.
Medium
- A30
- B36
- C18
- D24
15.Simplify: 4x - 12y + 10x + 25y
Medium
- A14x + 13y
- B14x - 13y
- C6x + 13y
- D14x + 37y
16.Simplify: 2b + 3b - a - b + 3a
Medium
- A4b + 2a
- B4b - 2a
- C6b + 2a
- D4b + 4a
17.Simplify: 7x + 2y - 3x + 5y
Medium
- A4x + 7y
- B10x + 7y
- C4x - 3y
- D10x - 3y
18.Simplify: 9p - 4q - 5p + 7q
Medium
- A4p + 3q
- B14p + 3q
- C4p - 11q
- D14p - 11q
19.Simplify: 6m + 3n - 2m - 8n
Medium
- A4m - 5n
- B8m - 5n
- C4m + 11n
- D8m + 11n
20.Simplify: 4a + 7b - a - 2b
Medium
- A3a + 5b
- B5a + 5b
- C3a + 9b
- D5a + 9b
21.Simplify: 2x + 5y + 3x - y
Medium
- A5x + 4y
- B5x + 6y
- Cx + 4y
- Dx + 6y
22.Simplify: 3c + 2d + 5c - 7d
Medium
- A8c - 5d
- B8c + 9d
- C2c - 5d
- D2c + 9d
23.Simplify: 8t - 3u - 5t + 6u
Medium
- A3t + 3u
- B13t + 3u
- C3t - 9u
- D13t - 9u
24.Simplify: 6x + 2y - 4x - 3y
Medium
- A2x - y
- B10x - y
- C2x + 5y
- D10x + 5y
25.Given that a = 5 and b = -2, find the value of 3a + 4b.
Easy
- A7
- B23
- C15
- D11
26.Given that x = 3 and y = -4, find the value of 2x² - 3y.
Medium
- A30
- B6
- C18
- D42
27.The formula for the area of a trapezium is A = (a + b)h/2. Find the value of A when a = 4, b = 6, and h = 5.
Easy
- A25
- B50
- C15
- D30
28.Simplify: 3(2x + 4) - 2(3x - 1)
Medium
- A14
- B12x + 14
- C12x + 10
- D10
29.If P = 2l + 2w, and P = 30, w = 5, find l.
Medium
- A10
- B12.5
- C20
- D5
30.Given that c = 5a - 2b, find the value of c when a = 8 and b = -3.
Medium
- A46
- B34
- C40
- D28
31.A pen costs 60 cents and a ruler costs 29 cents. Write an expression for the total cost, in cents, of x pens and y rulers.
Easy
- A60x + 29y
- B60y + 29x
- C89(x + y)
- D60x + 29
32.Simplify: 9x - 2y - 5x - y
Easy
- A4x - 3y
- B4x - y
- C14x - 3y
- D14x - y
33.A rectangle has length l cm and width w cm. Its perimeter is given by P = 2l + 2w. If the perimeter is 30 cm and the width is 6 cm, what is the length?
Medium
- A9 cm
- B12 cm
- C15 cm
- D18 cm
34.The formula for the area of a trapezium is A = (a + b)h / 2. Work out the value of h when A = 38.64, a = 5.5, and b = 3.7.
Medium
- A8.4
- B4.2
- C16.8
- D2.1
35.c = 5a - 2b. Make a the subject of the formula.
Medium
- Aa = (c + 2b) / 5
- Ba = (c - 2b) / 5
- Ca = 5c + 2b
- Da = (2b - c) / 5
36.The angles of a triangle are x, 2x, and 3x. Find the value of x.
Medium
- A30°
- B60°
- C90°
- D20°
37.A triangle has sides of length (x+2) cm, (2x-1) cm, and (3x-1) cm. Its perimeter is 30 cm. Find x.
Medium
- A4
- B5
- C6
- D7
38.What is the coefficient of x in the term 7x?
Easy
- A7
- Bx
- C7x
- D1
39.Which of the following is a term?
Easy
- A3x + 2
- B5y
- C2 = 2
- Dx + y = 3
40.Write an expression for 'a number n multiplied by 5, then increased by 3'.
Easy
- A5n + 3
- B5(n + 3)
- C5n - 3
- Dn + 15
41.What is the value of 2x + 3 when x = 4?
Easy
- A11
- B14
- C9
- D8
42.Simplify: 3a + 2b - a + 5b
Easy
- A2a + 7b
- B4a + 7b
- C2a + 3b
- D3a + 7b
43.In algebra, the expression 'ab' means a + b.
Easy
True or false?
44.What is the coefficient of y in the term -5y?
Easy
- A-5
- B5
- Cy
- D-y
45.The expression 4x² means 4 × x × x.
Easy
True or false?
46.Simplify: 4x - 3y + 2x + 5y
Easy
- A6x + 2y
- B6x - 8y
- C2x + 2y
- D4x + 2y
47.The expression 3ab means 3 + a + b.
Easy
True or false?
48.Match each algebraic term to its coefficient of x.
Medium
- 5x
- -3x²
- x
- 0x
- 5
- -3
- 1
- 0
49.Arrange these steps in the correct order to simplify 3x + 5 - 2x + 3.
Medium
- 3x - 2x + 5 + 3
- x + 8
- 3x + 5 - 2x + 3
- (3x - 2x) + (5 + 3)
50.Select all the expressions that are equivalent to 6x + 4y - 2x - 3y.
Medium
- A4x + y
- B8x + 7y
- C4x - y
- D6x - 2x + 4y - 3y
- E2(2x + y)
51.Given that y = 3x - 5, find the value of y when x = 4.
Easy
52.Complete the sentence.
Easy
In algebra, the expression a/b means a ____ b.
53.Find the value of 5p + 2q when p = 3 and q = -1.
Medium
54.Given that a = 3 and b = -2, find the value of 2a² - 3b.
Medium
55.From the list: 3x + 2 = 8, 5y - 1, 4z, write down an equation.
Easy
56.Given that y = 3x - 5, find the value of y when x = 4.
Easy
- A8
- B7
- C9
- D6
57.Find the value of 5p + 2q when p = 3 and q = -1.
Medium
- A13
- B14
- C15
- D12

रिवीज़न नोट्स

## Introduction to Algebra - Quick Revision ### Algebraic Notation - Letters represent unknown numbers (variables). - Multiplication: no symbol, e.g., `ab` means a × b. - Division: use fractions, e.g., `a/b` means a ÷ b. - Powers: `a²` means a × a. - Brackets: `3(a+b)` means 3 × (a+b). ### Algebraic Vocabulary - **Term**: a variable, constant, or product (e.g., `x`, `20`, `5x`). - **Coefficient**: the number in front of a variable (e.g., in `6x`, coefficient is 6). - **Expression**: no equals sign (e.g., `2x+5y`). - **Equation**: has an equals sign, can be solved (e.g., `2x=10`). - **Formula**: a rule linking quantities (e.g., `P=2l+2w`). ### Substitution - Replace letters with given numbers. - Use brackets around negative numbers: `x²` when x = -4 → `(-4)² = 16`. - Follow order of operations (BIDMAS). - Example: If `A = ¼ bc²`, b=3, c=6 → `A = ¼ × 3 × 36 = 27`. ### Collecting Like Terms - Like terms have same variable(s) and same powers. - Add/subtract coefficients only. - Example: `8a - 5b - 6a + 4b = (8a-6a) + (-5b+4b) = 2a - b`. - Simplify `1x` to `x`, `-1x` to `-x`. ### Key Formulas - Perimeter of rectangle: `P = 2l + 2w`. - Area of trapezium: `A = (a+b)h/2`. - From past paper: `c = 5a - 2b`; making a subject: `a = (c+2b)/5`.

Variable: A letter representing an unknown number.
Coefficient: The number multiplying a variable (e.g., in 5x, coefficient is 5).
Term: A single number, variable, or product of numbers and variables.
Expression: An algebraic statement without an equals sign.
Equation: An algebraic statement with an equals sign that can be solved.
Formula: A rule or relationship written in algebraic shorthand.
Substitution: Replacing a variable with a given numerical value.
Like terms: Terms with exactly the same variables and powers.
Collecting like terms: Simplifying an expression by adding/subtracting coefficients of like terms.

फ्लैशकार्ड

What is algebraic notation?

Algebraic notation uses letters to represent numbers. For example, 'ab' means a × b, and 'a/b' means a ÷ b.

How do you write multiplication in algebra?

No symbol is used; e.g., 'ab' means a × b, and '3ab' means 3 × a × b.

How do you write division in algebra?

Use fractions: 'a/b' means a ÷ b.

What does 'a²' mean?

a² means a × a (a squared).

What does '4a²' mean?

4a² means 4 × a × a (4 times a squared).

What does '√a' mean?

√a means the square root of a.

What does '3(a + b)' mean?

It means 3 × (a + b): add a and b first, then multiply by 3.

What is a term in algebra?

A term is a number, a variable, or a product of numbers and variables, e.g., 5x, 20, or x².

What is a coefficient?

The number in front of a variable; e.g., in 6x, the coefficient is 6; in -5y, it is -5.

What is a constant?

A constant is a term that does not contain a variable, e.g., 20.

What is an expression?

An algebraic statement without an equals sign, e.g., 2x + 5y.

What is an equation?

An algebraic statement with an equals sign that can be solved, e.g., 2x = 10.

What is a formula?

A rule or relationship written in letters, e.g., w = mg. It becomes an equation when values are substituted.

What does substitution mean?

Replacing a variable with a given number. Use brackets for negative numbers, e.g., if x = -4, then x² = (-4)² = 16.

Simplify: 6a - 3b + 2a - 4b

8a - 7b

Simplify: 4x + 3y + 2x - 8y

6x - 5y

Simplify: 3c - 5d - c + 2d

2c - 3d

Simplify: 5w + 3h - 7w + 8h

-2w + 11h

Simplify: 5c - d - 3d - 2c

3c - 4d

Simplify: 5t + 4t - 2t

Simplify: 8a + 3b - 2a + b

6a + 4b

Simplify: 4x - 12y + 10x + 25y

14x + 13y

Simplify: 2b + 3b - a - b + 3a

4b + 2a

Simplify: 9x - 2y - 5x - y

4x - 3y

If W = 3a + 5c, find W when a = 6 and c = 2.

W = 3(6) + 5(2) = 18 + 10 = 28

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