Algebra Toolkit

Học bằng cách chơi

Trả lời những câu hỏi này để kiếm năng lượng, rồi câu cá và khám phá. Không cần tài khoản.

Dành cho giáo viên: slide bài học, ghi chú ôn tập sẵn dùng cho Algebra Toolkit (Maths [CIE], Extended) — dùng trong bài giảng của bạn, hoặc chạy chủ đề như một hoạt động lớp học tương tác để học sinh chơi như một trò chơi trực tiếp.

Ghi chú bài học

Algebraic Notation

Algebra uses letters to represent general or unknown numbers; letters are called variables.
Multiplication is written without a symbol: ab means a × b, 3ab means 3 × a × b.
Division is written as a fraction: a/b means a ÷ b.
Powers (indices) and roots work as with numbers: a² means a × a, √a means square root of a.
Brackets indicate the operation inside is done first: 3(a + b) means 3 × (a + b).
Order of operations (BIDMAS) applies to algebra just as with numbers.

Algebraic Vocabulary

A term is a variable, a number (constant), or a product of numbers and variables (e.g., 5x, 4xy²).
The coefficient is the number in front of a variable: in -5y, the coefficient is -5.
A factor divides a term exactly: factors of 3x are 1, 3, x, and 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 relating quantities (e.g., P = 2l + 2w); substituting values turns it into an equation.

Substitution

Substitution means replacing a variable with a given number.
Always use brackets around negative numbers when substituting: if x = -4, then x² = (-4)² = 16.
Follow the order of operations (BIDMAS) carefully after substitution.
Substitution can produce an equation to solve (e.g., 20 = 2l + 8 gives l = 6).
On a calculator, put brackets around any substituted negative numbers.

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).
Collect like terms by adding or subtracting their coefficients: 2x + 3x = 5x; 4y - 10y = -6y.
The sign in front of a term belongs to that term; terms can be reordered with their signs.
Simplify coefficients of 1 or -1 to just the variable (e.g., 1x → x, -1y → -y).
Collect different types of like terms separately: 2x + 4y + 5x - 3y = 7x + y.

Slide

Step through every slide for this topic — plus flashcards and revision notes — with a free account.

ĐĂNG KÝ — MIỄN PHÍ ĐĂNG NHẬP

Câu hỏi luyện tập

Xem trước miễn phí — 8 trên 48 câu hỏi. Đăng ký để xem tất cả.

1.Simplify 3a + 7b - 4a + b.
Easy
- A-a + 8b
- B7a + 8b
- C-a + 6b
- D7a + 6b
2.Find the value of 7x + 3y when x = 12 and y = -6.
Easy
- A66
- B102
- C30
- D-18
3.Simplify 5c - d - 3d - 2c.
Easy
- A3c - 4d
- B7c - 4d
- C3c - 2d
- D7c - 2d
4.Complete the statement: When w = ______, 10w = 70.
Easy
- A7
- B700
- C0.7
- D60
5.Use the formula s = ut + 1/2 at². Calculate s when u = 5, t = 10 and a = 3.
Medium
- A200
- B80
- C350
- D65
6.Simplify 2p - q - 3q - 5p.
Easy
- A-3p - 4q
- B3p - 4q
- C-3p + 2q
- D7p - 4q
7.The body mass index B is given by B = m / h². Usman has mass 50 kg and height 1.57 m. Work out B correct to one decimal place.
Medium
- A20.3
- B31.8
- C20.2
- D32.0
8.Find the value of y when m = -2, x = -7 and c = -3 in y = mx + c.
Easy
- A11
- B-17
- C-11
- D17

Thêm câu hỏi

9.A = 4bc. If A = 100 and b = 2, work out the value of c.
Easy
- A12.5
- B50
- C200
- D25
10.x = 0.7. Work out the value of (x+1)² / (2x). Write down all the figures on your calculator display.
Medium
- A2.064285714
- B2.0643
- C2.06
- D2.064
11.w = 5y² - y³. Work out w when y = -2.
Medium
- A28
- B12
- C-12
- D36
12.y = x⁴ - 4x³. Find y when x = -1.
Medium
- A5
- B-3
- C-5
- D3
13.One solution of ax² + a = 150 is x = 7. Find the value of a.
Medium
- A3
- B25
- C6
- D150
14.y = p - 2qx². p = -10, q = 3, x = -5. Work out y.
Medium
- A-160
- B140
- C-140
- D160
15.Simplify 7a + 2b - 3a + 8a + 6b + 2a - b.
Easy
- A14a + 7b
- B14a + 9b
- C20a + 7b
- D20a + 9b
16.Kelly is trying to find values of w for which 3w - w³ = 2. Her values are 1 and -1. Are her values correct?
Medium
- ABoth correct
- BOnly 1 correct
- COnly -1 correct
- DNeither correct
17.What is the coefficient of x in the term -7x?
Easy
- A-7
- B7
- Cx
- D-1
18.Which of the following is an expression?
Easy
- A3x + 2
- B3x + 2 = 5
- Cy = 3x + 2
- D3x + 2 > 5
19.Simplify 4x² + 3x - 2x² + 5x.
Easy
- A2x² + 8x
- B6x² + 8x
- C2x² + 2x
- D6x² + 2x
20.If a = 3 and b = -2, find the value of 2a² - 3b.
Medium
- A24
- B6
- C18
- D12
21.Solve for x: 2(x + 3) = 5x - 9.
Medium
- A5
- B3
- C4
- D2
22.The formula for the area of a trapezium is A = 1/2 (a + b)h. Find h when A = 30, a = 4, b = 6.
Medium
- A6
- B3
- C10
- D2
23.Which of the following is a formula?
Easy
- Av = u + at
- B3x + 2
- C2x = 10
- Dx > 5
24.What is the value of 10 - 2x when x = 3?
Easy
- A4
- B16
- C24
- D-16
25.Simplify 3a − 5b − a + 2b.
Easy
- A2a − 3b
- B4a − 7b
- C2a − 7b
- D4a − 3b
26.f = 3g + 7h. Work out f when g = −5 and h = 2.
Easy
- A−1
- B29
- C−29
- D1
27.y = mx + c. Find y when m = −3, x = −2, and c = −8.
Easy
- A−2
- B2
- C14
- D−14
28.G = (c² − 4)/c. Find G when c = −5.
Medium
- A−4.2
- B4.2
- C−21/5
- D21/5
29.Amy has x beads. Billy has three more beads than Amy. Carly has four times as many beads as Billy. Which expression describes the number of beads that Carly has?
Medium
- A4x + 3
- B3x + 4
- C4(x + 3)
- Dx + 12
30.Which of the following is an algebraic expression?
Easy
- A3x + 2 = 5
- B4y - 7
- C5 = 2 + 3
- Dx > 2
31.What is the coefficient of x in the term -3x?
Easy
- A3
- B-3
- Cx
- D-x
32.The term '5' is a constant.
Easy
True or false?
33.If a = -3 and b = 4, what is the value of 2a + b²?
Medium
- A10
- B22
- C-2
- D14
34.Simplify 5x + 3y - 2x + y.
Easy
- A3x + 4y
- B7x + 4y
- C3x + 2y
- D7x + 2y
35.The terms 4x and 4x² are like terms.
Easy
True or false?
36.Which of the following are like terms with 3xy? (Select all that apply)
Medium
- A2xy
- B3x
- C5yx
- D3x²y
- Exy
37.Match each algebraic term with its coefficient of x.
Medium
- 3x
- -5x
- x
- 0x
- 3
- -5
- 1
- 0
38.Arrange the following steps to simplify 5a + 3b - 2a + 4b in the correct order.
Medium
- Combine a terms: 5a - 2a = 3a
- Combine b terms: 3b + 4b = 7b
- Write the simplified expression: 3a + 7b
- Identify like terms
39.Which of the following are like terms with 4xy? (Select all that apply)
Medium
- A3xy
- B4x²y
- C-2xy
- D4y
- Eyx
40.Complete the sentence using the correct algebraic vocabulary.
Easy
In the expression 7x + 3, the number 7 is called the ____ of x.
41.Write down an algebraic expression for 'three times a number added to five'.
Easy
42.Substitute x = 3 and y = -2 into the expression 2x² - 3y. What is the value?
Medium
43.Use the formula v = u + at. Find v when u = 10, a = -2, and t = 4.
Easy
44.Substitute x = -3 and y = 2 into the expression 2x² - 3y and find the value.
Medium
45.Explain the difference between an expression and an equation. Give an example of each.
Medium
46.Substitute x = 3 and y = -2 into the expression 2x² - 3y. What is the value?
Medium
- A24
- B28
- C22
- D26
47.Use the formula v = u + at. Find v when u = 10, a = -2, and t = 4.
Easy
- A3
- B4
- C1
- D2
48.Substitute x = -3 and y = 2 into the expression 2x² - 3y and find the value.
Medium
- A12
- B11
- C13
- D14

Ghi chú ôn tập

## Algebra Toolkit - Night Before Exam Summary ### 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 number, variable, or product (e.g., `5x`, `-3y²`). - **Coefficient**: the number in front of a variable (e.g., in `6x`, coefficient is 6). - **Expression**: no equals sign (e.g., `2x + 5`). - **Equation**: has an equals sign, can be solved (e.g., `2x = 10`). - **Formula**: a rule relating quantities (e.g., `s = ut + ½at²`). ### Substitution - Replace letters with given numbers. - Use brackets around negative numbers: `(-3)`. - Follow order of operations (BIDMAS). - Example: If `x = 2`, `y = -4`, then `2x(x + 3y) = 2×2×(2 + 3×(-4)) = -40`. ### Collecting Like Terms - Like terms have same variables and powers (e.g., `2x` and `5x`). - Add/subtract coefficients only. - Example: `8a - 5b - 6a + 4b = 2a - b`. ### Key Formulas - `s = ut + ½at²` (displacement with constant acceleration). - `y = mx + c` (straight line). - `B = m/h²` (body mass index). ### Tips - Simplify `1x` to `x`. - For negative substitution, e.g., `x = -4`, `x² = (-4)² = 16`.

Variable: A letter representing an unknown or general number.
Coefficient: The number multiplying a variable (e.g., in 5x, coefficient is 5).
Term: A single number, variable, or product (e.g., 3x, -2y²).
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 between quantities using letters.
Substitution: Replacing a variable with a given number.
Like terms: Terms with exactly the same variables and powers.
Collecting like terms: Simplifying by adding/subtracting coefficients of like terms.

Unlock all 48 questions & more

Tạo tài khoản miễn phí để xem mọi câu hỏi, slide, thẻ ghi nhớ và ghi chú ôn tập cho chủ đề này.

ĐĂNG KÝ — MIỄN PHÍ ĐĂNG NHẬP

Đề thi cũ

Luyện đề thi cũ cho chủ đề này sắp ra mắt.

Sắp ra mắt