Translating problems into equations

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課程筆記

Turning words into algebra

Choose a letter for the unknown and say what it stands for: "let x be the number of sweets."
Translate key phrases: "3 more than" is +3; "twice a number" is 2x; "5 less than" is x - 5; "the product of" means multiply; "the sum of" means add.
"Is" or "gives" or "equals" usually marks the equals sign.

Forming and solving equations

Write the information as an equation, solve it, then answer the original question in words with units.
A number is doubled and 7 is added, giving 25: 2x + 7 = 25, so x = 9.
Consecutive integers are n, n + 1, n + 2. Consecutive even integers are 2n, 2n + 2, 2n + 4 for integer n.

Geometry and perimeter problems

Use the perimeter or angle facts: a rectangle with sides x and x + 4 and perimeter 28 gives 2x + 2(x + 4) = 28, so x = 5.
Angles in a triangle sum to 180°; angles on a straight line sum to 180°; angles round a point sum to 360°.

Problems with two unknowns and quadratics

With two unknowns, form two equations and solve simultaneously.
Area problems often lead to quadratics: a rectangle of width x, length x + 3 and area 40 gives x² + 3x - 40 = 0; reject a negative length.

Checking

Substitute back into the words of the problem to check it makes sense.

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練習題

免費預覽——35 題中的 8 題。註冊即可查看全部。

1.What is \"five more than x\" in algebra?
Easy
- A5x
- Bx + 5
- Cx - 5
- D5 - x
2.What is "twice a number, plus 3"?
Easy
- A2(x + 3)
- B2x + 3
- Cx² + 3
- D3x + 2
3.A number is trebled and 4 is subtracted to give 20. Which equation is formed?
Easy
- A3x - 4 = 20
- B3(x - 4) = 20
- C3x + 4 = 20
- Dx - 4 = 60
4.A number is trebled and 4 is subtracted to give 20. What is the number?
Easy
- A8
- B5.33
- C24
- D16
5.Pens cost £p each. Five pens and a £2 notebook cost £12. What is p?
Easy
- A2
- B2.8
- C10
- D14
6.Two numbers add to 30. One is 6 more than the other. What is the smaller?
Easy
- A12
- B18
- C24
- D15
7.The sum of three consecutive integers is 48. What is the smallest?
Easy
- A15
- B16
- C17
- D14
8.Sam is 4 years older than Jo. Their ages sum to 30. How old is Jo?
Easy
- A13
- B17
- C15
- D26

更多題目

9.A rectangle has sides x and x + 4 and perimeter 28 cm. What is x?
Easy
- A5
- B6
- C7
- D4.5
10.The angles of a triangle are x, 2x and 3x. What is the smallest angle?
Medium
- A30°
- B60°
- C90°
- D20°
11.The angles of a triangle are x, x + 10 and x + 20. What is x?
Medium
- A50°
- B60°
- C40°
- D70°
12.A taxi charges £3 plus £2 per km. A journey costs £17. How far is it?
Medium
- A7 km
- B8.5 km
- C10 km
- D5 km
13.Tickets cost £8 each and a £5 booking fee is added. The total is £53. How many tickets?
Medium
- A5
- B6
- C7
- D8
14.A number squared is 5 more than 4 times the number. Which equation is formed?
Medium
- Ax² = 4x + 5
- Bx² = 5x + 4
- C2x = 4x + 5
- Dx² + 5 = 4
15.Three consecutive even numbers add to 54. What is the largest?
Medium
- A16
- B18
- C20
- D22
16.I think of a number, double it, and subtract 5. The result is the same as adding 3 to the number. What is it?
Medium
- A8
- B5
- C3
- D2
17.A rectangle is x wide and x + 3 long with area 40. Which equation is formed?
Medium
- Ax² + 3x - 40 = 0
- Bx² + 3 = 40
- C2x + 3 = 40
- Dx² - 3x = 40
18.A rectangle is x cm wide and (x + 3) cm long, with area 40 cm². What is its width?
Medium
- A5 cm
- B8 cm
- C3 cm
- D10 cm
19.Adult tickets cost £7 and child tickets £4. 10 tickets cost £52. How many adult tickets were bought?
Medium
- A4
- B5
- C6
- D7
20.The sum of the squares of two consecutive positive integers is 61. What are they?
Medium
- A5 and 6
- B4 and 5
- C6 and 7
- D3 and 4
21.Angles on a straight line add up to:
Easy
- A90°
- B180°
- C270°
- D360°
22.Angles around a point add up to:
Easy
- A180°
- B270°
- C360°
- D90°
23.Two angles on a straight line are 2x and x + 30. What is x?
Medium
- A50°
- B40°
- C60°
- D30°
24.A pen costs 20p more than a pencil. Together they cost £1.10. What does the pencil cost?
Medium
- A45p
- B65p
- C90p
- D55p
25.Why should you state what the unknown represents?
Easy
- Ato make the answer clearer and check the context
- Bto make the answer longer
- Cit is not necessary
- Dto avoid using algebra
26.In a word problem, x represents a physical length. An equation gives x = −3. What does this tell you about that candidate answer?
Medium
- Athe answer is correct
- Bthe solution must be rejected
- Clength is 3
- Dadd 6
27.Which equation matches "a number divided by 4, plus 2, equals 9"?
Easy
- A\frac{x}{4} + 2 = 9
- B\frac{x + 2}{4} = 9
- C4x + 2 = 9
- D\frac{4}{x} + 2 = 9
28."Twice a number" can be written 2x.
Easy
True or false?
29.Angles on a straight line add to 360°.
Easy
True or false?
30.You should check a solution back in the words of the problem.
Easy
True or false?
31.Consecutive integers can be written n, n + 2, n + 4.
Easy
True or false?
32.A negative length can be accepted as the final physical answer to an area problem.
Medium
True or false?
33.Which expressions mean "3 more than twice x"?
Medium
- A2x + 3
- B3 + 2x
- C2(x + 3)
- D3x + 2
- E2x - 3
34.Which statement is modelled by 2x + 4 = 18?
Easy
- Adouble a number and add 4 to get 18
- Badd 4 to a number and double it to get 18
- Cmultiply a number by 4 to get 18
- Dsubtract 4 and halve to get 18
35.The sides of a triangle are x, x + 2 and 2x - 1 cm. The perimeter is 21 cm. Find the longest side.
Medium

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