Algebra Worksheet for Secondary School Students. 中学学生的代数题

If you have a teenage child in your family, get this child to sit down and take this half hour test.

Of course, you need to print out the questions first and to hand this worksheet to your child to do.

And, of course, you need to time your child’s effort, recording the starting and ending times.

Then compare your child’s answers with the answers given below. After that, ask your child to explain the logical steps taken in obtaining each answer.

如果您的家人中有一个十几岁的孩子，请让这个孩子坐下并接受这个半小时的代数题测试。当然，您需要先打印出问题，然后将此工作题交给孩子去做。让孩子用半小时的时间，看一看他可以做完吗。您需要安排孩子的时间，记录开始和结束时间。然后将您孩子的答案与下面给出的答案进行比较。之后，请您的孩子解释获得每个答案所采取的逻辑步骤。

Mathematics Revision in Algebra for Secondary School Students.

# 1. Solve for x, y, and z.

4x = 112

5y + 4 = 54

12z - 12 = 0

6(y + 1) = 36

2(x + y + z) = 12 together with 3(x + y) = 9

20 = 4y + 8

4z - 5 = 21

2x - 5 = 35

48 = 12y

# 2. If a = 7 and b = 8, what is the answer to:

a + b

3b - 2a

a divided by b

4b + 2(3a + 7)

a + 2b - (5a + b)

a2 + b2

#3. Get answers to this number series and describe the pattern of each series in algebraic terms.

Series a: —- —- 55 67 79

Series b: 8 11 14 17 —- —- —-

Series c: 7 —- —- 34

Series d: 12 22 33 45 58 —- —-

Series e: pattern for nth term is 4n - 5, what are the 5th term, the 8th term and the 15th term?

#4. Expressing number problems in algebraic terms.

(a) A tiler calculates his price by the formula 7a + 8 where ‘a’ is the area of the floor to be tiled, in m2.

What is the cost of tiling an area of 125 m2?

If the total cost of tiling is $330, what is the floor area to be tiled?

(b) A painter’s hourly charge is $25.00. For each job, there is an additional charge of $38.00 for administration. Using ‘h’ as the number of hours worked, what is the formula that the painter is using to calculate his price?

(c) If ‘s’ represents the cost of the seeds of a crop and ‘w’ represents the cost of water required for the seed to grow, and the ratio ‘mn’ is equal to 48, what are the likely costs of the seeds and the water consumed?

(d) A home cleaner spends ‘h’ hours in cleaning a house. His hourly time rate is $13.50. If he spends $45.00 on other costs (like costs of cleaning liquids, transport, and so on) for every five hours work, give the formula for calculating the cleaning price for each hour that he works. What is the cost of cleaning a house where he estimates it will take an hour and a half for two cleaners?

ANSWERS:

# 1: 4x= 112; x = 112 divided by 4 = 28

5y + 4 = 54; 5y = 54 - 4 = 50; y = 10

12z - 12 = 0; 12z = 12; z = 12 divided by 12 = 1

6(y + 1) = 36; y + 1 = 36 divided by 6 = 6; y = 6 - 1 = 5

2(x + y + z) = 12; so, (x + y + z) = 12 divided by 2 = 6 Then, 3(x + y) = 9; (x + y) = 3; z = 6 - 3 = 3; and x + y is also equals to 3. Therefore either a or b = 1 or 2. Answer: x = 1, y = 2, z = 3 or x = 2, y = 1 and z = 3.

20 = 4y + 8; 4y = 20 - 8 = 12; y = 3.

4z - 5 = 21; so 4z = 16; z = 4.

2x - 5 = 35; 2x = 35 + 5 = 40; x = 20.

48 = 12y; y = 48 divided by 12 = 4.

# 2: a = 7; b = 8; a + b = 7 + 8 = 15.

3b - 2a = (3 x 8) - (2 x 7) = 24 - 14 = 10

a divided by b = 7 divided by 8. This can be a fraction 7/8. or a decimal 0.875

4b + 2(3a + 7) = (4 x 8) + (6 x7) + 14; This is equal to 32 + 42 + 14; = 88

a + 2b - (5a - b) = 7 + (2 x 8) - (5 x 7) + 8 = 7 + 16 - 35 + 8 = 3.

a2 + b2 = (2 x 7) + (8 x 2) = 14 + 16 = 30

# 3: series a: Pattern term n = pn + 12, ‘n’ = term; pn = previous ‘n’ so 55 - 12 = 43; then 43 - 12 = 31

31. 43. 55. 67. 79

series b: 8. 11. 14. 17. —- —- n = pn + 3; So, 8. 11. 14. 17. 20. 23.

series c: 7. —- —- 34. Difference is 38 - 7 = 27. There are three gaps. Each gap = 27/3. = 9

So, series will read as 7. 16. 25. 34. pattern is n + 9

series d: 12. 22. 33. 45. 58. Gap # 1 = 10; Gap # 2 = 11; Gap # 3 = 12; Gap # 4 = 13. pattern is n = 10 + pg + 1, ‘pg’ previous gap. Next two terms = 72. 87.

series e: 5th term = 4 x 5 - 5 = 20 - 5. = 15; 8th term = 4 x 8 - 5 = 27; 15th term = 4 x 15 - 5 = 55.

# 4 (a): pattern = 7a + 8. 125m2 answer is 7 x 125 + 8 = 883. Total cost is $330; so 7a + 8 = 330; 7a = 330 - 8; 7a = 322; area of floor = 322/7 = 46 m2

# 4 (b): Formula is 25h + 38

# 4 (c): mn = 48; m and n can be 1 and 48; or 2 and 24; or 3 and 16; or 4 and 12; or 6 and 8.

# 4 (d): Other cost is $45.00 for 5 hours. Each hour = $9.00. His hourly rate is $13.50. So, his total price per hour can be expressed as T = 22.5h where ‘h’ is the hour and T is the Total Price. One and a half hour for two cleaners charging the same rate is equal to 3 hours. Answer: 3 hours x 22.5 = $67.50