Algebraic expressions · Ages 12–13
Algebraic expressions & sequences worksheet
Covers: Words into algebra, Situations into algebra, Reading algebra as words, Substitution and input–output machines, Patterns in sequences, Growing patterns and the n-th term
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Algebraic expressions & sequences worksheet
Algebraic expressions · Ages 12–13
Numsprite
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Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.Take 9 from y, then multiply by 7. With y = 20, the value is .
Answer:
2.x hours 45 minutes = (x + 45) minutes; with x = 5, that is minutes.
Fill in each blank
Answer:
3.n books cost 90n + 35 dollars in all: each book is $, and postage is $ on top.
Fill in each blank
Answer:
4.When x = 9, 4x2 =
Answer:
5.When a = 7 and b = 9, 9(a + b) − ab =
Answer:
6.4-sided polygon numbers: 1, 4, 9, 16, … The gap grows by 2 each time. Number 5 is .
Answer:
7.Each term is the sum of the two before: 2, 9, 11, 20, ,
Fill in each blank
Answer:
8.The n-th term of a sequence is 12n + 1. Term 14 is .
Answer:
Part B: Choose, or true or false (2 marks each)
9.What is '5 times the sum of x and 4' as an algebraic expression?
- A. 5(x + 4)
- B. x + 20
- C. x + 9
- D. 5x + 4
Choose the right answer
Answer:
10.Ka-yan is x years old, and Dad is 36 years older. How old will Dad be in 11 years?
- A. x + 47
- B. x + 36
- C. x + 11
- D. x + 25
Choose the right answer
Answer:
11.How does 3(x + 9) read in words?
- A. 9 times the sum of x and 3
- B. 3 times x, plus 9
- C. x plus 27
- D. 3 times the sum of x and 9
Choose the right answer
Answer:
12.Count the matchsticks in each pattern. How many are in pattern n?
- A. 6n
- B. n + 5
- C. 5n + 6
- D. 5n + 1
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.An older sister has x stickers and a younger sister y. The older has 14 more than 8 times the younger's. Which is right?
- A. y = 8x + 14
- B. x = 8(y + 14)
- C. x = 8y + 14
- D. x + 14 = 8y
Choose the right answer
Working:
Answer:
14.A taxi charges $22 for the first 3 km, then $9 a km. How many dollars is a ride of n km (n more than 3)?
- A. 22 + 9(n − 3)
- B. 22 + 9n
- C. 49 + 9n
- D. (22 + 9)n
Choose the right answer
Working:
Answer:
15.May's three scores are x, y and 67. What does x + y + 673 stand for?
- A. The total of the three scores
- B. The average of the three scores
- C. One third of the third score
- D. The gap between the best and worst scores
Choose the right answer
Working:
Answer:
16.A stone falls from a height, dropping 10t2 metres in t seconds. How far has it dropped after 5 seconds?
Working:
Answer:
17.Ka-yee saves $45 in week 1, then $16 more each week. How many dollars are saved in week 13?
Working:
Answer:
18.Square n has n rows of n players. How many more are needed to go from square 15 to square 16?
Working:
Answer:
Show the answers and working
Algebraic expressions & sequences worksheet: Answers and working
Part A: Working out and filling in
1. 77
The expression is 7(y − 9). Put in the number: 20 − 9 = 11, 11 × 7 = 77.
2. 60, 345
One hour has 60 minutes, so x hours have 60x. Put in the number: 60 × 5 + 45 = 345.
3. 90, 35
The 90 multiplying n is the price of each book; the 35 alone doesn't change with n, so it is the fixed postage.
4. 324
The power first: 92 = 81, then times 4: 4 × 81 = 324. It isn't 362.
5. 81
ab is a × b: 9 × (7 + 9) − 7 × 9 = 9 × 16 − 63 = 144 − 63 = 81.
6. 25
The gaps are 3, 5, 7, then 2 more each time. Keep adding up to place 5: 25.
7. 31, 51
11 + 20 = 31, then 20 + 31 = 51.
8. 169
Put 14 for n: 12 × 14 + 1 = 168 + 1 = 169.
Part B: Choose, or true or false
9. A. 5(x + 4)
The sum x + 4 first, then times 5: 5(x + 4). Check with x = 10: (10 + 4) × 5.
10. A. x + 47
Dad is x + 36 now, and in 11 years x + 36 + 11 = x + 47.
11. D. 3 times the sum of x and 9
The bracket x + 9 first, times 3 last: '3 times the sum'.
12. D. 5n + 1
The sticks go 6, 11, 16, adding 5 each time. Compared with 5n, each is 1 more: 5n + 1.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. C. x = 8y + 14
8 times the younger's is 8y, and 14 more makes the older's: x = 8y + 14.
14. A. 22 + 9(n − 3)
$22 for the first 3 km, and n − 3 km more at $9: 22 + 9(n − 3).
15. B. The average of the three scores
The bracket is the total; dividing by 3, how many there are, gives the average.
16. 250
The power first: 52 = 25, then times 10: 250. It isn't 502, as the index belongs to t alone.
17. 237
From week 1 to week 13 there are 12 rises: 45 + 12 × 16 = 45 + 192 = 237.
18. 31
Square 15 has 152 = 225 and square 16 has 162 = 256: 256 − 225 = 31 more.
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