Algebra and equations · Ages 10–11
First algebra and simple equations worksheet
Covers: Algebra: letters for numbers, Words into algebraic expressions, Terms, coefficients and simplifying, Equations and setting them up, Simple equations
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First algebra and simple equations worksheet
Algebra and equations · Ages 10–11
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.When x = 8, the value of 6x is
Answer:
2.When n = 18, the value of n ÷ 6 + 9 is
Answer:
3.11m − m = m
Answer:
4.Given k + 15 = 29, the value of 3k is
Answer:
5.2x + 30 = 42, x = ?
Answer:
6.7x = 21, x = ?
Answer:
Part B: Choose, or true or false (2 marks each)
7.In which sentence does the letter stand for a number, as a letter in algebra does?
- A. A rope is 10 m long.
- B. A storybook costs y dollars, so 6 of them cost 6y dollars.
- C. Tsz-hin takes the 47A bus to the airport.
- D. Dad finds the way with the GPS on his phone.
Choose the right answer
Answer:
8.Which expression means “4 more than x”?
- A. x − 4
- B. 4x
- C. 4 − x
- D. x + 4
Choose the right answer
Answer:
9.Which expression means “x minus 7, then times 2”?
- A. x − 7 × 2
- B. 2(x − 7)
- C. 2x − 7
- D. 2x + 7
Choose the right answer
Answer:
10.Which expression means “a divided by 8, then plus 13”?
- A. (a + 13) ÷ 8
- B. a ÷ (8 + 13)
- C. a ÷ 8 + 13
- D. 8 ÷ a + 13
Choose the right answer
Answer:
11.3y + 3 + 4y simplifies to 7y + 3.
True or false?
Answer:
12.Which equation has the solution x = 11?
- A. 3x = 36
- B. 2x + 7 = 27
- C. x − 7 = 6
- D. x + 14 = 25
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.May is n years old, and May's dad is (4n + 3). When n = 13, how old is the dad?
Working:
Answer:
14.Each ballpoint pen costs x dollars. Chi-keung buys 8, paying 8x dollars. When x = 14, how many dollars does Chi-keung pay?
Working:
Answer:
15.Ka-yee has x dollars, buys a $17 book, then gets $11 pocket money. How many dollars does Ka-yee have now?
- A. x − 17 − 11
- B. x + 17 + 11
- C. x + 17 − 11
- D. x − 17 + 11
Choose the right answer
Working:
Answer:
16.A box holds b sweets. Ka-yee has 2 boxes and 5 loose sweets; Ming has 8 boxes and 4 loose. Together they have (b + ) sweets.
Fill in each blank
Working:
Answer:
17.Tsz-hin buys 5 boxes of the same chocolates, eats 20 and has 50 left. How many chocolates are in each box?
Working:
Answer:
18.Chi-keung has 10 stamps, which is 6 fewer than 2 times as many as Ka-lok has. How many stamps does Ka-lok have?
Working:
Answer:
Show the answers and working
First algebra and simple equations worksheet: Answers and working
Part A: Working out and filling in
1. 48
6x means 6 × x. Put 8 in place of x, then work it out.
6x means 6 × x: 6 × 8 = 48.
2. 12
Put 18 in place of n. In the usual order, divide first, then add.
Divide, then add: 18 ÷ 6 = 3, 3 + 9 = 12.
3. 10
What is the coefficient of m on its own? Write it in, then subtract.
m on its own has coefficient 1: 11m − 1m = 10m.
4. 42
The question asks for 3k, not k. Find k from k + 15 = 29 first, then multiply by 3.
Solve the equation first: take 15 from both sides, k = 29 − 15 = 14; then substitute: 3k = 3 × 14 = 42.
5. 2x + 30 = 42, x = 6
2x + 30 = 42: undo it in reverse, 42 − 30 = 12, 12 ÷ 2 = 6, so x = 6
6. 7x = 21, x = 3
7x = 21: undo it in reverse, 21 ÷ 7 = 3, so x = 3
Part B: Choose, or true or false
7. B. A storybook costs y dollars, so 6 of them cost 6y dollars.
Ask of each sentence: could the letter be swapped for a number? A letter in a unit, a name or a short form can't.
A letter in algebra stands for a number: y stands for a book's price. The letters in a unit (m, kg), a route's name (47A) or a short form (GPS) stand for no number.
8. D. x + 4
What operation does “4 more” mean? Think how x and 4 join up.
4 more is plus 4: x + 4.
9. B. 2(x − 7)
The first step is x minus 7. What must go round that part so the whole of it is multiplied by 2?
The part done first, x − 7, goes in brackets, then × 2: 2(x − 7).
10. C. a ÷ 8 + 13
See which step comes first. Division already comes before addition in the usual order, so are brackets needed?
Divide, then add, which is the usual order: a ÷ 8 + 13, no brackets needed.
11. True
Find the like terms first: 3y and 4y combine, but what about 3?
The y terms: 3y + 4y = 7y. The number term 3 can't join them: 7y + 3.
12. D. x + 14 = 25
Put x = 11 into each equation in turn and see which one balances.
Substitute x = 11 into each: only 11 + 14 = 25 holds.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 55 years old
Put May's age, 13, in place of n: work out 4 × 13, then add 3.
Put n = 13 in: 4 × 13 + 3 = 55, so the dad is 55 years old.
14. 112 dollars
8x means 8 × x. Put the price of one, 14, in place of x.
8x = 8 × 14 = 112 dollars.
15. D. x − 17 + 11
Write it a step at a time: buying the book takes money away, pocket money adds it. Deal with the $17 first.
Subtract the 17 spent, add the 11 received: x − 17 + 11.
16. 10, 9
Put both lots of boxes together (the b terms) and the loose sweets together (the numbers), and combine each lot.
2b + 5 + 8b + 4: the boxes make 10b and the loose ones 9, so 10b + 9.
17. 14 chocolates
Let each box hold x. 5 boxes hold 5x; after eating 20 there are 50: write the equation first.
A two-step equation: undo the subtraction of 20 first, then divide by 5.
Let each box hold x: 5x − 20 = 50. Add 20 to both sides: 5x = 70; divide both sides by 5: x = 14. Check: 5 × 14 − 20 = 50.
18. Chi-keung has 10 stamps, which is 6 fewer than 2 times as many as Ka-lok has. How many stamps does Ka-lok have? (Answer: 8 stamps)
Let Ka-lok have y: 2y − 6 = 10, so y = 8
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