Algebraic expressions · Ages 13–14
Changing the subject of a formula worksheet
Part of: Formulae & algebraic fractions
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Changing the subject of a formula worksheet
Algebraic expressions · Ages 13–14
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.Make x the subject of y = 7x − 12: x = y +
Fill in each blank
Answer:
2.Make x the subject of y = 5x − 9: x = y +
Fill in each blank
Answer:
3.Make x the subject of y = 6 − 4x: x = − y
Fill in each blank
Answer:
4.Make x the subject of y = 7 − 2x: x = − y
Fill in each blank
Answer:
Part B: Choose, or true or false (2 marks each)
5.Which is the formula P = 5n + 21 with n as its subject?
- A. n = P5 − 21
- B. n = P + 215
- C. n = 5(P − 21)
- D. n = P − 215
Choose the right answer
Answer:
6.Which is the formula P = 4n + 17 with n as its subject?
- A. n = P4 − 17
- B. n = P + 174
- C. n = P − 174
- D. n = 4(P − 17)
Choose the right answer
Answer:
7.Which is the formula y = x + 124 with x as its subject?
- A. x = 4y − 12
- B. x = 4y + 12
- C. x = y4 − 12
- D. x = 4(y − 12)
Choose the right answer
Answer:
8.From P = 5(l + w), it follows that l = P6 − w.
True or false?
Answer:
9.Which is the formula S = 6(m − t) with t as its subject?
- A. t = S6 − m
- B. t = m − 6S
- C. t = m − S6
- D. t = m − S6
Choose the right answer
Answer:
10.From P = 2(l + w), it follows that l = P3 − w.
True or false?
Answer:
11.Which is the formula y = x + 89 with x as its subject?
- A. x = 9y − 8
- B. x = 9y + 8
- C. x = 9(y − 8)
- D. x = y9 − 8
Choose the right answer
Answer:
12.Which is the formula M = p + q4 with q as its subject?
- A. q = 4(M − p)
- B. q = 4M − p
- C. q = 4M + p
- D. q = M4 − p
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.The mean of 6 numbers is M; 5 of them add to S, and the last is x: M = S + x6. Which is the formula with x as its subject?
- A. x = 6M + S
- B. x = 6(M − S)
- C. x = 6M − S
- D. x = M6 − S
Choose the right answer
Working:
Answer:
14.A city's taxi fare is about C = 30 + 5d, C in dollars and d the distance in km. With d as the subject: d = C − ; a $70 fare means about km.
Fill in each blank
Working:
Answer:
15.A data plan: using m GB, every GB over 20 GB costs $8, so C = 98 + 8(m − 20) (for m > 20). One month's bill was $186. How many GB were used?
Working:
Answer:
16.F = 9C5 + 32. With C as the subject: C = F − 32; when F = −13, C = .
Fill in each blank
Working:
Answer:
17.A rectangle's perimeter is P = 2(l + w). Make w the subject, then find the width w when P = 46 and l = 18. What is w?
- A. 14
- B. 10
- C. 41
- D. 5
Choose the right answer
Working:
Answer:
18.A club charges C = 83 + 5n. Put the steps of making n the subject in order.
- A. C − 83 = 5n
- B. C = 83 + 5n
- C. C − 835 = n
- D. n = C − 835
Write the letters in the right order
Working:
Answer:
Show the answers and working
Changing the subject of a formula worksheet: Answers and working
Part A: Working out and filling in
1. 12, 7
Add 12 to both sides: y + 12 = 7x; divide both by 7: x = y + 127.
2. 9, 5
Add 9 to both sides: y + 9 = 5x; divide both by 5: x = y + 95.
3. 6, 4
Move 4x to the left and y to the right: 4x = 6 − y; divide by 4: x = 6 − y4.
4. 7, 2
Move 2x to the left and y to the right: 2x = 7 − y; divide by 2: x = 7 − y2.
Part B: Choose, or true or false
5. D. n = P − 215
Take 21 from both sides: P − 21 = 5n; divide both by 5: n = P − 215.
6. C. n = P − 174
Take 17 from both sides: P − 17 = 4n; divide both by 4: n = P − 174.
7. A. x = 4y − 12
Multiply both sides by 4: 4y = x + 12; take 12 from both: x = 4y − 12.
8. False
Divide both sides by 5: P5 = l + w; take w from both: l = P5 − w.
9. C. t = m − S6
Divide both sides by 6: S6 = m − t; then move the terms: t = m − S6.
10. False
Divide both sides by 2: P2 = l + w; take w from both: l = P2 − w.
11. A. x = 9y − 8
Multiply both sides by 9: 9y = x + 8; take 8 from both: x = 9y − 8.
12. B. q = 4M − p
Multiply both sides by 4: 4M = p + q; take p from both: q = 4M − p.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. C. x = 6M − S
Multiply both sides by 6: 6M = S + x; take S from both: x = 6M − S.
14. 30, 5, 8
Take 30 from both sides, then divide by 5: d = C − 305; with C = 70, d = 70 − 305 = 8.
15. 31 GB
With m as the subject: m = C − 988 + 20. With C = 186: m = (186 − 98) ÷ 8 + 20 = 31.
16. 5, 9, −25
Take 32 from both sides: F − 32 = 9C5; times 5, then ÷ 9: C = 5F − 329. With F = −13, C = −25.
17. D. 5
w = P2 − l = 46 ÷ 2 − 18 = 5.
18. B → A → C → D
Take 83 from both sides, divide both by 5, then write n on the left.
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