Algebraic expressions · Ages 13–14
Substituting into formulae worksheet
Part of: Formulae & algebraic fractions
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Substituting into formulae 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.In the formula v = u + at, u = 2, a = 7 and t = 5: v =
Answer:
2.Celsius C to Fahrenheit F: F = 9C5 + 32. When C = 30, F =
Answer:
3.Celsius C to Fahrenheit F: F = 9C5 + 32. When C = −5, F =
Answer:
4.In the formula v = u + at, u = 14, a = 5 and t = 11: v =
Answer:
5.In the formula v = u + at, v = 63, u = 23 and t = 10: a =
Answer:
6.In the trapezium's area formula A = (a + b)h2, A = 95, a = 10 and h = 10: b =
Answer:
7.In the trapezium's area formula A = (a + b)h2, A = 63, a = 9 and h = 7: b =
Answer:
8.In the formula v = u + at, v = 7, u = 28 and t = 7: a =
Answer:
9.In the formula s = (u + v)t2, s = 55, u = 13 and t = 5: v =
Answer:
10.In the formula 1f = 1u + 1v, u = 5 and v = 17: f =
Answer in simplest form
Answer:
Part B: Choose, or true or false (2 marks each)
11.y = x2 − 9x. What is y when x = −2?
- A. 22
- B. −14
- C. −22
- D. 14
Choose the right answer
Answer:
12.y = x2 − 8x. What is y when x = −7?
- A. 7
- B. −7
- C. 105
- D. −105
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.By v = u + at: a motorbike speeds up from 6 m/s, gaining 3 m/s every second. After 4 s, v = m/s; it reaches 21 m/s after s.
Fill in each blank
Working:
Answer:
14.Hiring a camper van costs C = 50 + 300n, C in dollars and n the number of days. A family paid $2,150. For how many days?
Working:
Answer:
15.A quiz scores S = 5w − 2m, w right answers and m wrong ones. With 5 right and 7 wrong, what is the score S?
- A. 11
- B. 23
- C. 39
- D. 36
Choose the right answer
Working:
Answer:
16.Fahrenheit F and Celsius C are related by F = 9C5 + 32. It is −22 degrees Fahrenheit. How many degrees Celsius is that?
Working:
Answer:
17.By s = (u + v)t2: a bicycle speeds up steadily from 6 m/s to 30 m/s, covering 54 m. How many seconds did that take?
Working:
Answer:
18.A trapezium flower bed has area A = (a + b)h2. Its parallel sides are 3 m and 16 m and its area 57 m². What is its height h, in m?
Working:
Answer:
Show the answers and working
Substituting into formulae worksheet: Answers and working
Part A: Working out and filling in
1. 37
v = 2 + 7 × 5 = 37. Times before plus.
2. 86
F = 9 × (30) ÷ 5 + 32 = 86. A negative value goes in a bracket.
3. 23
F = 9 × (−5) ÷ 5 + 32 = 23. A negative value goes in a bracket.
4. 69
v = 14 + 5 × 11 = 69. Times before plus.
5. 4
Substituted: 63 = 23 + 10a, so 10a = 63 − 23 = 40, a = 4.
6. 9
95 = (10 + b) × 10 ÷ 2, so 10 + b = 95 × 2 ÷ 10 = 19, and b = 9.
7. 9
63 = (9 + b) × 7 ÷ 2, so 9 + b = 63 × 2 ÷ 7 = 18, and b = 9.
8. −3
Substituted: 7 = 28 + 7a, so 7a = 7 − 28 = −21, a = −3.
9. 9
55 = (13 + v) × 5 ÷ 2; times 2, then divide by 5: 13 + v = 22, v = 9.
10. 8522
1f = 15 + 117 = 2285; turned over, f = 8522 = 8522. Not 5 + 17.
Part B: Choose, or true or false
11. A. 22
y = (−2)2 − 9 × (−2) = 4 + 18 = 22.
12. C. 105
y = (−7)2 − 8 × (−7) = 49 + 56 = 105.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 18, 5
v = 6 + 3 × 4 = 18; 21 = 6 + 3t, so 3t = 21 − 6 and t = 5.
14. 7 days
Substitute: 2150 = 50 + 300n, so 300n = 2150 − 50 and n = 7.
15. A. 11
S = 5 × 5 − 2 × 7 = 11.
16. −30°C
−22 = 9C5 + 32, so 9C5 = −22 − 32 = −54 and C = −54 × 5 ÷ 9 = −30.
17. 3 s
54 = (6 + 30)t2, so 36t = 108 and t = 3.
18. 6 m
57 = (3 + 16)h2, so 19h = 114 and h = 6.
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