In the formula v = u + at, u = 9, a = 9 and t = 5: v = □

54. v = 9 + 9 × 5 = 54. Times before plus.

y = x^2 − 8x. What is y when x = −5? A. −65 B. −15 C. 15 D. 65 Choose the right answer

D. 65. y = (−5)^2 − 8 × (−5) = 25 + 40 = 65.

In the formula s = (u + v)t/2, s = 5, u = 0 and t = 2: v = □

5. 5 = (0 + v) × 2 ÷ 2; times 2, then divide by 2: 0 + v = 5, v = 5.

Formulae & algebraic fractions · Ages 13–14

Substituting into formulae

Substituted, it is an equation; bracket a negative value.

How to do it

Method

Substituted, it is an equation; bracket a negative value

v = u + at: 30 = 6 + 4a, a = 6

Another way

Change the subject first

a = v − ut = 30 − 64 = 6

In full

A formula says how some quantities are related, like v = u + at. Put in the values you know and you get an equation with one unknown; solve it. With v = 30, u = 6 and t = 4: 30 = 6 + 4a, 4a = 24, a = 6. Put a negative value in a bracket: when u = −5, u² is (−5)² = 25. Or change the subject first and then substitute: a = v − ut = 30 − 64 = 6, the same answer, and quicker when one formula takes many sets of values.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
In the formula v = u + at, u = 9, a = 9 and t = 5: v =
Show the answer and working
Answer: 54
v = 9 + 9 × 5 = 54. Times before plus.
Example 2
y = x² − 8x. What is y when x = −5?
- A. −65
- B. −15
- C. 15
- D. 65
Choose the right answer
Show the answer and working
Answer: D. 65
y = (−5)² − 8 × (−5) = 25 + 40 = 65.
Example 3
In the formula s = (u + v)t2, s = 5, u = 0 and t = 2: v =
Show the answer and working
Answer: 5
5 = (0 + v) × 2 ÷ 2; times 2, then divide by 2: 0 + v = 5, v = 5.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1.Celsius C to Fahrenheit F: F = 9C5 + 32. When C = 25, F =
Answer:
2.In the formula v = u + at, v = 57, u = 21 and t = 6: a =
Answer:
3.In the trapezium's area formula A = (a + b)h2, A = 30, a = 7 and h = 3: b =
Answer:
4.y = x² − 7x. What is y when x = −4?
- A. −44
- B. 44
- C. 12
- D. −12
Choose the right answer
Answer:
5.In the formula s = (u + v)t2, s = 42, u = 9 and t = 3: v =
Answer:

All the answers

1. 77
2. 6
3. 13
4. B. 44
5. 19

Free worksheet: Substituting into formulaeWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

VIP practice notes and papers

Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.

Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
Practice paper: Set out in parts like a school paper, marked, with answers and full working

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