Dr. J's Maths.com
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are explained in simple terms.

Algebra - Equations - Changing the subject.
Test Yourself 1.


 

In the questions below, the focus is on:
1. Basic formats.
2. Common factors.
3. Fractions.
4. Squares and square roots.
5. (a bit) harder examples.

 

Basic format 1. Change the subject to m:

y = mx + b

 2. Change the subject of the following velocity formula to a:

v2 = u2 + 2as
  3. Make y the subject of the equation

2x + dy = 5.

 4. Make d the subject of

T = a + (n - 1)d
  5. Rewrite the equation

T = 950 (1 - m)

to make m the subject.

 6. Make y the subject of .
  7. Make d the subject of . 8. Make b the subject of .
  9. The formula

H = 5m(Y - X)

is used to calculate the heat (H) required to raise the temperature of a steel rod of mass m from a temperature of X to a temperature of Y.

Rearrange the formula to make X the subject.

 10. Make x the subject in the equation:

3(x - 2) + 4(x - b) = b
  11. Rewrite the formula

V = 3r2h + 9

with r2 as the subject.

 12. The formula for the area of a triangle is .

Rewrite this equation with b as the subject.
  13. Make m the subject in Einstein's famous formula of

E = mc2.

 14. Change the subject in the following formula to V:

Common factors 15. Make y the subject in

a(x - b) + b(y - a) = xy

 16. Make x the subject of

xz = w - xy

 
  17. Make x the subject in the following equation:

ax - bx = 3 - 4a

 18. Change the subject to b:

A = 2ab + 2bc + 2ac
  19. Make z the subject in the following equation:

xy - yz + xz = 2

 20.Make m the subject of:

Fractions 21. Make m the subject of

22. Change the subject of the following equation to c:

  23. Change the subject to c:

24. For the following formula:

(i) Change the subject to x.

(ii) Change the subject to m.
  25. Make a the subject of

26. Rearrange this formula to make b the subject:

.
  27. Make r the subject of the equation

.

 
28. Rearrange this formula to make R the subject:

Squares and square roots.

For each of the following questions 29 - 42, rearrange the given equation to the subject indicated and state what restrictions must be assumed.
  29. Change the subject to u:

v2 = u2 + 2as

30. Make x the subject of

y = x2
  31. Make c the subject of

E = mc2

 32. Make r the subject of A = π r2
  33. Make v the subject of

34. Make r the subject of

  35. Make y the subject of

x2 + y2 - 2ax + c = 0

 36. Change the subject of the following formula to N:

M = 2N2.
  37. Change the subject of the following equation to c:

A = bc2 + d.

 38. Change the subject of
D = to b.
  39. Make y the subject in the following formula:

40. The time (in seconds) for a single swing of the pendulum in an old grandfather clock is given by the formula where L is the length of the pendulum (in cm).

(i) Change the subject of the equation to L.

(ii) It takes 2.5 seconds for a single swing of the pendulum. Calculate the length (L) of the pendulum.

Answer.Length = 61.25 cm.
  41. Given the formula

(i) Change the subject of the equation to a.

(ii) Find the value of a if b = 3 and c = 2 (correct to 3 significant figures).

Answer.a = + & - 5.48.		 42. Change the subject of the following equation from P to r:

.

Harder fractions

(do not consider restrictions here).

 43. Make y the subject of

44. Make y the subject of