Question 1

LEVEL 6

Rearrange the following formula to make m the subject.

Ft = mv-mu

Select the correct answer from the options below.

A: m = \dfrac{Ft + mu}{v}

B: m = \dfrac{Ft-mu}{v}

C: m = \dfrac{Ft}{u-v}

D: m = \dfrac{Ft}{v-u}

 

CORRECT ANSWER:   D: m = \dfrac{Ft}{v-u}

 

WORKED SOLUTION:

Firstly, we should factorise out m on the right-hand side, to get

Ft = m(v-u)

Then, dividing by (v-u) makes m the subject. This gives us

m = \dfrac{Ft}{v-u}

 

 

Question 2

LEVEL 6

Rearrange the following formula to make b the subject.

a=\dfrac{2b-1}{b+2}

Select the correct answer from the options below.

A: b = \dfrac{2a+1}{2-a}

B: b = \dfrac{2a}{2-a}

C: b = \dfrac{2a+1}{2+a}

D: b = \dfrac{2a+1}{a-2}

 

CORRECT ANSWER:   A: b = \dfrac{2a+1}{2-a}

 

WORKED SOLUTION:

Multiply both sides by b+2 and expand the brackets

a(b+2)=2b-1

ab+2a=2b-1

Add 1 and subtract ab from both sides

2a+1 = 2b-ab

Factorise the RHS

2a+1 = b(2-a)

Divide both sides by 2-a

b=\dfrac{2a+1}{2-a}

 

 

Question 3

LEVEL 6

Rearrange the following formula to make F the subject.

T = 3F - dF

Select the correct answer from the options below.

A: F = \dfrac{T}{3-d}

B: F = \dfrac{T}{3+d}

C: F = \dfrac{T}{d-3}

D: F = \dfrac{3-d}{T}

 

CORRECT ANSWER:   A: F = \dfrac{T}{3-d}

 

WORKED SOLUTION:

Factorise the RHS

T = F(3-d)

Divide both sides by 3-d

F=\dfrac{T}{3-d}

 

 

Question 4

LEVEL 6

Rearrange the following formula to make x the subject.

\dfrac{x}{x+1} = \dfrac{y}{2z}

Select the correct answer from the options below.

A: x = \dfrac{y}{2z-y}

B: x = \dfrac{y}{2z+y}

C: x = \dfrac{2z-y}{y}

D: x = \dfrac{y}{y-2z}

 

CORRECT ANSWER:   A: x = \dfrac{y}{2z-y}

 

WORKED SOLUTION:

Multiply both sides by x+1 and 2z

2xz = y(x+1)

Expand the bracket on the RHS

2xz = xy + y

Subtract xy from both sides

2xz - xy=y

Factorise the LHS

x(2z-y)=y

Divide both sides by 2z-y

x = \dfrac{y}{2z-y}

 

 

Question 5

LEVEL 6

Rearrange the following formula to make r the subject.

2r^2 = qr^2 + 4r

Select the correct answer from the options below.

A: r = \dfrac{4}{2-q}

B: r = \sqrt{\dfrac{4}{2-q}}

C: r = \dfrac{4}{2+q}

D: r = \dfrac{4}{q-2}

 

CORRECT ANSWER:   A: r = \dfrac{4}{2-q}

 

WORKED SOLUTION:

Divide both sides by r

2r = rq + 4

Subtract rq from both sides

2r - rq = 4

Factorise the LHS

r(2-q) = 4

Divide both sides by 2-q

r = \dfrac{4}{2-q}