Question 1

LEVEL 6

Rearrange the following formula to make mm the subject.

Ft=mv−muFt = mv-mu

Select the correct answer from the options below.

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

B: m=Ft−muvm = \dfrac{Ft-mu}{v}

C: m=Ftu−vm = \dfrac{Ft}{u-v}

D: m=Ftv−um = \dfrac{Ft}{v-u}

 

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

 

WORKED SOLUTION:

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

Ft=m(v−u)Ft = m(v-u)

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

m=Ftv−um = \dfrac{Ft}{v-u}

 

 

Question 2

LEVEL 6

Rearrange the following formula to make bb the subject.

a=2b−1b+2a=\dfrac{2b-1}{b+2}

Select the correct answer from the options below.

A: b=2a+12−ab = \dfrac{2a+1}{2-a}

B: b=2a2−ab = \dfrac{2a}{2-a}

C: b=2a+12+ab = \dfrac{2a+1}{2+a}

D: b=2a+1a−2b = \dfrac{2a+1}{a-2}

 

CORRECT ANSWER:   A: b=2a+12−ab = \dfrac{2a+1}{2-a}

 

WORKED SOLUTION:

Multiply both sides by b+2b+2 and expand the brackets

a(b+2)=2b−1a(b+2)=2b-1

ab+2a=2b−1ab+2a=2b-1

Add 11 and subtract abab from both sides

2a+1=2b−ab2a+1 = 2b-ab

Factorise the RHS

2a+1=b(2−a)2a+1 = b(2-a)

Divide both sides by 2−a2-a

b=2a+12−ab=\dfrac{2a+1}{2-a}

 

 

Question 3

LEVEL 6

Rearrange the following formula to make FF the subject.

T=3F−dFT = 3F - dF

Select the correct answer from the options below.

A: F=T3−dF = \dfrac{T}{3-d}

B: F=T3+dF = \dfrac{T}{3+d}

C: F=Td−3F = \dfrac{T}{d-3}

D: F=3−dTF = \dfrac{3-d}{T}

 

CORRECT ANSWER:   A: F=T3−dF = \dfrac{T}{3-d}

 

WORKED SOLUTION:

Factorise the RHS

T=F(3−d)T = F(3-d)

Divide both sides by 3−d3-d

F=T3−dF=\dfrac{T}{3-d}

 

 

Question 4

LEVEL 6

Rearrange the following formula to make xx the subject.

xx+1=y2z\dfrac{x}{x+1} = \dfrac{y}{2z}

Select the correct answer from the options below.

A: x=y2z−yx = \dfrac{y}{2z-y}

B: x=y2z+yx = \dfrac{y}{2z+y}

C: x=2z−yyx = \dfrac{2z-y}{y}

D: x=yy−2zx = \dfrac{y}{y-2z}

 

CORRECT ANSWER:   A: x=y2z−yx = \dfrac{y}{2z-y}

 

WORKED SOLUTION:

Multiply both sides by x+1x+1 and 2z2z

2xz=y(x+1)2xz = y(x+1)

Expand the bracket on the RHS

2xz=xy+y2xz = xy + y

Subtract xyxy from both sides

2xz−xy=y2xz - xy=y

Factorise the LHS

x(2z−y)=yx(2z-y)=y

Divide both sides by 2z−y2z-y

x=y2z−yx = \dfrac{y}{2z-y}

 

 

Question 5

LEVEL 6

Rearrange the following formula to make rr the subject.

2r2=qr2+4r2r^2 = qr^2 + 4r

Select the correct answer from the options below.

A: r=42−qr = \dfrac{4}{2-q}

B: r=42−qr = \sqrt{\dfrac{4}{2-q}}

C: r=42+qr = \dfrac{4}{2+q}

D: r=4q−2r = \dfrac{4}{q-2}

 

CORRECT ANSWER:   A: r=42−qr = \dfrac{4}{2-q}

 

WORKED SOLUTION:

Divide both sides by rr

2r=rq+42r = rq + 4

Subtract rqrq from both sides

2r−rq=42r - rq = 4

Factorise the LHS

r(2−q)=4r(2-q) = 4

Divide both sides by 2−q2-q

r=42−qr = \dfrac{4}{2-q}