1(a) Rearrange m(x+3)=2+x to make m the subject.
ANSWER: Multiple Choice (Type 1)
A: m = -1
B: m = (2 + x)(x + 3)
C: m = (x+3)
D: m = \bigg(\dfrac{2 + x}{3}\bigg) - x
Answer: C
Marks = 1
1(b) Rearrange 2px + 3p = 1 + 2x to make p the subject.
ANSWER: Multiple Choice (Type 1)
A: p = \dfrac{1 + 2x}{6x}
B: p = \dfrac{2x + 3}{1 + 2x}
C: p = \dfrac{6x}{1 + 2x}
D: p = \dfrac{1 + 2x}{2x + 3}
Answer: D
Workings:
p(2x + 3) = 1 + 2x
p = \dfrac{1 + 2x}{2x + 3}
Marks = 2
1(c) Rearrange 2mx+10=3x+m to make x the subject.
ANSWER: Multiple Choice (Type 1)
A: x = \dfrac{m - 10}{2m - 3}
B: x = \dfrac{m + 10}{2m - 3}
C: x = \dfrac{m - 10}{2m + 3}
D: x = \dfrac{m + 10}{2m + 3}
Answer: A
Workings:
2mx - 3x = m - 10
x(2m - 3) = m - 10
x = \dfrac{m-10}{(2m-3)}
Marks = 3
Question 2
Rearrange the formula below to make m the subject.
n = \dfrac{m-4}{m+3}
ANSWER: Multiple Choice (Type 1)
A: m = \dfrac{-4 - 3n}{n-1}
B: m = -\bigg(\dfrac{4+3n}{n-1}\bigg)
C: m = \dfrac{4-3n}{n-1}
D: m = \dfrac{4-3n}{n+1}
Answer: A
Workings:
n(m + 3) = m - 4
mn + 3n = m - 4
mn -m = -4 - 3n
m(n-1) = -4 - 3n
m = \dfrac{-4 - 3n}{n-1}
Marks = 4
Question 3
Rearrange the formula below to make x the subject.
y + 1 = \dfrac{2x - 10}{x + 1}
ANSWER: Multiple Choice (Type 1)
A: x = \dfrac{y+10}{y-1}
B: x = \dfrac{-y - 10}{y-1}
C: x = \dfrac{y + 11}{1-y}
D: x = \dfrac{y - 11}{1+y}
Answer: C
Workings:
(y+1)(x+1) = 2x - 10
xy + x + y + 1 = 2x - 10
y + 11 = x - xy
y + 11 = x(1-y)
x = \dfrac{y + 11}{(1-y)}
Marks = 4
Question 4
The formula for the volume of a cone, V cm^3, is shown below:
V = \dfrac{1}{3}\pi r^2 h
Given that the height of the cone is twice the radius, find r in terms of V.
ANSWER: Multiple Choice (Type 1)
A: r = \sqrt[3]{\dfrac{2\pi}{3V}}
B: r = \sqrt[3]{\dfrac{3V}{2\pi}}
C: r = \sqrt{\dfrac{3V}{2\pi h}}
D: r = \sqrt{\dfrac{2\pi h}{3V}}
Answer: B
Workings:
h = 2r
V = \dfrac{1}{3}\pi r^2(2r)
V = \dfrac{2}{3}\pi r^3
r^3 = \dfrac{3V}{2\pi}
r = \sqrt[3]{\dfrac{3V}{2\pi}}
Marks = 3