Formulae - Challenging

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Question 1: Find the value of

x

in the formula

c = a x^{2} + 5

, if

a = 8

c = 7

x = \frac{1}{2}

\lor

x = - \frac{1}{2}

x = \frac{1}{4}

\lor

x = - \frac{1}{4}

x = 2

x = 4

Question 2: Find the value of

x

in the formula

t = \sqrt[3]{x} + s^{2}

, if

s = \frac{1}{2}

t = 3 \frac{1}{4}

x = 9

x = 25

x = 18

x = 27

Question 3: Rearrange the formula

y = \frac{x - 1}{5} + 1

to make

x

a subject

x = \frac{y}{5} + 1

x = \frac{y - 1}{5} + 1

x = 4 y + 5

x = 5 y - 4

Question 4: Rearrange the formula

y = \frac{x - 2}{3} + \frac{x - 1}{4}

to make

x

a subject

x = \frac{3}{7} y + \frac{4}{7}

x = \frac{7}{12} y - \frac{7}{11}

x = 12 y - 11

x = 1 \frac{5}{7} y + 1 \frac{4}{7}

Question 5: Rearrange the formula

p = \frac{q - r}{q + s} - 1

to make

q

a subject

q = - \frac{r}{p} - \frac{s}{p} - 1

q = \frac{s - r - 1}{p}

q = \frac{- r - s - 1}{p}

q = \frac{- (r + s)}{p} - s

Question 6: Rearrange the formula

n = \frac{2 m + s}{t}

to make

m

a subject

m = \frac{s - n t}{2}

m = \frac{2 n - s}{t}

m = \frac{n t - s}{2}

m = \frac{2 n - t}{s}

Question 7: Transpose the following formula for

V

u = \sqrt{\frac{V - 2}{V + 3}}

V = - \frac{3 u^{2}}{u^{2} - 3}

V = \frac{3 u^{2} + 2}{u^{2} - 2}

V = \frac{- 3 u^{2} - 2}{u^{2} - 1}

V = \sqrt{3 \frac{u^{2} + 1}{u^{2} - 1}}

Question 8: Transpose the following formula for

x

y = \frac{1}{2} \sqrt[3]{\frac{x^{2} - z^{2}}{v}}

x = 2 \sqrt[3]{\frac{y^{2} - z^{2}}{v}}

x = \sqrt{8 y^{3} v + z^{2}}

x = \frac{1}{2} \sqrt{y^{2} v \frac{3}{} - z^{2}}

x = 2 \sqrt{y^{3} v^{2} + z^{2}}

Question 9: Rearrange the formula

\frac{1}{3} p x + \frac{2}{3} q y = 3 q x - p y

to make

x

a subject

x = \frac{- y (3 p + 2 q)}{p - 9 q}

x = - y (3 p - 2 q) (2 p + 3 q)

x = - y (3 p + 2 q) (p - 3 q)

x = \frac{y (2 p - 3 q)}{3 p - 6 q}

Question 10: Rearrange the formula

a x - p = 2 x p - a

to make

a

a subject

a = p (x - 1) (x + 1)

a = \frac{p (2 x + 1)}{x + 1}

a = p (2 x - 1) (x - 1)

a = \frac{2 x p + 1}{x + 1}

Test: Formulae - Challenging