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7.7D Rearranging Harder Formulae: Fluency and Exam Drill

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 60 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Work out x from 18 = 5x + x.

(Total for Question 1 is 1 mark)

Rearrange the formula R = rk/(k + r) to make r the subject. Give your answer in simplest form.

(Total for Question 2 is 3 marks)

Make f the subject of 1/f = 1/a + 1/b.

(Total for Question 3 is 2 marks)

Rearrange t = √(2s)/g to make s the subject.

(Total for Question 4 is 2 marks)

Make x the subject of y = √x + 1.

(Total for Question 5 is 2 marks)

Rearrange S = 3x/(x + 2) to make x the subject. Give your answer in simplest form.

(Total for Question 6 is 3 marks)

Make a the subject of s = ut + 0.5 a t².

(Total for Question 7 is 2 marks)

Rearrange m = √(x + 4)/(2x) to make x the subject. Give your answer in simplest form.

(Total for Question 8 is 3 marks)

Rearrange y = kx + m/x to make x the subject. Give your answer using the quadratic formula.

(Total for Question 9 is 4 marks)

The period of a mass on a spring is given by T = 2pi √m/k. Rearrange this formula to make k the subject.

(Total for Question 10 is 3 marks)

Make t the subject of s = vt + 0.5 a t². Give your answer in terms of s, v and a.

(Total for Question 11 is 4 marks)

Rearrange R = (x + 3)/(2x) to make x the subject. Give your answer in simplest form.

(Total for Question 12 is 3 marks)

Rearrange p = (x² + 2x)/(x - 1) to make x the subject. Give your answer using the quadratic formula.

(Total for Question 13 is 4 marks)

Rearrange y = (a x + b)/(c x + d) to make x the subject. Give your answer in simplest form.

(Total for Question 14 is 4 marks)

Mark scheme · 7.7D Rearranging Harder Formulae: Fluency and Exam Drill

Question 1

B1 x = 3 cao
Answer: 3

Question 2

M1 multiply both sides by (k + r) to obtain Rk + Rr = rk
M1 collect r terms to get Rk = r(k - R) or equivalent
A1 r = Rk/(k - R) cao
Answer: r = Rk/(k - R)

Question 3

M1 combine RHS: 1/f = (a + b)/(ab)
A1 f = ab/(a + b) cao
Answer: f = ab/(a + b)

Question 4

M1 square both sides to get t² = 2s/g
A1 s = g t²/2 cao
Answer: s = g t²/2

Question 5

M1 isolate √x: √x = y - 1
A1 x = (y - 1)² cao
Answer: x = (y - 1)²

Question 6

M1 multiply both sides by (x + 2) to get S(x + 2) = 3x
M1 collect x terms to reach x(3 - S) = 2S
A1 x = 2S/(3 - S) cao
Answer: x = 2S/(3 - S)

Question 7

M1 isolate the a term: s - ut = 0.5 a t²
A1 a = 2(s - ut)/t² cao
Answer: a = 2(s - ut)/t²

Question 8

M1 square both sides to get m² = (x + 4)/(2x) and clear fraction to 2m² x = x + 4
M1 collect x terms to give x(2m² - 1) = 4
A1 x = 4/(2m² - 1) cao
Answer: x = 4/(2m² - 1)

Question 9

M1 multiply both sides by x to obtain yx = kx² + m
M1 rearrange to quadratic form kx² - yx + m = 0
M1 apply the quadratic formula with a = k, b = -y, c = m
A1 x = [y ± √y² - 4km]/(2k) cao
Answer: x = [y ± √y² - 4km]/(2k)

Question 10

M1 isolate the square root: T/(2pi) = √m/k, then square both sides
M1 obtain T²/(4pi²) = m/k and rearrange to k = 4pi² m/T²
A1 k = 4pi² m/T² cao
Answer: k = 4pi² m/T²

Question 11

M1 rearrange to quadratic form 0.5 a t² + v t - s = 0 (or multiply by 2 to a t² + 2v t - 2s = 0)
M1 identify coefficients and use quadratic formula
M1 substitute and simplify the discriminant to v² + 2as
A1 t = [ -v ± √v² + 2as ] / a cao
Answer: t = [ -v ± √v² + 2as ] / a

Question 12

M1 multiply both sides by 2x to get 2R x = x + 3
M1 collect x terms to x(2R - 1) = 3
A1 x = 3/(2R - 1) cao
Answer: x = 3/(2R - 1)

Question 13

M1 multiply both sides by (x - 1) and expand to get p(x - 1) = x² + 2x
M1 rearrange to quadratic form x² + (2 - p)x + p = 0
M1 apply the quadratic formula with a = 1, b = (2 - p), c = p
A1 x = [ -(2 - p) ± √(2 - p)² - 4p ]/2 cao
Answer: x = [ -(2 - p) ± √(2 - p)² - 4p ]/2

Question 14

M1 multiply both sides by (c x + d) to get y(c x + d) = a x + b
M1 collect x terms to reach x(y c - a) = b - y d
M1 divide to isolate x
A1 x = (b - y d)/(y c - a) cao
Answer: x = (b - y d)/(y c - a)

Rearranging Harder Formulae: Fluency and Exam Drill - Worksheets, Questions and Revision