5.6H Changing the Subject of a Formula: Higher Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 65 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Make x the subject of the formula 7x + 3y = 25. Give your answer in terms of y.

(Total for Question 1 is 2 marks)

Rearrange the formula p = 3/(2t + 5) to make t the subject. Give your answer in terms of p.

(Total for Question 2 is 3 marks)

The area A of a trapezium is given by A = (h/2)(a + b), where a and b are the parallel sides and h is the height. Rearrange this formula to make h the subject. Then find h when A = 84, a = 6 and b = 10.

(a)Rearrange A = (h/2)(a + b) to make h the subject.(2)

(b)Find h when A = 84, a = 6 and b = 10.(2)

(Total for Question 3 is 4 marks)

Rearrange the formula for the frequency f of a wave: v = f * λ, to make λ the subject. Then a wave has speed v = 330 m/s and frequency f = 440 Hz. Calculate the wavelength λ to 3 significant figures.

(a)Make λ the subject of v = f * λ.(1)

(b)Calculate λ for v = 330 m/s and f = 440 Hz and give the answer to 3 significant figures.(4)

(Total for Question 4 is 5 marks)

The formula for the period T of a pendulum of length L is T = 2pi*√L/g, where g is gravitational acceleration. Show that L = gT²/(4pi²). (You do not need to evaluate numerically.)

(Total for Question 5 is 6 marks)

A formula relates the concentration C (in g/L) of a solution to mass m (in g) and volume V (in L): C = m/V. Rearrange this formula to make m the subject. Then a chemist has a solution with concentration 0.12 g/L and volume 250 mL. Calculate the mass m in grams. Give your answer to 2 decimal places. (Note: 1 L = 1000 mL.)

(a)Make m the subject of C = m/V.(1)

(b)Calculate m when C = 0.12 g/L and V = 250 mL. Give your answer to 2 decimal places.(5)

(Total for Question 6 is 6 marks)

Mark scheme · 5.6H Changing the Subject of a Formula: Higher Tier Practice

Question 1

M1 subtract 3y from both sides or equivalent to isolate 7x
A1 x = (25 - 3y)/7 cao
Answer: x = (25 - 3y)/7

Question 2

M1 multiply both sides by (2t + 5): p(2t + 5) = 3 or equivalent
M1 expand or collect terms to isolate t: 2pt + 5p = 3 -> 2pt = 3 - 5p
A1 t = (3 - 5p)/(2p) cao
Answer: t = (3 - 5p)/(2p)

Question 3

(a) M1 multiply both sides by 2 then divide by (a + b): 2A = h(a + b) or equivalent
(a) A1 h = 2A/(a + b) cao
(a) Answer: h = 2A/(a + b)
(b) M1 substitute values into h = 2A/(a + b): h = 2*84/(6 + 10)
(b) A1 h = 168/16 = 10.5 cao
(b) Answer: 10.5

Question 4

(a) B1 λ = v/f cao
(a) Answer: λ = v/f
(b) M1 substitute values and divide: λ = 330/440
(b) A1 0.75 cao
(b) B1 units m stated or implied
(b) SC1 answer correct to 3 s.f. (0.75) award
(b) Answer: 0.75 m

Question 5

M1 divide both sides by 2pi to isolate the square root: T/(2pi) = √L/g or equivalent
M1 square both sides to remove the square root: T²/(4pi²) = L/g
M1 multiply both sides by g: g * T²/(4pi²) = L
M1 reorder to the conventional form L = gT²/(4pi²) or state equivalent algebraic rearrangement
A1 L = gT²/(4pi²) cao
C1 communication: algebraic justification shown clearly, steps shown and logically ordered
Answer: L = gT²/(4pi²)

Question 6

(a) B1 m = CV cao
(a) Answer: m = CV
(b) M1 convert 250 mL to 0.25 L and substitute: m = 0.12 * 0.25
(b) M1 multiply to get 0.03
(b) A1 0.03 cao
(b) B1 round to 2 decimal places correctly: 0.03 (awrt) or 0.03
(b) B1 units g stated or implied
(b) Answer: 0.03 g

Changing the Subject of a Formula: Higher Tier Practice - Worksheets, Questions and Revision