Literal Equations and Rearranging Formulae
You're viewing free preview questions — 4 questions previewing here — subscribe to unlock 62 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Literal Equations and Rearranging Formulae — Free MYP4 Mathematics (Standard) Practice Questions

1QuestionUnderstanding Literal EquationsConcept Practice
2 marks~3 minCriterion A
A community garden is being enclosed with fencing. The garden is rectangular, with length ll and width ww, and its perimeter is given by

P=2l+2w.P = 2l + 2w.

The available fencing is 26 m. The garden measures l=8l = 8 m and w=5w = 5 m.
a
State what PP represents and write down the formula rearranged to make ll the subject. [1]
b
Using the given dimensions, calculate PP and justify whether the available fencing is sufficient to enclose the garden. [1]
Question diagram

Solutions

2QuestionCommon Mistakes in RearrangingAssessment Practice
4 marks~6 minCriterion C
A mobile data plan charges a monthly fee according to the formula C=3d+2C = 3d + 2, where CC is the total cost in dollars and dd is the data used in gigabytes. A customer receives a bill of C=5C = 5 dollars and wants to find dd.

A classmate claims the formula can be rearranged to give d=3C+2d = 3C + 2.
a
Show that the correct rearrangement of C=3d+2C = 3d + 2 to express dd in terms of CC is d=C−23d = \dfrac{C - 2}{3}. [1]
b
Explain the error in the classmate's rearrangement d=3C+2d = 3C + 2. [1]
c
Using both formulas with C=5C = 5, calculate the two values of dd and advise the customer which result to trust, justifying your answer using the cost structure of the plan. [2]
Question diagram

Solutions

3QuestionRearranging to Make a Variable the SubjectAssessment Practice
4 marks~6 minCriterion D
The graph shows the linear relationship between degrees Celsius (CC) and degrees Fahrenheit (FF). The line passes through (0,32)(0, 32) and (100,212)(100, 212).
a
Deduce the equation of the line in the form F=mC+bF = mC + b. [1]
b
Rearrange your equation to make CC the subject. [1]
c
A storage facility for temperature-sensitive medication requires the internal temperature to remain below 25 °C. A sensor records F=77F = 77 °F. Advise the facility manager whether the storage requirement is currently being met, justifying your answer with a calculation. [2]
Question diagram

Solutions

4QuestionUnderstanding Literal EquationsAssessment Practice
6 marks~9 minCriterion B
A ball is dropped from rest and falls freely under gravity. The distance fallen is recorded below.

Time (s): 0, 1, 2, 3, 4

Distance (m): 0, 4.9, 19.6, 44.1, 78.4
a
Analyse the data to identify the relationship between distance fallen and time. [2]
b
Deduce a formula for the distance dd (in metres) fallen after tt seconds, justifying your formula using values from the table. [2]
c
A sensor is placed 130 m below the drop point. Advise whether the ball has reached the sensor after 5 seconds, supporting your recommendation with a calculation. [2]

Solutions

Questions 5-66

Unlock these questions with Premium

Sign Up →

That's every free question here — 4 of 66.

+62 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade