Linear Equations in One Variable
You're viewing free preview questions — 4 questions previewing here — subscribe to unlock 98 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Linear Equations in One Variable — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionEquations Involving Brackets and FractionsConcept Practice
2 marks~3 minCriterion A
A personal trainer designs a 45-minute session split into three identical blocks. Each block includes a 5-minute warm-up plus 2x2x minutes of circuit training, where xx is the number of circuit rounds.
a
Show that the total session time gives the equation 3(2x+5)=453(2x + 5) = 45, and solve for xx. [1]
b
The trainer states: "Each block has time for at least 4 circuit rounds." Using your value of xx, justify whether this statement is correct. [1]
Question diagram

Solutions

2QuestionWord Problems Involving Linear EquationsAssessment Practice
4 marks~6 minCriterion D
A school fundraiser sells adult tickets for 12 USD and student tickets for 7 USD. A total of 20 student tickets are sold alongside xx adult tickets, generating total revenue RR (in USD).
a
Write the equation that represents RR in terms of xx. [1]
b
The total revenue collected was 284 USD. Calculate the number of adult tickets sold. [2]
c
The organiser claims that selling twice as many adult tickets would double the total revenue. Justify whether this claim is correct, and interpret what your answer means for the fundraiser. [1]
Question diagram

Solutions

3QuestionSolving One-Step and Two-Step EquationsAssessment Practice
4 marks~6 minCriterion C
A taxi company charges a flat fee of 3 USD plus 2 USD per kilometre travelled. A passenger pays a total fare of 13 USD.
a
Write an equation in one variable to represent this situation. [1]
b
Determine the number of kilometres travelled. Show your working clearly. [2]
c
A second passenger uses a different taxi company that charges a flat fee of 6 USD and 2 USD per kilometre, paying a total fare of 26 USD. Justify whether the two passengers travel the same number of kilometres. [1]
Question diagram

Solutions

4QuestionChecking Solutions and SubstitutionAssessment Practice
6 marks~9 minCriterion B

Data

x+2=5,x=3x + 2 = 5, \quad x = 3
2x+4=10,x=32x + 4 = 10, \quad x = 3
3x+6=15,x=33x + 6 = 15, \quad x = 3
4x+8=20,x=34x + 8 = 20, \quad x = 3
A water treatment plant adjusts chemical dosing using equations of the form ax+2a=5aax + 2a = 5a, where aa is a non-zero real number and xx represents the dosing multiplier.

The following equations and proposed solutions are
a
Deduce the solution to 10x+20=5010x + 20 = 50. [1]
b
Show that every equation of the form ax+2a=5aax + 2a = 5a, where a≠0a \neq 0, has solution x=3x = 3. [3]
c
The plant requires a dosing multiplier strictly greater than 3 to safely treat a new water source. The engineer models this situation with the equation 100x+200=500100x + 200 = 500. Solve this equation and advise the engineer whether the plant can safely treat the new water source under this model. [2]

Solutions

Questions 5-102

Unlock these questions with Premium

Sign Up →

That's every free question here — 4 of 102.

+98 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade