Forming equations from contextIB MYP Maths Standard: Subtopic test

1. 1
   A mobile phone plan in Singapore costs a fixed charge of 12 Singapore dollars (SGD) per month plus SGD 0.05 for each minute of calls. The monthly bill is $C$ dollars when $m$ minutes of calls are made.

   (a)

   Which formula gives $C$ in terms of $m$?

   [1 mark]

   • A$C=12m+0.05$
   • B$C=(12+0.05)m$
   • C$C=0.6m$
   • D$C=12+0.05m$

   (b)

   One month's bill is SGD 30.50. How many minutes of calls were made?

   [1 mark]

   • A$610$
   • B$370$
   • C$18.5$
   • D$850$

   (c)

   Maria wants her monthly bill to be at most SGD 20. Form and solve an inequality to find the greatest number of minutes of calls she can make.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A rectangle has length $(2x+3)$ cm and width $(x-1)$ cm. Its perimeter is 46 cm.

   (a)

   Which equation is correct?

   [1 mark]

   • A$2(3x+2)=46$
   • B$(2x+3)(x-1)=46$
   • C$(2x+3)+(x-1)=46$
   • D$2(2x+3)+(x-1)=46$

   (b)

   Find the value of $x$.

   [1 mark]

   • A$\frac{44}{3}$
   • B$\frac{25}{3}$
   • C$7$
   • D$\frac{23}{3}$

   (c)

   Hence find the area of the rectangle.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A school is hiring a coach for a trip. Company A charges AED 360 plus AED 12 for each student. Company B charges AED 20 for each student and has no fixed charge.

   (a)

   Form and solve an equation to find the number of students, $s$, for which both companies charge the same amount.

   [3 marks]

   (b)

   The school expects 38 students. Which company should it choose? Justify your answer with calculations.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   Ama is $a$ years old. Her brother Kofi is 4 years older than Ama. In 6 years' time the sum of their ages will be 50.

   (a)

   (i) Write an expression for Kofi's age now. Hence form an equation in $a$ for the sum of their ages in 6 years' time.
   (ii) Solve your equation and state both ages now.
   (iii) Check that your ages fit the information in the question.

   [6 marks]

   (b)

   (i) In $n$ years' time from now the sum of their ages will be at most 60. Form and solve an inequality to find the greatest whole number of years $n$.
   (ii) Their cousin Zuri is 5 years old. Ama says that in some number of years, $t$, she will be exactly three times as old as Zuri. Form an equation, solve it, and decide whether Ama's claim is possible.

   [6 marks]

   Total for question 4: 12 marks

End of questions