NumberIB MYP Maths Standard: Topic test

1. 1
   Priya is practising the laws of exponents with powers of $2$ and with algebraic terms.

   (a)

   What is the value of $2^{5}\times2^{-3}$?

   [1 mark]

   • A$\frac{1}{4}$
   • B$4$
   • C$256$
   • D$2^{-15}$

   (b)

   Which expression is equal to $(3x^{2})^{3}$?

   [1 mark]

   • A$9x^{6}$
   • B$27x^{5}$
   • C$3x^{6}$
   • D$27x^{6}$

   (c)

   Simplify $\dfrac{12a^{5}b^{-2}}{3a^{2}b}$. Give your answer with positive exponents only.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   On a maize farm in Kenya, the yield rose from $3.2$ tonnes per hectare in 2023 to $3.76$ tonnes per hectare in 2024.

   (a)

   What was the percentage increase in the yield from 2023 to 2024?

   [1 mark]

   • A$17.5\%$
   • B$14.9\%$
   • C$56\%$
   • D$117.5\%$

   (b)

   In 2025 the yield falls by $10\%$ from its 2024 value. What is the yield in 2025?

   [1 mark]

   • A$3.66$ tonnes per hectare
   • B$4.136$ tonnes per hectare
   • C$3.384$ tonnes per hectare
   • D$0.376$ tonnes per hectare

   (c)

   Write the ratio of the 2023 yield to the 2024 yield in its simplest form, using whole numbers.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Hassan is training for a triathlon in Dubai. In one session he runs $6$ km at an average speed of $12$ km/h and then walks $4$ km at an average speed of $5$ km/h.

   (a)

   Calculate the time he takes for each stage and the total time for the session. Give your answers in hours.

   [3 marks]

   (b)

   Calculate his average speed for the whole session in km/h to $3$ significant figures. Then convert this average speed to m/s, giving your answer to $3$ significant figures.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A virologist in Singapore measures a virus particle of diameter $1.2\times10^{-7}$ m. A human hair has width $8\times10^{-5}$ m. A sample contains $3.6\times10^{9}$ virus particles in $2.4\times10^{-3}$ litres of liquid.

   (a)

   (i) Calculate how many times wider the hair is than one virus particle. Give your answer in standard form to $3$ significant figures. (ii) Round your answer to part (i) to $1$ significant figure. (iii) Using the exact value of the ratio, find the percentage error in your answer to part (ii). Decide whether the rounded value is a reasonable estimate and give a reason.

   [6 marks]

   (b)

   (i) Calculate the number of virus particles per litre in the sample. Give your answer in standard form. (ii) A test needs $6\times10^{6}$ virus particles. Calculate the volume of the sample, in litres, that contains this number of particles. Give your answer in standard form. (iii) Convert your answer to part (ii) into millilitres, in standard form.

   [6 marks]

   Total for question 4: 12 marks

5. 5
   Mia writes down five numbers: $\sqrt{81}$, $\sqrt{20}$, $-\frac{5}{8}$, $\frac{\pi}{3}$ and $0.125$.

   (a)

   How many of Mia's numbers are rational?

   [1 mark]

   • A$1$
   • B$2$
   • C$3$
   • D$4$

   (b)

   Which expression is $\sqrt{20}$ written in its simplest surd form?

   [1 mark]

   • A$2\sqrt{5}$
   • B$4\sqrt{5}$
   • C$5\sqrt{2}$
   • D$10$

   (c)

   Write $\sqrt{20}+\sqrt{45}$ in the form $a\sqrt{5}$, where $a$ is an integer.

   [2 marks]

   Total for question 5: 4 marks

6. 6
   A drone must hover at a height $h$ metres above the ground that satisfies $|h-30|<5$.

   (a)

   Which of these heights is allowed?

   [1 mark]

   • A$25$ m
   • B$35$ m
   • C$36$ m
   • D$33$ m

   (b)

   Which inequality is equivalent to $|h-30|<5$?

   [1 mark]

   • A$h<35$
   • B$25<h<35$
   • C$25\le h\le35$
   • D$h<25$ or $h>35$

   (c)

   Write the allowed heights in set notation, where $h$ is a real number. State how many whole-number heights (in metres) are allowed.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   A crew of $8$ workers can resurface a school playground in $15$ days. All workers work at the same steady rate.

   (a)

   The number of workers $w$ and the number of days $d$ are inversely proportional. Find the constant of proportionality, write $d$ in terms of $w$, and find how many days $12$ workers would take.

   [3 marks]

   (b)

   The crew of $8$ works for $5$ days. Then $3$ workers leave and the remaining workers finish the job. How many more days do they need?

   [4 marks]

   Total for question 7: 7 marks

8. 8
   A path in a park in Lisbon is made of white tiles in a straight row, with a border of black tiles all the way around them. Pattern $1$ has $1$ white tile and $8$ black tiles, Pattern $2$ has $2$ white tiles and $10$ black tiles, and Pattern $3$ has $3$ white tiles and $12$ black tiles. The pattern continues in the same way.

   (a)

   (i) Write down the number of black tiles in Pattern $4$. (ii) Find an expression for the number of black tiles in Pattern $n$. (iii) Which pattern has $50$ black tiles? (iv) Explain why no pattern has exactly $75$ black tiles.

   [6 marks]

   (b)

   Black tiles cost AED $4$ each and white tiles cost AED $6$ each. (i) Show that the cost of Pattern $n$ is $(14n+24)$ dirhams. (ii) The budget is AED $500$. Find the largest pattern the budget can pay for, and explain why your answer is the largest.

   [6 marks]

   Total for question 8: 12 marks

End of questions