Real Number & Integers - Practice 1
In this lesson, we’ll tackle 7 carefully selected practice questions drawn from past-year exam papers, focusing on the most commonly tested question types in the Real Number System chapter.
Related Lessons:
Practice 1 - Question 1
Arrange the following numbers in ascending order:
\(
\frac{1}{3} \quad 40\% \quad \sqrt[3]{-8} \quad \frac{2}{7} \quad 0.3\)
Solution:
Now, the approach is to convert all the items to decimals. Here is the answer to the question:
\(
\sqrt[3]{-8} \quad \frac{2}{7} \quad 0.3 \quad \frac{1}{3} \quad 40\% \)
Practice 1 - Question 2
The temperature inside an igloo is \(x°C\), and the temperature outside it is \(-y°C\). Given that \(x\) and \(y\) are positive integers, write down an expression for the
a) difference between the two temperatures,
b) average of the two temperatures
Solution:
a) \(x-\left(-y\right)=x+y\)
b) \(\frac{x-y}{2}\)
Practice 1 - Question 3
Estimate, correct to 1 significant figure, the value of \(\frac{4.11\times\sqrt[3]{215.6}}{11.62}\).
Solution:
\[
\begin{align*}
\frac{4.11\times\sqrt[3]{215.6}}{11.62}&≈\frac{4\times\sqrt[3]{216}}{12}\\
&=\frac{4\times6}{12}\\
&=2\ \left(1s.f.\right)\
\end{align*}
\]
Practice 1 - Question 4
The temperature at sea level is \(18°C\). The temperature 10,000m above sea level is \(-27°C\).
- Find the difference between the two temperatures.
- If the temperature at 15,000m above sea level is 5 degrees Celsius lower than at 10,000m, find the temperature 15,000m above sea level
Solution:
a) \(18-\left(-27\right)=45°C\)
b) \(-27-\left(-5\right)=-32°C\)
Practice 1 - Question 5
Using as much of the information below as necessary, without the use of a calculator, find the value of \(\sqrt{17750}\). Show all the workings clearly.
\(\left[\sqrt{1.775}=1.332,\ \sqrt{17.75}=4.213\right]\)
Solution:
\[
\begin{align*}
\sqrt{17750}&=\sqrt{1.7750\times10000}\\
&=\sqrt{1.7750}\times\sqrt{10000}\\
&=1.332\times100\\
&=133.2
\end{align*}
\]
Practice 1 - Question 6
The shop owner bought 1000 pieces of key chain at a cost of 50 cents each. He intends to sell them for a profit of 200%.
a) Find his selling price for each key chain
The shop owner also provides engraving services, excluding the price of the key chain, at the following charges.
- Order below 50 pieces – $1 per key chain
- Order 50 pieces and above – $0.80 per key chain
b) James bought 40 pieces of key chain with engraving. How much did James pay?
c) Another customer, Ethan ordered 300 pieces of key chain with engraving. How much did Ethan pay?
d) The shop owner sold the remaining key chains, without engraving at 80 cents each. How much did he profit from selling all the key chains?
Answer:
a) $1.50
b) $100
c) $690
d) $818
This is a basic mathematics question. For full solution, refer to the video at the end.
Practice 1 - Question 7
Without using a calculator, showing all your working, evaluate the expression \(\left(-2\right)^3-\left(-11+3\right)+\left(-4\right)^2\).
Answer = 16
This is another basic mathematics question. For full working without using a calculator, refer to the video solution below.
Step By Step Full Solution
Learning through video solutions is far more effective than relying on text alone, as students are able to see clearly how each step of the solution is developed. Below is the complete step-by-step video solution for the 7 questions above, guiding through the full working and reasoning behind the solution.