IB Mathematics AA SL Standard Form Study Notes
IB Mathematics AA SL Standard Form Study Notes Offer a clear explanation of standard form, including various formula, rules, exam style questions as example to explain the topics. Worked Out examples and common problem types provided here will be sufficient to cover for topic Standard Form
What is Standard form
A number in the format , \( \pm a \times10^k \) , where \(1\leqslant a\leqslant 10 \) and \(k\in Z\) (k is an integer)
Number in the form \(a \times 10^ k\) such as \(4.7 \times 10^5\) instead of 475,000 may be called Specific notation or Standard form
\( 2 \times 10^{3.3} \): NOT in the Standard form (k is not an integer)
\( 0.29 \times 10^{-3} \): NOT in the Standard form, because \( a < 1 \). Should be: \( 2.9 \times 10^{-3} \)
\( 2.1 \times 10^8 \): ✓, IN the Standard form . this means 210,000,000
Converting to Standard Form
The number 410,000 could theoretically be written: \( 4.1 \times 10^5 \), \( 41 \times 10^4 \), \( 0.41 \times 10^6 \), and so on. However, to simplify things, we say that ‘a’ & ‘k’ must have the following:
– \( 1 \leq |a| < 10 \)
– \( k \in \mathbb{Z} \)
Meaning: ‘a’ is between 1 and 10 (+ve or -ve), and ‘k’ is an integer.
Graphic Display Calculator TI-84 Plus
To write a number in standard form on the TI-84 Plus, use the EE key. To convert a number to standard form, use the SCI mode.
IB Mathematics AA SL Standard Form Study Notes - Exam Style Worked Out Questions
Question
Nickel in the asteroid 16 Psyche is said to be valued at 8973 quadrillion euros (EUR), where one quadrillion = 1015.
Write down the value of the Nicke in the form a × 10k where 1 ≤ a < 10 , k∈Z . [2]
Charlie believes the asteroid is approximately spherical with radius 113 km. He uses this information to estimate its volume.
Calculate Charlie’s estimate of its volume, in km3. [2]
The actual volume of the asteroid is found to be 6.074 × 106 km3 .
Find the percentage error in Charlie’s estimate of the volume. [2]
Answer/Explanation
Ans:
(a)
8.97 × 1018 (EUR)(8.973 × 1018)
(b)
\(\frac{4\times \pi 113^{3}}{3}\)
\(6040000(km^{3})(6.04\times 10^{6},\frac{5771588\pi }{3}, 6043992.82)\)
(c)
\(|\frac{6043992.82-6.074\times 10^{6}}{6.074 \times 10^{6}}|\) x 100
0.494(%) (0.494026…(%))
Question
Write down the following numbers in increasing order.
a. \(3.5\), \(1.6 \times 10^{−19}\), \(60730\), \(6.073 \times 10^{5}\), \(0.006073 \times 10^6\), \(\pi\), \(9.8 \times 10^{−18}\).[3]
Answer/Explanation
Markscheme
\(1.6 \times 10^{−19}\), \(9.8 \times 10^{−18}\), \(\pi\), \(3.5\), \(0.006073 \times 10^6\), \(60730\), \(6.073 \times 10^{5}\) (A4)
Award (A1) for \(\pi\) before 3.5
Award (A1) for \(1.6 \times 10^{−19}\) before \(9.8 \times 10^{−18}\)
Award (A1) for the three numbers containing 6073 in the correct order.
Award (A1) for the pair with negative indices placed before 3.5 and \(\pi\) and the remaining three numbers placed after (independently of the other three marks).
Award (A3) for numbers given in correct decreasing order.
Award (A2) for decreasing order with at most 1 error (C4)[3 marks]
The median is 3.5. (A1)(ft)
Follow through from candidate’s list. (C1)[1 mark]
\(\pi\) is irrational. (A1) (C1)[1 mark]