Unit notes and practice questions
Everything here is for unit 2 of the Grade 9 Mathematics textbook: what the chapter covers, the short notes, practice questions with their answers, and the lesson video where one exists.
The cards filed under this chapter on the Grade 9 Mathematics page. Open one at a time.
When you use it
Use when finding the unique quotient and remainder of positive integers, or when expressing division relations.
Watch out
The remainder r must always satisfy 0 <= r < b. It can never be negative or greater than or equal to the divisor.
Drafted from Grade 9 Mathematics, pages 1-86, then checked twice before it went up
When you use it
Use when finding the LCM or GCF of two numbers given their product and one of the values.
Watch out
This product formula holds only for two numbers. It is not true for three or more numbers.
Drafted from Grade 9 Mathematics, pages 1-86, then checked twice before it went up
When you use it
Use when simplifying square roots or combining like irrational terms in addition and subtraction.
Watch out
Square roots can only be combined by addition if they have identical radicands, so simplify each term first.
Drafted from Grade 9 Mathematics, pages 1-86, then checked twice before it went up
10 multiple-choice questions written against this chapter, each with its answer and the reason. Try one before you open the answer.
Question 1
Which of the following numbers is irrational?
Answer: C √7
Why
7 is not a perfect square, so √7 has a decimal that never ends and never repeats. √16 equals 4, which is rational. A repeating decimal is always rational, so 0.3333... is 1/3. And 22/7 is a fraction, so it is rational, even though it is often used as an approximation for π.
Question 2
Simplify √50.
Answer: B 5√2
Why
Split 50 into a perfect square times something else: 50 = 25 x 2. Then √50 = √25 x √2 = 5√2. Option A comes from forgetting to take the square root of 25.
Question 3
Write 0.363636... as a fraction in lowest terms.
Answer: B 4/11
Why
Let x = 0.363636... Two digits repeat, so 100x = 36.363636... Subtracting gives 99x = 36, so x = 36/99. Divide top and bottom by 9 to get 4/11. Option A is right before simplifying, and the question asks for lowest terms.
Question 4
Rationalise the denominator of 6/√3.
Answer: A 2√3
Why
Multiply top and bottom by √3: (6 x √3) / (√3 x √3) = 6√3 / 3 = 2√3. Option B forgets to divide by the 3 that appears in the denominator.
Question 5
What is the highest common factor of 36 and 60?
Answer: B 12
Why
36 = 2² x 3² and 60 = 2² x 3 x 5. Take the shared primes at their lowest powers: 2² x 3 = 12. Option D is the lowest common multiple, which takes the highest power of every prime instead.
Question 6
Express 0.00056 in scientific notation.
Answer: A 5.6 x 10⁻⁴
Why
Move the point four places to the right to reach 5.6, so the power is negative four. Options C and D have the right value but the wrong form, because scientific notation needs the first number to be at least 1 and below 10.
Question 7
Simplify 3√2 + 5√2 - √2.
Answer: A 7√2
Why
Like surds add and subtract the way like terms do in algebra: 3 + 5 - 1 = 7, so the answer is 7√2. Option B forgets to subtract the last term, which counts as 1√2.
Question 8
Which set contains every rational and every irrational number?
Answer: C The real numbers
Why
The real numbers are defined as the rationals together with the irrationals. The integers, naturals and whole numbers are all subsets of the rationals, so none of them can contain √2.
Question 9
Rationalise the denominator of 1/(4 + √3).
Answer: A (4 - √3) / 13
Why
Multiply top and bottom by the conjugate 4 - √3. The denominator becomes 4² - (√3)² = 16 - 3 = 13, so the answer is (4 - √3) / 13. Option B uses the same sign instead of the conjugate, which leaves a surd in the denominator.
Question 10
Round 0.0045678 to three significant figures.
Answer: B 0.00457
Why
Leading zeros are not significant, so the figures start at 4. The first three are 4, 5 and 6, and the next digit is 7, which rounds the 6 up to 7. That gives 0.00457. Option C keeps the 6 without rounding.
Unit 2 runs from page 17 to page 86 of the Ministry of Education edition.
Ministry of Education edition, English, 337 pages
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