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grade8_whole_numbers_quiz1 draws its questions at random from a bank of 10 questions, with full worked solutions for every one.
A few of the question types, with full solutions, so you know what to expect.
Which property is shown by: \(3 \times (4 + 5) = 3 \times 4 + 3 \times 5\)?
Answer: Distributive Law
\(\text{The distributive law states: } a(b+c) = ab + ac\)
\(\text{The 3 is distributed to both the 4 and the 5 inside the bracket.}\)
What is the Highest Common Factor (HCF) of 24 and 36?
Answer: 12
\(24 = 2^3 \times 3\)
\(36 = 2^2 \times 3^2\)
\(\text{HCF uses the lowest powers of common primes: } 2^2 \times 3\)
What is the Lowest Common Multiple (LCM) of 6 and 8?
Answer: 24
\(6 = 2 \times 3\)
\(8 = 2^3\)
\(\text{LCM uses the highest powers of all primes: } 2^3 \times 3\)
Calculate: \(\sqrt{144} + 3^2\)
\(\text{First, find the square root: } \sqrt{144} = 12\)
\(\text{Next, find the square: } 3^2 = 9\)
\(\text{Finally, add them together: } 12 + 9\)
Simplify using BODMAS: \(10 - 2 \times 3\)
Answer: 4
\(\text{BODMAS: Multiplication comes before Subtraction.}\)
\(\text{First multiply: } 2 \times 3 = 6\)
\(\text{Then subtract: } 10 - 6\)
*Common mistake: Doing 10 - 2 first to get 8 × 3 = 24.