Mathematics grade 8 Revision test Question 1 1.1 Determine the highest common factor (HCF) of 54 and 90. 1.2 Determine the lowest common multiple (LCM) of 14; 28 and 30. (3) [6] Question 2 2.1 Write the following ratios ratio in simplest form. 2.1.1 36:120 2.1.2 \( 5 \mathrm{~m}: 30 \mathrm{~cm} \) (3) 2.2 A diesel vehicle uses 12 litres diesel every 200 km. How many Kilometres can this vehicle travel with 18 litres of diesel? 2.3 Increase 45 in the ratio \( 5: 9 \). 2.4 Decrease 16 in the ratio \( 4: 3 \). (2) 2.5 The minimum wage for a worker in South Africa is R180 for 9 hours work. 2.5.1 What is the minimum wage per hour? (2) 2.5.2 How much will a worker earn if he/she works for 12 hours? 2.5.3 How long will a worker have to work for to earn R300? (2) 2.6 Tim and Brett went out for lunch. The bill was R470. They decided to share the bill in the ratio \( 2: 3 \) since Brett's meal was cheaper than Tim's. How much did each pay? (3) [18] Question 3 3.1 The exchange rate on a specific day is \( \$ 1=R 18,74 \). You would like to exchange R1 200 for dollars. How many dollars will you get? 3.2 You earn 8,2\% simple interest per annum on an investment of R5 000 for 10 years. Calculate the interest earned after 10 years and hence the value of the investment at the end of the 10 years. [6] TOTAL MARKS: 30
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The Deep Dive
Here's a fun fact: The concept of highest common factor (HCF) dates back to ancient civilizations! The Greeks were among the first to study the relationship between numbers, and mathematicians like Euclid developed methods for determining the HCF using the Euclidean algorithm. These foundational approaches are still relevant today in helping us simplify fractions and solve problems involving ratios and divisibility. Now, speaking of ratios, they are everywhere in real life! Whether you're cooking (scaling a recipe) or budgeting your finances (dividing expenses), ratios help you maintain proportion. For instance, if you have a recipe that serves 4 people and you need to serve 10, using ratios ensures that every ingredient remains proportionately correct. It’s like mathematics sneaking into your kitchen and finances, making everything just a bit tastier and better organized!