CSEE (Form 4) Basic Mathematics — practice by topic

1. The set is $S=\{1,2,3,\dots,52\}$, so $n(S)=52$. 2. The multiples of 5 in it are $\{5,10,15,20,25,30,35,40,45,50\}$, so $n(E)=10$. 3. Apply $\%n(E)=\dfrac{n(E)}{n(S)}\times100\%$. 4. That gives $\dfrac{10}{52}\times100\%=19.2307\%$. 5. Rounded to one decimal place the answer is $19.2\%$. Answering $20.0\%$ assumes 10 out of 50 rather than 52. _Source: NECTA CSEE 2022 Basic Mathematics 041, Question 1: Numbers, Fractions, Percentages and Logarithms_

1. Fractions cannot be ordered by comparing denominators alone — a bigger denominator does not always mean a smaller fraction. 2. Convert each to a decimal: $\tfrac12=0.500$, $\tfrac29=0.222$, $\tfrac38=0.375$, $\tfrac1{12}=0.083$, $\tfrac25=0.400$. 3. Sorting those decimals from smallest gives $0.083,0.222,0.375,0.400,0.500$. 4. So the order is $\tfrac1{12},\tfrac29,\tfrac38,\tfrac25,\tfrac12$. 5. Multiplying through by the LCM of the denominators gives the same order; using the GCF instead, a recorded error, does not. _Source: NECTA CSEE 2022 Basic Mathematics 041, Question 1: Numbers, Fractions, Percentages and Logarithms_

1. First write the denominator in standard form: $0.000035=3.5\times10^{-5}$. 2. The expression becomes $\dfrac{7\times10^{4}}{3.5\times10^{-5}}$. 3. Divide the numbers: $\dfrac{7}{3.5}=2$. 4. Subtract the exponents: $10^{4-(-5)}=10^{9}$. 5. So the answer is $2\times10^{9}$. Writing $20\times10^{8}$ has the right value but is not standard form, since the first factor must lie between 1 and 10. _Source: NECTA CSEE 2022 Basic Mathematics 041, Question 1: Numbers, Fractions, Percentages and Logarithms_