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Home Question Bank Math Archive 2025 February 12

Math Questions from Feb 12,2025

Browse the Math Q&A Archive for Feb 12,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Simplify. \( 4^{-\frac{1}{4}} \cdot 4^{-\frac{1}{4}} \) \( \square \) Given: \( f(x)=2 x^{3}-5 x^{2}-4 x+3 \) 1.1 Neatly draw the graph of \( f \) on the given graph paper in ANNEXURE A. Clearly indicate all intercepts with the axes and coordinates of turning points. 1.2 Determine the first derivative of \( f \) and call it \( g \). (1) 1.3 Draw the graph of \( g \) on the same system of axes as \( f \) in ANNEXURE A. Clearly indicate all intercepts with the axes and coordinates of turning points. (4) 1.4 Determine the second derivative of \( f \) and call it \( h \). Then sketch the graph of \( h \) on the same system of axes as \( f \) and \( g \) in ANNEXURE A. Clearly indicate all intercepts with the axes. (3) 1.5 What do you notice about the \( x \)-intercepts of the quadratic function and the \( x \)-coordinates of the turning points of the cubic function? 1.6 The inflection point can be determined by firstly solving \( f^{\prime \prime}(x)=0 \). It can also be determined by calculating the midpoint between the turning points of the cubic graph. Hence determine the inflection point of \( f \). (3) 1.7 What do you notice about the axis of symmetry of \( g \), the \( x \)-intercept of \( h \) and the \( x \)-coordinate of the inflection point of \( f \) ? (1) [20] What is \( \frac{8}{5}+\frac{4}{5} \) ? Write your answer as a fraction greater than one and as a mixed number. Simplify. \( 5^{\frac{1}{2}} \cdot 5^{\frac{1}{2}} \) \( \square \) \[ \begin{array}{l} \sqrt{\frac{3}{4}-\frac{1}{3}-\frac{1}{2} \cdot\left(1-\frac{5}{6}\right)+\frac{2}{3}} \\ \sqrt{\left[\left(1-\frac{3}{4}\right): \frac{1}{8}\right]:\left[\left(1+\frac{1}{2}\right)-\frac{3}{4}:\left(1-\frac{1}{4}\right)\right]} \\ \sqrt{\left(\frac{5}{2}-\frac{1}{4}\right) \cdot\left[1+\left(\frac{2}{5}+\frac{1}{10}\right) \cdot\left(1-\frac{1}{2}\right)\right]:\left[\frac{1}{2}+1:\left(1+\frac{1}{3}\right)\right]} \\ \left(\frac{6}{7}: \frac{2}{21}\right) \cdot\left(1-\frac{3}{4}\right)^{2} \cdot \sqrt{\frac{3}{4}-\frac{11}{36}} \end{array} \] 5. \[ \left[\left(\frac{17}{20}-\frac{4}{15}\right) \cdot \frac{16}{21}-\left(1-\frac{3}{4}\right)\right]: \sqrt{\left(1-\frac{1}{6}\right) \cdot \frac{10}{3}} \] 6. \[ \sqrt{\left\{4-\left(\frac{3}{4}+\frac{1}{2}+\frac{5}{4}\right)-\left[\left(\frac{5}{3}+\frac{2}{5}-2\right)+\frac{3}{5}\right]\right\} \cdot \frac{1}{30}} \] 7. \( \sqrt{\left(\frac{19}{30}-\frac{11}{20}\right): \frac{5}{12}+\left(\frac{13}{12}-\frac{11}{15}\right) \cdot \frac{16}{35}} \) 8. \[ \sqrt{\left[\left(3+\frac{7}{3}-\frac{24}{5}\right) \cdot \frac{5}{4}+\left(\frac{11}{10}-\frac{5}{6}\right): \frac{2}{9}\right]} \cdot \frac{7}{15} \] 1. 78 miles on 3 gallons The number of stamps in the set he bought is divisible by \( 2,3,5,6 \), and 9 . Which set is it? Divide. \[ 8.14 \div 10 \] Simplify. \( 27^{\frac{3}{2}} \cdot 3^{\frac{3}{2}} \) \( \square \) \( \square \) Divide. \( 64.8 \div 100 \)
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