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Home Question Bank Math Archive 2025 February 04

Math Questions from Feb 04,2025

Browse the Math Q&A Archive for Feb 04,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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6 Use the formula \( m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \) to find the slope of the line that passes through each pair of points: \( \begin{array}{lll}\text { (i) }(2,2) \text { and }(3,5) & \text { (ii) }(1,5) \text { and }(3,6) & \text { (iii) }(4,7) \text { and }(5,7) \\ \text { (iv) }(-1,5) \text { and }(4,6) & \text { (v) }(-5,-2) \text { and }(4,-6) & \end{array} \) 6. When 6 is multiplied by the following fractions, which of the products will be greater (4) \( \frac{4}{5} \) (8) \( \frac{10}{9} \) (a) \( \frac{3}{3} \) (D) \( \frac{13}{14} \) Determine whether the statements a through \( e \) are true and give an explanation or counterexample. b. If \( F^{\prime}(x)=f(x) \), then \( f \) is the antiderivative of \( F \). Adding and subtracuing Aigebraic 7ractions \[ \frac{x^{2}-16}{5 x-20}-\frac{x^{2}-3 x+2}{3 x-3}+\frac{4}{2 x^{2}} \] The start of a quadratic sequence is shown below. By first working out the \( n^{\text {th }} \) term rule, calculate the \( 10^{\text {th }} \) term of the sequence. \[ -5, \quad 4, \quad 19, \quad 40, \quad 67, \quad \ldots \] 4. Determina los elementos que forma cada conjunto dado a. \( A=\{x \in \mathbb{Z} \mid x \) está entre \( -4 y 2\} \) b. \( B=\{x \in \mathbb{Z} \mid x \) es menor que -6\( \} \) c. \( C=\{x \in \mathbb{Z} \mid x \) no es negativo \( \} \) Determine whether the statements a through e are true and give an explanation or counterexample. a. \( F(x)=x^{3}-4 x+100 \) and \( G(x)=x^{3}-4 x-100 \) are antiderivatives of the same function. Directions: Find the missing endpoint if \( K \) is the midpoint \( \overline{L M} \). 10. \( L(-9,4) \) and \( K(2,-1) \); Find \( M \). (a) Factorise the following quadratic trinomials fully: \( \begin{array}{llll}\text { (1) } x^{2}-11 x+28 & \text { (2) } x^{2}-5 x-84 & \text { (3) } x^{2}+6 x+9 \\ \text { (4) } x^{2}-4 x-12 & \text { (5) } a^{2}-9 a+20 & \text { (6) } a^{2}-11 a-12 \\ \text { (7) } a^{2}-12 a+35 & \text { (8) } a^{2}-2 a-48 & \text { (9) } m^{2}+5 m+6 \\ \text { (10) } m^{2}-5 m-6 & \text { (11) } m^{2}+5 m-6 & \text { (12) } m^{2}-5 m+6 \\ \text { (13) } x^{2}+7 x+12 & \text { (14) } x^{2}-7 x+12 & \text { (15) } x^{2}+4 x-12 \\ \text { Factorise fully: } & & & \\ \text { (1) } 2 x^{2}-2 x-12 & \text { (2) } 3 x^{2}-21 x-54 & \text { (3) } 4 a^{2}+12 a-40 \\ \text { (4) } 6 a^{2}+24 a-30 & \text { (5) } x^{3}+2 x^{2}-8 x & \text { (6) } 90-45 x+5 x^{2}\end{array} \) The start of a quadratic sequence is shown below. By first working out the \( n^{\text {th }} \) term rule, calculate the \( 10^{\text {th }} \) term of the sequence.
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