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Ireland
6. (a) \( 2 x^{2}+2 x+3 x^{2}+5 x \) (b) \( 3 m^{2}+2 m+4 m^{2}-3 m \) (c) \( -8 q^{2}-3+4 q^{2}-q \)
Algebra Jan 22, 2025
(a) \( 3 x+2 y+4+6 x+5 y+9 \) (b) \( 8 m+2 n+5-3 m-2 n+3 \) (c) \( 12 p+24 q-5-5 q-12 p-5 \)
Algebra Jan 22, 2025
7. Find an expression for the \( n \)th term of each of the quadratic sequences: \( \begin{array}{lll}\text { (i) } 7,10,15,22,31, \ldots & \text { (ii) } 2,7,14,23, \ldots & \text { (iii) } 2,8,18,32,50, \ldots\end{array} \) 8. Show that the \( n \)th term of the quadratic sequence \( 8,15,26,41,60, \ldots \) is given by \( T_{n}=2 n^{2}+n+5 \)
Pre Algebra Jan 21, 2025
In the second experiment the student dissolved sucrose in water. They used some of the following components to investigate if the resulting solution could conduct electricity. Buzzer Wires Battery (s) Using electrical circuit symbols, draw a labelled diagram of a circuit the student could have used to carry out this investigation. You may use the symbols on pages \( 72-78 \) of the Formulae and Tables booklet to help you answer this question.
Chemistry Jan 21, 2025
8) Find the midpoints of the line segments joining the following pairs of points: \( \begin{array}{ll}\text { (i) }(3,2) \text { and }(5,4) & \text { (ii) }(1,5) \text { and }(7,3) \\ \text { (iii) }(3,7) \text { and }(5,9) & \text { (iv) }(-1,4) \text { and }(5,6)\end{array} \)
Geometry Jan 20, 2025
(5) Find the midpoints of the line segments joining the following pairs of points: \( \begin{array}{ll}\text { (i) }(3,2) \text { and }(5,4) & \text { (ii) }(1,5) \text { and }(7,3) \\ \text { (iii) }(3,7) \text { and }(5,9) & \text { (iv) }(-1,4) \text { and }(5,6)\end{array} \)
Geometry Jan 20, 2025
15. Josic takes a card at random from this pack and koops it Then she takes a second card at random. Find the probability that she takes one odd number and one even number (in either order).
Probability Jan 20, 2025
(c) The height of Harry's ball during its fall, \( h(t) \), is given by: \[ h(t)=1+18 t-5 t^{2} \] Use this, and the fact that \( g(t)=18+10 t-5 t^{2} \), to answer the following questions. These are the same questions as in part (b), but here you will need to use algebra to answer them. (i) How much higher than Harry's ball is Gina's ball, half a second after Gina drops her ball ( \( t=1.5 \) )? Show your working out. (ii) Use calculus to find how long it takes Harry's ball to reach its maximum height.
Calculus Jan 20, 2025
(ii) Find the value of \( f^{\prime}(x) \) when \( x=1 \). \[ f(x)=6(1)^{2}-6(1)^{1}+7=6-6+^{\prime} \] (iii) Find the equation of the tangent to the curve \( y=f(x) \) at \( x=1 \). (A,
Calculus Jan 20, 2025
\( g(x) \) is the following function in \( x \in \mathbb{R} \) : \[ g(x)=x^{2}+8 x-6 \] Find the value of \( g(-5) \). \[ (-5)^{2}+8(-5)-6=25-40-6=- \] Use calculus to find the value of \( x \) which gives the minimum value of \( g(x) \).
Calculus Jan 20, 2025
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