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Ireland
10. If \( \sin x=\frac{1}{2} \) and \( 0 \leqslant x \leqslant \frac{\pi}{2} \), find the value of \( \sin \left(x+\frac{\pi}{4}\right) \) without using a calculator.
Trigonometry Jan 15, 2025
(ii) \( \sin 2 \theta \cos \theta+\cos 2 \theta \sin \theta \)
Trigonometry Jan 15, 2025
5. Simplify each of the following: (i) \( \frac{\tan 2 A+\tan A}{1-\tan 2 A \tan A} \)
Trigonometry Jan 15, 2025
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 15, 2025
3. (a) \( 4 x+2 y-3 x-y \) (b) \( 3 p+2 q+7 q-4 p \) (c) \( 7 p-6 q-4 p-q \) (d) \( -3 m+2 n-4 m+3 n+4 \) (e) \( 8 a-4 b-3 b+2 a \) 4. (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 15, 2025
(ii) The \( n \)th term in the sequence is given by the expression, for \( n \in \mathbb{N} \) : \[ T_{n}=n^{2}+b n+c \text {, where } b, c \in \mathbb{Z} \text {. } \] Find the value of \( b \) and the value of \( c \).
Algebra Jan 15, 2025
(ii) The \( n \)th term in the sequence is given by the expression, for \( n \in \mathbb{N} \) : \[ T_{n}=n^{2}+b n+c \text {, where } b, c \in \mathbb{Z} \]
Algebra Jan 15, 2025
The \( n \)th term in the sequence is given by the expression, \[ T_{n}=n^{2}+b n+c \text {, where } b, c \in \mathbb{Z} \] Find the value of \( b \) and the value of \( c \).
Algebra Jan 15, 2025
(b) If this pattern continued, how many fruit flies would be in the jar after (i) 36 days, (ii) 72 days? (i) Could this pattern of growth continue indefinitely? Explain your answer. 5 A manufacturing company models its total cost in euro for producing \( x \) items using the cost function \( C(x)=500+90 x \). It models the total revenue in euro from the sales of the xitems using the revenue function \( R(x)=150 x-x^{2} \). The company expects to sell all the items it produces. (a) The company produced 50 items on one day. Find the production cost and total revenue for the 50 items.
Algebra Jan 15, 2025
S A erundacturing company models its total cost in euro for producing x items using the ant furcion \( (x)=500+90 x \). It models the total revenue in euro from the sales of the \( x \) ferco ving the ceverve function \( P(x)=150 x-x^{2} \). The company erpects to sell all the tams e pioduces. (4) The romeany produred 50 items on one day, find the production cost and total rever to for the 50 terms
Algebra Jan 15, 2025
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