Algebra: Expression Positive, Negative And Zero Essay Sample
1. ( a ) Express degree Fahrenheit ( x ) = x2 – 6x + 14 in the signifier degree Fahrenheit ( x ) = ( x – H ) 2 + k. where H and K are to be determined. ( B ) Hence. or otherwise. compose down the co-ordinates of the vertex of the parabola with equation Y – x2 – 6x + 14. ( Entire 4 Markss )
2. The diagram shows the graph of the map Y = ax2 + bx + degree Celsius.
Complete the tabular array below to demo whether each look is positive. negative or nothing. Expression|positive|negative|zero|
a||||
c||||
b2 – 4ac||||
b||||
( Entire 4 Markss )
3. The diagram shows the parabola Y = ( 7 – ten ) ( fifty + x ) . The points A and C are the x-intercepts and the point B is the maximal point.
Find the co-ordinates of A. B and C.
( Entire 4 Markss )
4. Find the amount of the arithmetic series
17 + 27 + 37 +…+ 417.
( Entire 4 Markss )
5. See the arithmetic sequence 2. 5. 8. 11. … . .
( a ) Find u101.
( 3 )
( B ) Find the value of Ns so that un = 152.
( 3 )
( Entire 6 Markss )
6. Gwendolyn added the multiples of 3. from 3 to 3750 and found that 3 + 6 + 9 + … + 3750 = s.
Calculate s.
( Entire 6 Markss )
7. Find the coefficient of a5b7 in the enlargement of ( a + B ) 12. ( Entire 4 Markss )
8. Find the term incorporating x10 in the enlargement of ( 5 + 2?2 ) 7. ( Entire 6 Markss )
9. The 2nd term of an arithmetic sequence is 7. The amount of the first four footings of the arithmetic sequence is 12. Find the first term. a. and the common difference. d. of the sequence. ( Entire 4 Markss )
10. See the arithmetic series 2 + 5 + 8 +… .
( a ) Find an look for Sn. the amount of the first N footings. ( B ) Find the value of N for which Sn = 1365.
( Entire 6 Markss )
11. Find the amount to eternity of the geometric series
( Entire 3 Markss )
12. The first and 4th footings of a geometric series are 18 and severally. Find
( a ) the amount of the first n footings of the series ;
( 4 )
( B ) the amount to eternity of the series.
( 2 )
( Entire 6 Markss )
13. Find the coefficient of x7 in the enlargement of ( 2 + 3x ) 10. giving your reply as a whole figure. ( Entire 3 Markss )
14. Find the coefficient of the x3 term in the enlargement of ( Entire 6 Markss )
