Power of Maths Paper 1 OL

Power of Maths: Paper 1 – Section 3

7. If y = x 2 + px is the equation of the curve below, fi nd p.

y

(d) x 2 – 10x + 21 = 0 for x and hence 2

( x – 18 ___

x ) – 10

( x – 18 ___

x ) + 21 = 0 for x

(e) 5 x 2 – 23x + 12 = 0 for x and hence ( y – 2)2 – 4⋅6( y – 2) = –2⋅4 for y

(0, 0) (3, 0)

8. Form the quadratic equations with the following roots:

(a) 1, 2 (b) 3, 3 (c) –1, –2 (d) 5, –6 (e) 1

_ 2 , 3

_ 2

9. Solve the following: (a) x 2 = 13x + 5

_______ 6

(b) 3 __

x + 5 (c) 6 (d) (e) 1

_____ x + 2 = 2

_____ x – 1 – 1

_______ x – 5 + 8

x(x – 7)

_____ x + 1 – 1 place

_____ x – 1 = 1

_____ x – 5 = x

__ 3 = 1

__ 3

_____ x + 2 , correct to one decimal

10. Solve the following:

(a) x 2 – 7x + 10 = 0 for x and hence (y – 2 ) 2 – 7(y – 2) + 10 = 0 for y

(b) 6 x 2 – 11x – 10 = 0 for x and hence 6(t – 1) 2 – 11(t – 1) – 10 = 0 for t

(c) 3 x 2 – 7x + 4 = 0 for x and hence 3

( y __

3 – 1 ) 2 – 7

( y __

3 – 1 ) + 4 = 0 for y x

11. (a) In a round-robin hockey tournament, each team is paired with every other team once. If there are x teams, the number N of

games that are played is given by N = x 2 – x

how many teams entered?

_____ 2

(b) When the sum of 6 and twice a natural number is subtracted from the square of the number, the result is 2. Find this number.

(c) The profi t P in € made by selling x computers is modelled by the equation P = –5 x 2 + 1200x + 6000. How many computers must be sold to make a profi t of €53 500?

(d) The total resistance R of two resistors in parallel is given by 1

__ R = 1

r r + 3 If R = 2 ohms, fi nd r in ohms.

(e) A golf ball is thrown up on the moon. The equation of the ball’s height h (m) above the lunar surface t seconds after launch is given by h = 12⋅8t – 0⋅8 t 2 . Find when it is 22·4 m above the surface.

(f) A regulation tennis court for a doubles match is laid out so that its length is 1⋅85 m longer than twice its width. The area of the doubles court is 267 m2. Find the length and breadth of a doubles court, correct to two decimal places.

Anyone for tennis?

__ r + 1

_____ r + 3 .

. If 66 games are played,

106

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