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**Q.1**

The length, d m(meters), of a retangular field is 40m greater than the width.

The perimeter of the field is 400m

i) Write this info in the form of an equation for d

ii) Solve the equation and so find the area of the field

The length, d m(meters), of a retangular field is 40m greater than the width.

The perimeter of the field is 400m

i) Write this info in the form of an equation for d

ii) Solve the equation and so find the area of the field

Ans i) 4d - 80 = 400

Ans ii) 4d = 480

d = 480 / 4

d = 120m

120 * 80 = 9600m2

**Q.2**

A) In the Formula S = ut+ 1/2 at2 make 'u' the subject

B) In the Formula T = 2Pi SQRT l/g make 'l' the subject

A) In the Formula S = ut+ 1/2 at2 make 'u' the subject

B) In the Formula T = 2Pi SQRT l/g make 'l' the subject

Ans A) u = s - 1/2 at

Ans B) T = 2Pi SQRT l/g

T / 2Pi = SQRT l /g

T2/4Pi2 = l/g

l = T2 g / 4Pi2

(sorry this looks so complicted, but I don't know how to add the right symbols)

**Q.3**

Write the following as simple fractions

i) x/3 + x/4

ii) 3/x + 4/x

iii) x2/x * x4/x3 - this is supposed to read xsquared over x multiplyed by x to the power of 4 divided by x to the power of 3

Write the following as simple fractions

i) x/3 + x/4

ii) 3/x + 4/x

iii) x2/x * x4/x3 - this is supposed to read xsquared over x multiplyed by x to the power of 4 divided by x to the power of 3

i) 7x/12

ii) 7/x

iii) (Not sure about this one) x2/x * x4/x3 = x6/x4

**Q.4**

Two resistors; r1 and r2 are placed in parallel so that their combined resistance R is given by:

1/R = 1/r1 + 1/r2

If r1 = 2x and r2 = 3x, find the formula for R in terms of x (show all your workings)

Two resistors; r1 and r2 are placed in parallel so that their combined resistance R is given by:

1/R = 1/r1 + 1/r2

If r1 = 2x and r2 = 3x, find the formula for R in terms of x (show all your workings)

1/R = 1/r1 + 1/r2

1/R = 1/2x + 1/3x

1/R = 3/6x + 2/6x

1/R = 5/6x

1 = 5/6x *R

R = 6x/5

**Q4.**

Solve the following quadratic equations by either factorising or using the "b2-4ac" formula (to 3 S.F.)

i) x2 + x - 12 = 0

ii) 6x2 + x -2 = 0

Solve the following quadratic equations by either factorising or using the "b2-4ac" formula (to 3 S.F.)

i) x2 + x - 12 = 0

ii) 6x2 + x -2 = 0

Ans i) x2 + x - 12 = 0

(x -3 )(x +4) = 0

x-3 = 0 x+4 = 0

x=-4 x=-3

Ans ii) Using the formula x = -b +/- SQRTb2 - 4ac

_____________________

2a

When a = 6

b = 1

c = -2

(I can't really write the full workings because it looks too complicated without using the correct symbols ect.) The answers are:

x = -1 + 7 = 6 = 1

______ ___ __

12 12 2

x = -1 - 7 -8 -2

______ ___ __

12 12 3

**Q5.**

A stone this thrown into the aid and its height, h metres above the ground, is given by the equation:

h = pt - qt2

A) Where p and q are constants and t seconds is t time is has been in the air. Given that h = 40 when t = 2 and that h = 45 when t = 3, show that

p - 2q = 20

and

p-3q = 15

B) Use these equations to calculate the values of p and q Hence show that the equation for h can be expressed in the form 5t2 - 30t + h = 0

C) Use this equation to find the values of t when h = 17, gving your answers correct to two decimals places. Explain the significance of the two values of t

A stone this thrown into the aid and its height, h metres above the ground, is given by the equation:

h = pt - qt2

A) Where p and q are constants and t seconds is t time is has been in the air. Given that h = 40 when t = 2 and that h = 45 when t = 3, show that

p - 2q = 20

and

p-3q = 15

B) Use these equations to calculate the values of p and q Hence show that the equation for h can be expressed in the form 5t2 - 30t + h = 0

C) Use this equation to find the values of t when h = 17, gving your answers correct to two decimals places. Explain the significance of the two values of t

Ans A)

h = pt - qt2

when h = 40 and t = 2

40 = 2p - 4q

40/2 = 2p - 4q/2

p - 2q = 20

When h = 45 and t = 3

45 = 3p - 9q

45/3 = 3p - 9q/3

p - 3q = 15

Ans B)

(p- 2q = 20) - (p-3q = 15)

q = 5

p-2q=20

p-2 * 5 = 20

p - 10 = 20

p = 30

therefore h = 30t - 5t2 and 5t2 - 30t + h = 0

Ans C) (this is similar to Q4 ii using the formula

x = -b +/- SQRTb2 - 4ac

_____________________

2a

Therefore I've minimised my workings here)

5t2 - 30t + 17 = 0

t = -30 +/- 23.6

_____________

10

t = -30 - 23.6 = 0.63

__________

10

t = -30 + 23.6 = 5.37

__________

10

**My own Question**

I'm trying to explain the significance of the two values of t but I'm stugling to see what they are. Could someone help explain?

Well, thats it! I hope someone can give them the quick once over :)

Matt