50 add maths question

8/12/2019 50 add maths question

http://slidepdf.com/reader/full/50-add-maths-question 1/6

g(x)x

02

46

-2

k

0

4

1. Diagram 2 shows the linear function . g

(a) State the value of k .

(b) Using the function notation, express g in terms of x.

[2marks]

2.Diagram 3 shows the function 0,:

x

x

k x x g where k is a constant.

Find the value of k .

[2marks]

3. Given the function 1: x x g , find the value of x such that 2)( x g .

[2marks]

4. The following information refers to the function f and g .

Find )(1 x g f

.

[3 marks]

5.Given the function h x x g 3: and

2

1:1

kx x g , where h and k are constants. Find

the value of h and of k .

[3marks]

Diagram 2

3

x

Diagram 3



6. Form the quadratic equation which has the roots 7 and3

2 . Give your answer in the form

02 cbxax , where a , b and c are constants.

[2 marks]

7. Given the roots of the quadratic equation 24 8 0kx hx are equal. Express k in terms of h.[2 marks]

8. The straight line y = 9 4 px is a tangent to the curve y = 21 . p x Find the possible values

of p. [5 marks]

9. The straight line y =2 x1 does not intersect the curve y = 2 2 . x x p Find the range of

values of

p. [5 marks]

10. The quadratic equation2

3 0 x kx h has roots

4 and 3. Find the values of k and h.

11. The quadratic function f ( x) = a( x+ p)2

+ q, where a, p and q are constants, has a maximum

value of 5. The equation of the axis of symmetry is x=3.

State(a) the range of values of a,

(b) the value of p

(c) the value of q [3 marks]

12. The quadratic function f ( x) = x2

6 x + 5 can be expressed in the form f ( x) = ( x + m)

2+ n where m and n are constants.

Find the value of m and of n. [3

marks]



13. The following diagram shows the graph of quadratic function y = g ( x).

The straight line y = 9 is a tangent to the curve y = g ( x).

(a) Write the equation of the axis of symmetry of the curve

(b) Express g ( x) in the form ( x + b)

2

+ c where b and c are constant. [3 marks]

14. The following diagram shows the graph of a quadratic function 2)(25)( p x x f , where

p is a constant.

The curve )( x f y has a maximum point at A(1, q), where q is a constant. State

(a) the value of p,

(b) the value of q,

(c) the equation of the axis of symmetry.

[3 marks ]

15. The quadratic equation x(p x ) = x + 4 has no real roots. Find the range of values of p

[3 marks ]

x

y

O 15

y = 9

A(1, q)

.

0

x

y



16 Solve the simultaneous equations 82 x y and x - 3 x – y = 2

[5 marks]

17Solve the simultaneous equations j – k = 2 and j + 2k = 8. Give your answers correct to

three decimal places

[5 marks]

18 Solve the simultaneous equations x + 2 y = 1 and y - 10 = 2 x.

[5 marks]

19 Solve the simultaneous equations 2 x + y = 1 and x + y + xy = 7.

[5 marks]

20 Solve the following simultaneous equations.82 y x

374 22 y x

Give your answers correct to three decimal places.

[5 marks]



1 (a) 2k 1

(b) 2)( x x g 1

2 1k 1

3 1 x 3 x 1

.4

3

h y x

1

5

3

1k

1

2

3h

1

6

014193

0237

2

x x

x x

1

1

7 12

128

hk

1

8 p = 3 and p =

4

3

1

9 p > 3 1

10 k = -3 and h = -36 111 (a) a<0 1

(b) p=3 1

(c) q=5 1

12 m = 3 n = 4 1,1

13 (a) x = 2 1

(b)

g ( x) = ( x + 2)2 9

1,1

14 (a) p = 1 1

(b) q =5 1

(c) x=1 115 3 < p < 5 1

16 y = -4, y = - 21

17 = 0.606 = - 6.606 1



18 = -3, = 13

1

19 y= 1 – 2(- 1), y = 1 – 2(2)

= 3, = - 3 1

20 x = 8 + 2(- 1.209), x = 8 + 2(-2.791)

= 5.582, = 2.418 1

50 add maths question

Documents

Transcript of 50 add maths question