form 5 addmath testa

8/11/2019 Form 5 addmath TestA

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Gan Sin Qi

PAPER 1

1. Given that -3 is one of the roots of the quadratic equation x 2 – x + p = 0, find the value of p. [2]2. Solve the quadratic equation (x - 1 )( x + 2) = 3 ( x – 1 ). [3]3. Given 1/3 and -7 are roots of a quadratic equation. Write the equation on the form of ax 2 + bx + c = 0. [3]

4. Given the quadratic equation x 2 + ( 1 – p ) x + 4 = 0 has one real root only, find the values of p. [3]5. Find the range of values of k if the straight line y = 3x – k intersects the curve y = 4 – x2 at two different

points. [4]6. Express the equation x 2 – 8x – 5 = 0 in the form a ( x + b ) 2 + c = 0. [3]7. Find the range of values of x for 2x 2 < 5x + 3. [3]8. Find the range of x if given ( )( ) ( )( ). [3]9. The minimum value of the quadratic function f(x) = m ( x + n ) 2 + p, where m, n and p are constants is -6.

The equation of the axis of symmetry is x = 2. Statea) The range of values of m,

b)

The value of n,c) The value of p. [3]10. The maximum value of the quadratic equation f(x) = - x 2 + 6x + a 2 is 13. Find the values of a. [3]11. In diagram, the curve of y = 2 ( x + a ) 2 + 7 has the minimum point (3, b). State

a) The values of a and b, b) The equation of the axis of symmetry. [3]

12. Solve the equation: . [3]13. Solve the equation: . [3]14. Solve the equation: . [3]15. Solve the equation: ( ) . [3]

16. Solve the equation: . [4]

17. Solve the equation: ( ) [4]18. Given , express x in terms of y. [4]

19. Given that and , express in terms of m and n. [4]

20. Given that and , calculate . [4]

1. √

2.

3.

4. ( )

5.

6.

7.

8.

9.

10. ̅ ∑∑



PAPER 2

1. The quadratic equation x 2 + 6 ( 2x – k ) = 0, where k is a constant has roots h and 3h.a) Find the value of h and k. [4]

b) Hence, form the quadratic equation which has the roots h – 2 and h + 10. [3]2. Diagram shows a curve of a quadratic equation f(x) = x 2 + mx + 7. The curve has the minimum point at

P(3, t) and intersects the f(x) – axis at point Q.

a) State the coordinates of point Q. [1] b) By using the method of completing the square, find the values of m and t. [4]c) Determine the range of values of x, if f(x) < 7. [3]

3. Solve the simultaneous equations and . [5]

4. Solve the simultaneous equations . [5]5. Table shows the prices and the price indices for four ingredients A, B, C and D, used in the production

of a particular kind of cake. Diagram is a pie chart which represents the amount of the ingredients A, B,C and D, used in producing the cakes.

a) Find the values of p, q and r. [3] b) i) Calculate the composite index for the cost of producing cake in the year 2011 based on the year

2009. [2]ii) Hence, calculate the corresponding cost of making these cakes in the year 2009 if the cost in the

year 2011 was RM 3450. [2]c) The cost of making these cakes are expected to increase by 35% from the year 2011 to the year 2013.

Find the expected composite index for the year 2013 based on the year 2009. [3]



Foo Jia Hao

PAPER 1

1. It is given that -3 is one of the roots of the quadratic equation 2x 2 – 7x + k = 0. Find the value of k. [2]2. Solve the quadratic equation 3x( x - 2) = ( 1 – x ) ( x + 6 ). [3]3. Form the quadratic equation which has the roots -5 and 2/3. Give your answer in the general form. [3]

4. Given that the quadratic equation ( p – 1)x 2 – 8x = 4 has no roots. Find the possible value of p. [3]5. The straight line y = 3 – 2x does not intersect the curve y = 2kx 2 + 5x. Find the range of value of k. [4]6. Express the equation 2x 2 + 4x + 1 = 0 in the form a ( x + b ) 2 + c = 0. [3]7. Find the range of values of x for ( 2x + 1 )( x + 4 ) > 4x + 11. [3]8. Find the range of values of x for ( ) . [3]9. The maximum value of the quadratic function f(x) = m ( x + h ) 2 + k, where m, h and k are constants is 9.

The equation of the axis of symmetry is x = 4. Statea) The range of values of m,

b) The value of h,

c)

The value of k. [3]10. The quadratic function f(x) = - x 2 + 6x + m 2 is18. Find the values of m. [3]11. The diagram shows the graph of a quadratic function f(x) = -2 ( x + k ) 2 + 4, where k is a constant. The

curve y = f(x) has a maximum point (3, h). State

a) The values of k and h. b) The equation of the axis of symmetry. [3]

12. Solve the equation: . [3]13. Solve the equation: . [3]14. Solve the equation: . [3]

15. Solve the equation: √ . [4]16. Solve the equation: ( ) . [3]17. Solve the equation: ( ) . [4]

18. Given , express y in terms of x. [4]19. Given that and , express in terms of x and y. [4]

20. Given that and , calculate . [4]

1. √

2.

3.

4. ( )

5.

6.

7.

8.

9.

10. ̅ ∑∑



PAPER 2

1. The quadratic equation x 2 + 6 ( 3x + p ) = 0, where p is a constant has roots q and 2q.a) Find the value of p and q. [4]

b) Hence, form the quadratic equation which has the roots q + 2 and q – 5. [3]2. Diagram shows a curve of a quadratic equation f(x) = -x 2 + mx - 11. The curve has the maximum point

at Q(-3, k) and intersects the f(x) – axis at point P.

a) State the coordinates of point P. [1] b) By using the method of completing the square, find the values of k and m. [4]

c) Determine the range of values of x, if f(x) > -3. [3]3. Solve the simultaneous equations and . [5]4. Solve the simultaneous equations . [5]5. Table shows the prices and price indices for five items A, B, C, D and E. Diagram is a bar chart

indicating the monthly cost of the items for the year 2006.

a) Find the value of p, q and r. [3]

b) Calculate the composite index for items in the year 2008 based on the year 2006. [2]c) The total yearly cost of the items in the year 2006 is RM 1350. Calculate the corresponding yearly

cost for the year 2008. [2]d) The cost of the item increases by 15% from the year 2008 to the year 2010. Find the composite index

for the year 2010 based on the year 2006. [3]



Ang Chen Ni

PAPER 1

1. It is given that -3 is one of the roots of the quadratic equation 2x 2 – 7x + r = 0. Find the value of r. [2]2. Solve the quadratic equation (2 – x )( x + 1) = ¼ x ( x – 5 ). [3]3. Given that -3 and m – 2 are the roots of the quadratic equation x 2 – ( n + 1 ) x + 15 = 0, where m and n

are constants. Find the values of m and n. [3]4. The quadratic equation 4nx 2 + x + 4nx + n – 2 = 0 has two equal roots. Find the value of n. [3]5. Find the value of p if the straight line y = 2x – 1 is a tangent to the curve y = x 2 + p. [4]6. Express the equation 3x 2 - 6x - 1 = 0 in the form a ( x + b ) 2 + c = 0. [3]7. Find the range of values of x for ( x - 2 ) 2 < 14 – x. [3]8. Given that f(x) = 16x 2 – 9, find the range of the values of x which f(x) is always positive. [3]9. The maximum value of the quadratic function f(x) = m ( x + p ) 2 + q, where m, p and q are constants is 6.

The equation of the axis of symmetry is x = - 4. Statea) The range of values of m,

b)

The value of p,c) The value of q. [3]10. Given 13 is the maximum value for the quadratic equation f(x) = - x 2 – 8x + k – 1. Find the value of k. [3]11. Diagram shows the graph of quadratic function y = f(x). The straight line y = -9 is a tangent to the curve

y = f(x).

a) State the equation of axis of symmetry. b) Express f(x) in the form of ( x + p) 2 + q where p and q are constants. [3]




15. Solve the equation: √ . [4]16. Solve the equation: ( ) . [3]17. Solve the equation: ( ) . [4]

18. Given that and , express in terms of m and n. [4]

19. Given that and , calculate . [4]20. Given , express T in terms of V. [4]

1. √

2.

3.

4. ( )

5.

6.

7.

8.

9.

10. ̅ ∑∑



Pan Lee Xian

PAPER 1

1. Given that -2 is one of the roots of the quadratic equation 2x 2 – 5x + p = 0, find the value of p. [2]2. Solve the quadratic equation ( 2x – 1 ) 2 = 3 ( x + 5 ) – 9. [3]3. Given h + 1 and k – 3 are the roots of the equation x 2 + 7x = -12. Find the values of h and k. [3]

4. The straight line y = 2 – m is the tangent to the curve y = 4x 2 + mx – 1. Find the values of m. [4]5. Given the quadratic equation x 2 – 2x = 9 ( 2x – 5) – 5p has equal roots. Find the possible value of p. [3]6. Express the equation 3x 2 + 9x + 10 = 0 in the form a ( x + b ) 2 + c = 0. [3]7. Find the range of values of x for 5x 2 – 11x – 12 < x ( 2x + 5 ). [3]8. Given that f(x) = 36x 2 – 9, find the range of the values of x which f(x) is always positive. [3]9. The minimum value of the quadratic function f(x) = m ( x + p ) 2 + q, where m, p and q are constants is -

12. The equation of the axis of symmetry is x = - 3. Statea) The range of values of m,

b) The value of p,

c)

The value of q. [3]10. The quadratic equation f(x) = q – 8x – 2x 2 has the maximum value of 2p + 5, express p in terms of q. [3]11. The diagram shows the graph of the quadratic function f(x) = (x + 5) 2 + 3k – 4, where k is a constant.

a) State the equation of the axis of the symmetry of the curve. b) Given the minimum value of the function is 11. Find the value of k. [3]

12. Solve the equation: . [3]13. Solve the equation: . [3]14. Solve the equation: . [3]15. Solve the equation:. ( ) . [3]


17. Solve the equation: ( ) . [4]

18. Given that and , express in terms of h and k. [4]19. Given that and , calculate . [4]

20. Given , express T in terms of V. [4]

1. √

2.

3.

4. ( )

5.

6.

7.

8.

9.

10. ̅ ∑∑



PAPER 2

1. The quadratic equation 4x 2 - ( 3k - 2 ) x + 16p = 0 has roots 2 and -3.a) Find the value of k and p. [4]

b) Hence, form the quadratic equation which has the roots p – 2 and k + 1. [3]

2.

Diagram shows a curve of a quadratic equation f(x) = -x2

+ hx - 11. The curve has the maximum point atQ(-3, k) and intersects the f(x) – axis at point P.

a) State the coordinates of point P. [1] b) By using the method of completing the square, find the values of k and h. [4]c) Determine the range of values of x, if f(x) > -7. [3]

3. Solve the simultaneous equations and . [5]

4. Solve the simultaneous equations . [5]5. Table shows the prices of four ingredients, E, F, G and H, used in making a particular kind of biscuit.

a) The index number of ingredient H in the year 2011 based on the year 2010 is 90. Calculate the valueof c. [2]

b) The index number of ingredient F in the year 2011 based on the year 2010 is 130. The price per kg ofingredient F in the year 2011 is RM 3 more than its corresponding price in the year 2010. Calculatethe values of a and b. [3]

c) The composite index for the cost of making the biscuit in the year 2011 based on the year 2010 is114.2. Calculatei) The price of the biscuit in the year 2010 if its corresponding price in the year 2011 is RM

1.75. [2]ii) The value of n if the amount of ingredients E, F, G and H used are in the ratio 3: 5 : n : 6. [3]

form 5 addmath testa

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