C O R E

SUBJECT : MATHEMATICS

CLASS / PROGRAMME : Grade 10 / General

DAY / DATE : Saturday, December, 1 2007

TIME : 07.00 - 09.00

Directions:

1. This test consist of three parts, and you must answer all of the questions.

2. The score is given at the end of each question.

3. The total score for part I is 45. Both part II and III are 40.

Part I

1.

ScoreSimplify the following form:

[2]a. in the form 2n

[2]b.

solution:

answer

a.

b.

[2]Simplify the following form:

a.

[2]b. =

solution:

answer

a.

b.

Rationalize the denominator, and write in the simplest form.

[2]

[2]a.

b.

solution:

answer

a.

b

[2]Simplify the following form:

log 250 – log 2 + log 8 = . . .

[4]= . . . .

solution:

answer

a.

b.

factorize the following form:

[1]

[2]

[3]6x – 3x2

x 2 + 2x – 3

6x2 + x – 12

solution:

answer

a.

b.

c.

Change the following to complete square form

[2]

[3]

x2 + 2x + 10

2x2 – 6x - 13

solution:

answer

a.

b.

[2]

[3]

[4]

If p and q are the roats of quadratics equation x2 + x + 1 = 0, find values of :

p + q and pq

p2 + q2

solution:

answer

a.

b.

c.

[2]

[4]

Given quadratic function f(x) = 2x2 +x – 3

f(1) = . . .

if f(x) = 9, find the possible value of x.

solution:

answer

a.

b.

Part II.

Solve the equation [ 10]

Solution

Answer

The equation x2 – mx + 9 = 0 has two real roots. What can you deduce about the value of m? [10]

Solution

Answer

solve the inequalities [10]

Solution

Answer

Find the coordinates of the points of intersection between y = x2 – x – 6 and y – x + 3 = 0 [10]

Solution

Answer

Part III

If and , express in the form a and b! [10]

Solution

Answer

Point P is the intersection of two roads which cross at right angles; one road from north to south, the other from east to west. Find the least distance a part of two motorbikes A and B which are initially approaching P on different roads. A is 120 meter from P traveling at 20 m/s and B is 80 from P traveling at 10 m/s. [10]

Solution

a. Express the distance A and P as function of time, t! [1]

b. Express the distance B and P as function of time, t! [1]

c. Express the distance A and B as function of time, t! [1]

d. Find the least distance apart of two motorbike, (hint: find the minimum valve of function! [5]

Answer

A curve y = ax² + bx + c crosses the x-axis at (- 4, 0) and ( 3, 0), and also passes through the point (2, 6).

a. find the value of a,b and c [4]

b. find the vertex [6]

Solution

Answer

Prove that quadratics function y = x2 + 4x + 6 and y = 3 – 2x – x2 do not meet each other.

a. by calculating [4]

b. by sketch both of the graphs at the same diagrams. [6]

Solution

a).

Answer a):

b).

-= GOOD LUCK =-

SUBJECT : MATHEMATICS

CLASS / PROGRAMME : Grade 10 / General

DAY / DATE : Saturday, December, 1 2007

TIME : 07.00 - 09.00

Directions:

1. This test consist of three parts, and you must answer all of the questions.

2. The score is given at the end of each question.

3. The total score for part I is 45. Both part II and III are 40.

Part I

1.

ScoreSimplify the following form:

[2]a. in the form 2n

[2]b.

solution:

answer

a.

b.

[2]Simplify the following form:

a.

[2]b. =

solution:

answer

a.

b.

Rationalize the denominator, and write in the simplest form.

[2]

[2]a.

b.

solution:

answer

a.

b

[2]Simplify the following form:

log 250 – log 2 + log 8 = . . .

[4]= . . . .

solution:

answer

a.

b.

factorize the following form:

[1]

[2]

[3]6x – 3x2

x 2 + 2x – 3

6x2 + x – 12

solution:

answer

a.

b.

c.

Change the following to complete square form

[2]

[3]

x2 + 2x + 10

2x2 – 6x - 13

solution:

answer

a.

b.

[2]

[3]

[4]

If p and q are the roats of quadratics equation x2 + x + 1 = 0, find values of :

p + q and pq

p2 + q2

solution:

answer

a.

b.

c.

[2]

[4]

Given quadratic function f(x) = 2x2 +x – 3

f(1) = . . .

if f(x) = 9, find the possible value of x.

solution:

answer

a.

b.

Part II.

Solve the equation [ 10]

Solution

Answer

The equation x2 – mx + 9 = 0 has two real roots. What can you deduce about the value of m? [10]

Solution

Answer

solve the inequalities [10]

Solution

Answer

Find the coordinates of the points of intersection between y = x2 – x – 6 and y – x + 3 = 0 [10]

Solution

Answer

Part III

If and , express in the form a and b! [10]

Solution

Answer

Point P is the intersection of two roads which cross at right angles; one road from north to south, the other from east to west. Find the least distance a part of two motorbikes A and B which are initially approaching P on different roads. A is 120 meter from P traveling at 20 m/s and B is 80 from P traveling at 10 m/s. [10]

Solution

a. Express the distance A and P as function of time, t! [1]

b. Express the distance B and P as function of time, t! [1]

c. Express the distance A and B as function of time, t! [1]

d. Find the least distance apart of two motorbike, (hint: find the minimum valve of function! [5]

Answer

A curve y = ax² + bx + c crosses the x-axis at (- 4, 0) and ( 3, 0), and also passes through the point (2, 6).

a. find the value of a,b and c [4]

b. find the vertex [6]

Solution

Answer

Prove that quadratics function y = x2 + 4x + 6 and y = 3 – 2x – x2 do not meet each other.

a. by calculating [4]

b. by sketch both of the graphs at the same diagrams. [6]

Solution

a).

Answer a):

b).

-= GOOD LUCK =-

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