Integers

Answer all of the following.

Objective.

1. Which of the following numbers are integers?

(a) -3.5 (b) -7 (c) 1.55 (d) -2 2/5

2. -15, x, -9, -3, 0

(a) -18 (b) -14 (c) -12 (d) -10

3. Ali is on level x in a lift. When he goes up 2 levels he will be in level 6. What is the value of x?

(a) 2 (b) 4 (c) 8 (d) 12

4. An internet cafe has 25 customer. 2 minuters later another 7 customers enter the cafe. Then 20 minuters later 12 customer exit the cafe. How many of the customers are left in the cafe?

(a) 6 (b) 20 (c) 30 (d) 44

5. The temperature of Town A is -2 degree celcius at 12 midnight, 55 degree celcius at 12 noon and 30 degree celcius at 6.00 in the evening. What is the difference between the coldest and the warmest temperature of Town A (in degree celcius) ?

(a) 28 (b) 53 (c) 57 (d) 83

Subjective

1. Find the value of

(a) 2-7

(b) 12-30+2

2. Calculate

(a) -18+7-10

(b) 25-48+15

3. Find the value of

(a) 1128-1015+22

(b) -218+50-12

4. Calculate

(a) 5(20-27)+(-12)

(b) -3(20-16)-(7-11)

5. Dave is working at a basement 2 of a building. Then he goes up in a lift at level 20. What is the total levels that he pass through ?

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Partial Fractions

Answer all the following. Show all working.


1. express 3/((x+1)(x-2)) in partial fractions


2. Express (2x+1)/((2x-1)(x+2))


3 Express (3x-1)/((2x^2+1)(x-2))

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Algebraic Expressions

Try the following questions

1. Simplify

(a) x + 3x + 2x

(b) (a+b)+(2a-b)

(c) x(x+y)

(d) (5x+2y)-(3x-7y)

(e) 2(2a+b)+3b

2. Simplify the following

(a) (x+1)(x+1)

(b) (x+4)(x-2)

(c) (x^2-2xy)/x

(d) (4x^2y-3xy)/(xy)

(e) Ali has x pen and y pencil. If the price of pen and pencil are RM2 and RM1 respectively, what is the total price of pen and pencil that Ali has?

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Modulus

Modulus of x is written as |x|. It is defined as x if x > 0 or -x if x < 0.
If |x| = b then x = b or x=-b for any real number.
If |x| < b then -b < x < b
If |x| > b then x <-b or x >b

Try the following question.

1. Find the value of x for the following modulus equation.

(a) |x| =3

(b) |3x| = 12

2. Solve the following inequalities and express your answer in an interval notation.

(a) |x| < 5

(b) |x| > 2

(c) |x-1| > 6

(d) |2x+3| > 2

(e) |2-x| > 7

Linear Equation

Solve the following linear equation

1. x + 1 = 5

2. 2x - 3 = 8

3. x/2 = 7

4. (x-5)/2 = 2

5. (2x-7)/3 = 5

6. 5-2x = 5x - 9

7. (x - 2)/5 = 2x

8. p - 7 = 3p + 3

9. 100m = 50m -20

10. (3p+1)/3 = 2p-1

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Polynomials

Answer all of the following.

1. A polynomial P(x)= 2x³ +3x²-2x-3

(a) Find P(2), P(-1)

(b) Determine if x-1 is a factor.


2. Given that a polynomial P(x) = x³ +2x² -7x+4.

(a) If x+4 is a factor of P(x), find the other two factors,

(b) Find the set of values of x for which P(x)>0


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Statistics I

Answer all of the following.

Objective

1. Which of the following data is collected by measuring?

A. Numbers of cars passing at a certain bus stop.
B. Weight of a fish caught by a fisherman
C. Number of books sold in a bookstore.
D. Number of students enrolled in a certain school.

4, 4, 4, 5, 6, 7, 7, 8, 9,10

2. The above numbers are scores made by 10 students in a certain game. What is the percentage of sudents who scored more than 5 ?

A. 30%
B. 60%
C. 70%
D. 100%

Subjective

1. 1,2, 3,3, 4,4, 5, 5, 6, 6, 6, 7, 7, 8, 9

The data above shows the size of shoes in a group 15 girls.

(a) Find the mode and median for the above data.

(b) Calculate the percentage of the size that is more than 4.


2. 35, 45, 55,60,70,75, 80, 90

The data above shows the marks for a certain math test for 8 students.

(a) Find the mean marks for the test.

(b) If the passing mark is 50, calculate the percentage of the students who pass the test.


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