S-4 Math - Ans.fyi 參考答案

S-4 Math

2012-08-22 3:11 am

Please to slove the following questions:

1. The product of two consecutive positive even integers is 48.
Find the two integers.

2. Roger is 42 years younger than his father. 2 years later, the square of his
age is equal to his father's age. Find the age of Roger now.

3.If the graph of 2x^2 - 8x +k = 0 has no x-intercepts, find the smallest
integral value of k.

4.It is given that 5 and k are the roots of a quadratic equation in x,
where k is a constant.
a) If the sum and product of the roots are equal, find the value of k.
b) Hence, write the quadratic equation in general form.

5.Straight lines L1: 2x - 3y + q = 0 and L2: px + 15y - 1 = 0 are parallel.
a) Find the value of p
b) Find the value of q if the x-intercept of L1, is equal to the y-intercept
of L2

6. Straight lines L1: 3x - 4y + 7 = 0 and L2 are parallel. If L2 passes
through (-1 , -1), find the equation of L2.

7.If the sum of two consecutive even numbers is not greater than 40,
what is the largest possible value of the larger number?

8.There are 20 multiple-choice questions in a quiz. 5 marks are given to
each correct answer, 2 marks are deducted for each wrog answer
and 1 mark is deducted for each unattempted question. Doris finished
the quiz with two unattempted questions. If she obtains more than 60 marks
in the quiz, what is the minimum number of questions she has answered
correctly?

9.Consider the function f(x) = (x-3)(x+1) - (x-2)(x+2)
a) Determine the type of function f(x)
b) Find the x-intercept(s) and y-intercept of the graph of y=f(x)

10.There are 5 cards numbered with the first five multiples of 3. A card
is picked at random from these cards. Find the probabjility that the
number on the card chosen is

a. an even number
b. a prime number
c. a factor of 12

回答 (1)

用戶26240

2012-08-22 3:59 am

✔ 最佳答案

1.
Let the two integers be n and n+ 2.

n(n + 2) = 48
n² + 2n - 48 = 0
(n + 8)(n - 6) = 0
n = -8(rejected) or n = 6

The two integers are 6 and 8.

=====
2.
Let r be the age of Roger now, and f be that of his father.

f - r = 42 ...... [1]
(r + 2)² = f + 2 ...... [2]

From [1] :
f = r + 42 ...... [3]

Put [3] into [2] :
(r + 2)² = (r + 42) + 2
r² + 4r + 4 = r + 44
r² + 3r - 40 = 0
(r + 8)(r - 5) = 0
r = -8(rejected) or r = 5

Roger is 5 years old now.

=====
3.
The equation 2x² -8x + k = 0 has no real roots. Δ< 0
(-8)² - 4(2)(k) < 0
64 - 8k < 0
8k > 64
k > 8

=====
4.
(a)
5 + k = 5k
4k = 5
k = 5/4

(b)
The equation :
x² - [5 + (5/4)]x + [5 * (5/4)] = 0
x² - (25/4)x + (25/4) = 0
4x² - 25x + 25 = 0

=====
5.
(a)
Slope of L1 = Slope of L2
-2/(-3) = -p/15
3p = -30
p = -10

(b)
Put y = 0 into the equation of L1 :
2x - 0 + q = 0
x = -q/2
The x-intercept of L1 = -q/2

Put x = 0 into the equation of L2 :
0 + 15y - 1 = 0
y = 1/15
The y-intercept of L2 = 1/15

-q/2 = 1/15
15q = -2
q = -2/15

=====
6.
Slope of L2
= Slope of L1
= -3/(-4)
= 3/4

The equation of L2 :
(y + 1)/(x + 1) = 3/4
4y + 4 = 3x + 3
3x - 4y - 1 = 0

=====
7.
Let the larger number be n.
Then, the smaller number = n - 2

n + (n - 2) ≤ 40
2n - 2 ≤ 40
2n ≤ 42
n ≤ 21

The largest possible value of thelarger number is 20.

=====
8.
Let n be the number of correctly answered questions.
Then, the number of wrongly answered questions = 20 - n - 2 = 18 - n

5n - 2(18 - n) - 1(2) > 60
5n - 36 + 2n - 2 > 60
7n > 98
n > 14

The minimum number of correctlyanswered questions is 15.

=====
9.
(a)
f(x)
= (x - 3)(x + 1) - (x - 2)(x + 2)
= (x² -2x - 3) - (x² - 4)
= x² -2x - 3 - x² + 4
= -2x + 1

It is a linear function.

(b)
y = -2x + 1
When x = 0, y = 1
When y = 0, x = 1/2

The x-intercept is 1/2, and the y-intercept is 1.

=====
10.
The five cards are : 3, 6, 9, 12, 15

(a)
P(even number)
= P(6 or 12)
= 2/5

(b)
P(prime number)
= P(3)
= 1/5

(c)
P(factor of 12)
= P(3, 6 or 12)
= 3/5

參考: 土扁

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