Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

Maths Questions & Answers for Secondary School
1
...

3
...


Find the roots of the quadratic equation 2x^2 + 5x - 3 = 0
...

Find the value of cos(45°) - sin(60°)
...
The profit margin on product
A is 20% and on product B it is 15%
...
A car travels a distance of 300 km in 5 hours
...

6
...

7
...

8
...
Find the acceleration of the
particle at t = 2s
...
A straight line passes through the point (1, 2) and has a slope of -2
...

10
...

11
...

12
...
The cost of
producing a unit of A is Rs
...
75
...
30,000, how many units of each type can
be produced?
13
...

14
...

15
...

16
...

17
...
meters
...
Find the width of the path
...
If the coordinates of three points A, B, and C are (1, 2), (3, 4), and (5, k)
respectively, find the value of k if the points are collinear
...
To find the roots of 2x^2 + 5x - 3 = 0, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 2, b = 5, and c = -3
...
Using the properties of logarithms, we can simplify the expression as:
log(4x) + log(5) - log(x/3)
= log(4x*5/(x/3))
= log(60)
3
...
Substituting
these values, we get:
cos(45°) - sin(60°) = (√2/2) - (√3/2)
= (√6 - √3) / 2
4
...
Then, the profit
margins for product A and B can be expressed as 0
...
6x and 0
...
75x respectively
...
6x +
0
...
18
...
35x / 8x = 0
...
6x / 3x) * 100 = 20%
...
We can use the formula distance = speed * time to find the time taken to
cover each part of the distance
...
75 hours
...
5 hours
...
75 + 2
...
25 hours
...
25
= 312
...
The derivative of f(x) = x^2 + 3x - 2 can be found using the power rule:
f'(x) = 2x + 3
7
...

8
...
The equation of a line with slope m passing through point (x1, y1) is given by
y - y1 = m(x - x1)
...
Therefore, the equation of the line is y
= -2x + 4
...
Using the formula for the sum of angles in a geometric series, we have:
sin(180°/7) + sin(360°/7) + sin(540°/7)
= sin(180°/7) + sin(180°/7 + 180°/7) + sin(180°/7 + 360°/7)
= sin(180°/7) + sin(360°/7 - 180°/7) + sin(540°/7 - 360°/7)
= sin(180°/7) + sin(180°/7) - sin(180°/7) = sin(180°/7)
11
...
The discriminant is given by b^2 - 4ac, where a = 2, b = -a, and c = 1
...

12
...
We have the following constraints:
x ≥ 200 (produce at least 200 units of A)
y ≥ 300 (produce at least 300 units of B)
50x + 75y ≤ 30,000 (budget constraint)
To maximize the number of units produced, we want to produce as much of A and B
as possible subject to the constraints
...
The feasible
region is a polygon bounded by the lines x = 200, y = 300, and 50x + 75y = 30,000
...

To maximize x + y, we evaluate the objective function at each vertex and choose the
one with the largest value:
(200, 300): x + y = 500
(200, 400): x + y = 600
(320, 300): x + y = 620
450, 250): x + y = 700

Therefore, the manufacturer should produce 320 units of A and 300 units of B to
maximize the number of units produced subject to the constraints
...
Find the inverse of the matrix A = [3 2; 1 4]:
The inverse of a 2x2 matrix A = [a b; c d] is given by (1/det(A)) * [d -b; -c a], where
det(A) is the determinant of A
...

Therefore, the inverse of A is (1/10) * [4 -2; -1 3]
...
If sin(x+20) = cos(x-10), find the value of x:
Using the identity sin(a+b) = sin(a)cos(b) + cos(a)sin(b), we can rewrite the given
equation as sin(x)cos(20) + cos(x)sin(20) = cos(x)cos(10) + sin(x)sin(10)
...
9619 (approx)
...
9619 is approximately -42
...
738 radians)
...
738 = -20
...
362 radians)
...
If the sum of the first n terms of an arithmetic progression is 5n^2 - 3n, find the
10th term:
The sum of the first n terms of an arithmetic progression is given by the formula Sn =
n/2[2a + (n-1)d], where a is the first term and d is the common difference
...

Subtracting S9 from S10, we get the 10th term (which is the difference between the
sums of the first 10 terms and the first 9 terms):
T10 = S10 - S9 = (10/2)[2a + (10-1)d] - (9/2)[2a + (9-1)d]
Simplifying this, we get T10 = 92 - 6d
...
Using the formula for S9
and S10, we can set up two equations in two variables:
S9 = 9/2[2a + (9-1)d] = 5(9)^2 - 3(9)
S10 = 10/2[2a + (10-1)d] = 5(10)^2 - 3(10)
Simplifying these equations, we get:
9a + 36d = 360
10a + 45d = 515
Solving for a and d, we get a = 5 and d = 4
...

Therefore, the 10th term of the arithmetic progression is 68
...
Let the side of the square park be "a"
...
meters,
so a = 12 meters
...
Then, the side of the new square formed by the
outer edge of the path is (a + 2x) meters
...


17
...

The slope of the line passing through points (1, 2) and (3, 4) is:
m = (y2 - y1) / (x2 - x1) = (4 - 2) / (3 - 1) = 1
So the equation of the line passing through (1, 2) and (3, 4) is y = x + 1
...




---