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Surds Homework

The document contains a series of mathematical problems and exercises covering topics such as quadratic inequalities, coordinate geometry, and trigonometry. It includes tasks like finding values of variables, completing the square, expanding expressions, and determining coordinates of points and midpoints. The exercises are designed for revision and practice, requiring the use of various mathematical concepts and techniques.

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9 views2 pages

Surds Homework

The document contains a series of mathematical problems and exercises covering topics such as quadratic inequalities, coordinate geometry, and trigonometry. It includes tasks like finding values of variables, completing the square, expanding expressions, and determining coordinates of points and midpoints. The exercises are designed for revision and practice, requiring the use of various mathematical concepts and techniques.

Uploaded by

kefun.aw
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Revision mostly

Easy stuff for you (Show all your workings on a foolscap). You can use the empty space to do ur work as well.

1. Find the values of a and b such that the solutions of x 2+ ax−b> 0 is satisfied by x ←2
or x >5 (Hint: You’ll need to draw the graph of the quadratic equation then determine
the equation)
2. By completing the square, show that 2 x 2−4 x +3 is always positive.
3. Coordinate Geometry Revision:

4. Find the values of x & y that will satisfy the following equations:
(Hint: Use your laws of indices)

5. Find the values of n for which 9 x 2+ 8 n x+2 n2 >8 for all real values of

x
6. Expand ¿ . Hence, explain why the curve y=(x +3)( x 2−3 x +6) is always positive for
x >−3
7. Three of the vertices of a parallelogram ABCD are A(-3,1), B(4,9) and C(11,-3). Find the
midpoint of the diagonal AC, as well as the coordinates of the fourth vertex D
8. Three of the vertices of a rhombus PQRS are P(1,-2), R(5,0) and Q(7,4). Find the
coordinates of the fourth vertex S.
9. Given that the line x+2y = 5 meets the curve 5 x 2+ 4 y 2=29−12 x at points A and B,
find the coordinates of the midpoint of AB.
10. The coordinates of three points are A(-1,-6), B(3,-12) and C(k,6). Find the value of k if
a.I) AB is perpendicular to AC
b.II) A, B and C are collinear
11. The coordinates of 3 points are A(-1,-3), B(2,3) and C(6,k). If AB is perpendicular to BC,
find
a.I) The value of k
b.II)The gradient of AC
c.III) The acute angle that AC makes with the x-axis
12. Find the equation of the perpendicular bisector of the line segment joining C(5,7) and D
(-7,1)
13. For the following circle, find the coordinates of the centre as well as its radius:
¿

14. For the following circles, express its equation in standard form:
a. Centre: (-2,3), Radius 4
b. Centre (4,-1), Circle passes through (-2,0)
15. A diameter of a circle has its end points at A(0,-1) and B(2,3). Find the equation of the
circle.
16. (Trigo Revision). Without using a calculator, find the exact value of each of the following:
π
cos
sin 30 cos 60 4
a. b.
cos 45−tan 45 π π
+ tan 2
tan
4 6
b.

−4 1
17. Given that A and B are angles in the same quadrant such that cos A= and tan B=
5 3
, find the value of each of the following without a calculator:
a. sin A b. tan A c. sin B d.
sec B

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