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DT Math

The document contains a series of mathematical problems including simplification of algebraic expressions, expansion and simplification of polynomials, evaluation using special products, and solving equations. It also includes a geometry problem involving the area of a square picture and its frame. The problems are numbered and cover various algebraic concepts and techniques.

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Yolanda Effieta
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23 views3 pages

DT Math

The document contains a series of mathematical problems including simplification of algebraic expressions, expansion and simplification of polynomials, evaluation using special products, and solving equations. It also includes a geometry problem involving the area of a square picture and its frame. The problems are numbered and cover various algebraic concepts and techniques.

Uploaded by

Yolanda Effieta
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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1.

2.

3.

4.

5.
6. Simplify fully:
2
4 k −1
a) 3 2
6 k −3 k

3 c
4 c −100
b)
4 c+20

2
2 x −32
c) 2
x +9 x +20

2
4 y −9
d) 2
2 y −11 y+ 12

2
3 x +1 9 x+ 6
e) 2
9 x +6 x +1

7.

8.

9. Expand and simplify


2 2
5 p −( 2 p−q ) + ( p +2 q ) ( p−2 q ).

10. Evaluate the following using special products of algebraic expressions.


a) 49. 52
b) 9 5 ×10 5

11. Given that ( 3 x−2 y )2=49 and 9 x 2+ 4 y 2 =85. Find the value of:
a) xy
b) ( 3 x+ 2 y )2
( )
2
2 1 1
12. If x + 2
=12 and x >0, find the value of x− .
x x

13. In the diagram, a square picture PQRS of side 6x cm is mounted on a square frame
ABCD, leaving a uniform border of with 2 cm.

a) Express the area of ABCD as a quadratic expression in x.


b) If the area of the border is 400 cm2, find the area of the picture.

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