forming equations (algebra)1.docx

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Mathematics Forming Equations (algebra) 2010

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1. In a set of three numbers,

the first is a positive integer,

the second is more than the first

and the third is the square of the seconds.

(a) The first number in the set is .

Write the second and third numbers in terms of .

(b) The sum of the three numbers is .

(i) Write down an equation in .

(ii) Show that your equation simplifies to .

(iii) Solve the equation .

(iv) Write down the three numbers.

2.

The diagram shows two rectangles and .

( ) cm, ( ) cm, ( ) cm and cm.

(a) For one value of , the area of rectangle is more than the area of

rectangle .

(i) Show that .

(ii) Factorise .

(iii) Solve the equation .(iv) Calculate the size of angle .

( ) cm

( ) cm ( ) cm

cm

NOT TO

SCALE

C D

A B

S R

P Q




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(a) When the area of triangle is cm.

(i) Show that .

(ii) Solve the equation .

(iii) Write down the length of .

(b) When tan

, find the value of .

(c) When the length of is cm,

(i) Show that ,

(ii) Solve the equation ,

(Show your working and give your answers correct to decimal places.)

(iii) Calculate the perimeter of triangle .

3. Three positive integers are ( ), and ( ).

When they are multiplied together the answer is times their sum.

(a) (i) Write down an equation in .

(ii) Show that your equation simplifies to .

(b) Factorise completely .

(c) Find three positive integers.

NOT TO

SCALE




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4.

In triangle , the line is perpendicular to .

( ) cm, ( ) cm and the height ( ) cm.

(a) The area of triangle is cm.

(i) Show that .

(ii) Solve the equation .

(iii) Calculate the length of .

5. A rectangle is ( x + 3) cm long and y cm wide.

The perimeter of the rectangle is 20 cm.

(a) Show that y = 7 – x

(b) The area of the rectangle is 19 cm2. Show that

x 2 – 4 x – 2 = 0

(c) Solve the equation x 2 – 4 x – 2 = 0. Give your answers to 2 decimal places.

(d) Write down the length and the width of the rectangle.

NOT TO

SCALE




4

6. (a) (i) The cost of a book is $ x .

Write down an expression in terms of x for the number of these books which are bought

for $40.

(ii) The cost of each book is increased by $2.

The number of books which are bought for $40 is now one less than before.

Write down an equation in x and show that it simplifies to x 2

+ 2 x – 80 = 0

(iii) Solve the equation x 2

+ 2 x – 80 = 0

(iv) Find the original cost of one book.

(b) Magazines cost $m each and newspapers cost $n each.One magazine costs $2.55 more than one newspaper.

The cost of two magazines is the same as the cost of five newspapers.

(i) Write down two equations in m and n to show this information.

(ii) Find the values of m and n.




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forming equations (algebra)1.docx

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