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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
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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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