Practice questions 14.5
1. Simplify the following. (i)
( 5 a2 + 6a) ÷ a (ii) ( 10 x 2 x2 − 4x) ÷ 2x
2. Simplify the following. (i)
________ x + 2
+ 5x + 6 (ii) x2
__________ x − 2
− 10x + 16
3. Simplify the following. (i) m2
_________ m + 1
+ 3m + 2 (ii) 2 x2
___________ x + 3
+ 14x + 24
4. Divide the quadratic expression (x2 by the linear expression (x + 5 )
5. Divide (m2 6. Divide ( 2 x2 7. Divide (n2 8. Divide ( x2 9. Divide ( 4y2
− 9m − 10 ) by (m + 1 ) − 7x − 15 ) by (x − 5 ) − 3n − 10 ) by (n − 5 ) + 10x + 16 ) by (x + 8 ) − 25 ) by ( 6y2
________ 16x − 12
− 15x (ii)
__________ n2
n2 + 8n + 7 + 11n + 28
________ a + 1
+ 5a + 4 + 2x − 15 ) (iii) 2 n2
___________ n − 8
− 22n + 48
(iii) ( 18 y2 (iv) ( 16 y2
(iii) x2 + 6y) ÷ 6y − 32y) ÷ 16y
________ x + 4
+ x − 12
12. The width of a rectangle is equal to (area) ÷ (length). The area of a rectangular football fi eld is t2
+ 17t − 18 and its width
is t − 1 . Find the length of the football fi eld, in terms of t.
13. The expression 3x² + 10x + 8 represents the number of people who go on a camping trip.
Each tent can hold x + 2 people. Find an expression, in terms of x , for the number of tents the group needs to bring.
14. Steve starts reading a new book. The book has 5x² + 12x + 7 pages and he reads x + 1 pages each night.
Find an expression, in terms of x , for how many nights it will take him to fi nish the book.
15. 15x² + 2x − 8 children are waiting to get on a ride at an amusement park.
Each carriage holds 3x − 2 people. Find an expression, in terms of x , for the number of carriages the children will fi ll.
− 11y − 10 )
10. By factorising, simplify the following. (i) 20 x2
(iii) a2 (iv) y2
________ a2
− 5a + 4 + 3a − 4
__________ y2
+ 13y + 36 + 9y + 20
11. By factorising, simplify the following. (i) a2
(ii) x2
__________ x2
− 14x + 48 − 13x + 42
(iii) n2 (iv) p2
__________ n2
− 13n + 40 − 11n + 30
________ p2
+ 8p + 7 + 3p + 2
14.6 Solving quadratic equations by graphing and factorising
Solving quadratic equations by graphing Graph the quadratic function.
1 2
Identify the values for x where the graph crosses the x -axis. These are the solutions, or roots, of the function (i.e. the values of x where y = 0 ).
By the end of this section you should be able to: ● solve quadratic equations by graphing ● solve quadratic equations by factorising
Section B Advancing mathematical ideas
239
14 Working with non-linear equations – quadratics
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