FISA DE LUCRU _formule de calcul prescurtat
FISA DE LUCRU _formule de calcul prescurtat
FISA DE LUCRU _formule de calcul prescurtat
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
<strong>FISA</strong> <strong>DE</strong> <strong>LUCRU</strong><br />
(<strong>formule</strong> <strong>de</strong> <strong>calcul</strong> <strong>prescurtat</strong>)<br />
1. Efectuati:<br />
a) (x + 2y) 2 ; (x – 3y) 2 ; (2x + 5y) 2 ;<br />
(2x – 5y) 2<br />
b) (x – 2y)(2y + x) ; ( 2x + 3y)(<br />
3y<br />
− 2x)<br />
2. Calculati, folosind <strong>formule</strong>le <strong>de</strong> <strong>calcul</strong> <strong>prescurtat</strong>:<br />
a) 13• 15 b) 14• 16<br />
3. Calculati:<br />
a) ( +<br />
b) (<br />
2<br />
4 9)<br />
+ ( 2 −<br />
2<br />
3<br />
−<br />
3<br />
)<br />
2<br />
2<br />
+ (<br />
3)<br />
3<br />
2<br />
2<br />
−<br />
2<br />
)<br />
3<br />
4. Fie numerele:<br />
a) x=(<br />
2<br />
2<br />
3 + 2)<br />
+ (<br />
4<br />
2<br />
3 − 2)<br />
si y=2• 37<br />
3<br />
b) x= ( 3 + 3 ) • 30 + ( 9 + 7 − 4)<br />
si y=750<br />
2<br />
Calculati in fiecare caz media aritmetica si media geometrica a<br />
numerelor x si y.<br />
5. Efectuati:<br />
a) (2 3 + 4 5)(<br />
4 5 − 2 3)<br />
b) 14 − 6 • 14 + 6<br />
6. Daca a=<br />
<strong>calcul</strong>ate:<br />
2 3 5,<br />
= 5 + 6 7<br />
(a 2 – 2ab + b 2 ) c<br />
2<br />
− b si c=( 2 7 • 14 − 14 − 14)<br />
1<br />
• ,<br />
7. Completati spatiile libere corespunzator <strong>formule</strong>lor <strong>de</strong> <strong>calcul</strong><br />
<strong>prescurtat</strong> invatate:<br />
a) (x + ……..) 2 = ………+ 4xy + ………<br />
2<br />
b) (…….. - 2 3 ) = 2 - ……. + ………<br />
c) 14x 2 – 6 = ( 14 x<br />
− ........)( ........ + .........)
8. Calculati: (2a – 3) 2 – (3a + 4) 2 + (4a – 5)(4a + 5)<br />
1<br />
=<br />
w<br />
9. Daca w + 14,<br />
<strong>calcul</strong>ate w 2 1<br />
+ 2<br />
w si w4 + 4<br />
w<br />
10. Determinati numerele reale m si n daca:<br />
m 2 + n 2 – 8m +6n + 25 = 0<br />
11. Sa se arate ca: a 2 + b 2 – 4a + 4b + 14 ≥ 0, ∀ x; y ∈ R<br />
12. Sa se <strong>de</strong>termine minimul expresiei: x 2 – 14x + 51, ∀ x ∈ R<br />
13. Sa se <strong>de</strong>termine maximul expresiei: - y 2 – 12y – 35, ∀ y ∈ R<br />
14. Sa se arate daca: 196 n + 4• 14 n + 4 este patrat perfect.<br />
2<br />
1