Sura ya 6 Mazoezi Mapitio
- Page ID
- 177836
Sura ya 6 Mazoezi Mapitio
Kuongeza na Ondoa Polynomials
Kutambua Polynomials, Monomials, Binomials na Trinomials
Katika mazoezi yafuatayo, onyesha kama kila moja ya polynomials zifuatazo ni monomial, binomial, trinomial, au polynomial nyingine.
- \(11 c^{4}-23 c^{2}+1\)
- \(9 p^{3}+6 p^{2}-p-5\)
- \(\frac{3}{7} x+\frac{5}{14}\)
- 10
- 2y-12
- \(a^{2}-b^{2}\)
- 24\(d^{3}\)
- \(x^{2}+8 x-10\)
- \(m^{2} n^{2}-2 m n+6\)
- \(7 y^{3}+y^{2}-2 y-4\)
- Jibu
-
- binomial
- monomial
- ya trinomial
- ya trinomial
- nyingine polynomial
Kuamua Shahada ya Polynomials
Katika mazoezi yafuatayo, tambua kiwango cha kila polynomial.
- \(3 x^{2}+9 x+10\)
- 14\(a^{2} b c\)
- 6y+1
- \(n^{3}-4 n^{2}+2 n-8\)
- 19-19
- \(5 p^{3}-8 p^{2}+10 p-4\)
- \(-20 q^{4}\)
- \(x^{2}+6 x+12\)
- \(23 r^{2} s^{2}-4 r s+5\)
- 100
- Jibu
-
- 3
- 4
- 2
- 4
- 0
Kuongeza na Ondoa Monomials
Katika mazoezi yafuatayo, ongeza au uondoe monomials.
\(5 y^{3}+8 y^{3}\)
\(-14 k+19 k\)
- Jibu
-
5k
12q (-6q)
-9c—18c
- Jibu
-
-27c
12x-4y-9x
\(3 m^{2}+7 n^{2}-3 m^{2}\)
- Jibu
-
7\(n^{2}\)
\(6 x^{2} y-4 x+8 x y^{2}\)
13a+b
- Jibu
-
13a+b
Kuongeza na Ondoa Polynomials
Katika mazoezi yafuatayo, ongeza au uondoe polynomials.
\(\left(5 x^{2}+12 x+1\right)+\left(6 x^{2}-8 x+3\right)\)
\(\left(9 p^{2}-5 p+3\right)+\left(4 p^{2}-4\right)\)
- Jibu
-
\(13 p^{2}-5 p-1\)
\(\left(10 m^{2}-8 m-1\right)-\left(5 m^{2}+m-2\right)\)
\(\left(7 y^{2}-8 y\right)-(y-4)\)
- Jibu
-
\(7 y^{2}-9 y+4\)
Ondoa
\(\left(3 s^{2}+10\right)\) kutoka\(\left(15 s^{2}-2 s+8\right)\)
Kupata jumla ya\(\left(a^{2}+6 a+9\right)\) na\(\left(5 a^{3}-7\right)\)
- Jibu
-
\(5 a^{3}+a^{2}+6 a+2\)
Tathmini Polynomial kwa Thamani iliyotolewa ya Variable
Katika mazoezi yafuatayo, tathmini kila polynomial kwa thamani iliyotolewa.
Tathmini\(3 y^{2}-y+1\) wakati:
- y=5
- y=-1
- y=0
Tathmini 10-12x wakati:
- x=3
- x=0
- x=-1
- Jibu
-
- -26
- 10
- 22
Randee matone jiwe mbali 200 mguu juu mwamba katika bahari. Polynomial\(-16 t^{2}+200\) inatoa urefu wa jiwe t sekunde baada ya kushuka kutoka mwamba. Pata urefu baada ya sekunde t=3.
Mtengenezaji wa wasemaji wa sauti ya stereo amegundua kwamba mapato yaliyopatikana kutokana na kuuza wasemaji kwa gharama ya dola p kila mmoja hutolewa na polynomial\(-4 p^{2}+460 p\). Kupata mapato kupokea wakati p=75 dola.
- Jibu
-
12,000
Tumia Mali ya kuzidisha ya Watazamaji
Kurahisisha Maneno na Watazamaji
Katika mazoezi yafuatayo, kurahisisha.
\(10^{4}\)
\(17^{1}\)
- Jibu
-
17
\(\left(\frac{2}{9}\right)^{2}\)
\((0.5)^{3}\)
- Jibu
-
0.125
\((-2)^{6}\)
\(-2^{6}\)
- Jibu
-
-64
Kurahisisha Maneno Kutumia Mali ya Bidhaa kwa Watazamaji
Katika mazoezi yafuatayo, kurahisisha kila kujieleza.
\(x^{4} \cdot x^{3}\)
\(p^{15} \cdot p^{16}\)
- Jibu
-
\(p^{31}\)
\(4^{10} \cdot 4^{6}\)
8\(\cdot 8^{5}\)
- Jibu
-
\(8^{6}\)
\(n \cdot n^{2} \cdot n^{4}\)
\(y^{c} \cdot y^{3}\)
- Jibu
-
\(y^{c+3}\)
Kurahisisha Maneno Kutumia Mali ya Nguvu kwa Wasanii
Katika mazoezi yafuatayo, kurahisisha kila kujieleza.
\(\left(m^{3}\right)^{5}\)
\(\left(5^{3}\right)^{2}\)
- Jibu
-
\(5^{6}\)
\(\left(y^{4}\right)^{x}\)
\(\left(3^{r}\right)^{s}\)
- Jibu
-
\(3^{r s}\)
Kurahisisha Maneno Kutumia Bidhaa kwa Mali ya Nguvu
Katika mazoezi yafuatayo, kurahisisha kila kujieleza.
\((4 a)^{2}\)
\((-5 y)^{3}\)
- Jibu
-
\(-125 y^{3}\)
\((2 m n)^{5}\)
\((10 x y z)^{3}\)
- Jibu
-
1000\(x^{3} y^{3} z^{3}\)
Kurahisisha Maneno kwa kutumia Mali kadhaa
Katika mazoezi yafuatayo, kurahisisha kila kujieleza.
\(\left(p^{2}\right)^{5} \cdot\left(p^{3}\right)^{6}\)
\(\left(4 a^{3} b^{2}\right)^{3}\)
- Jibu
-
64\(a^{9} b^{6}\)
\((5 x)^{2}(7 x)\)
\(\left(2 q^{3}\right)^{4}(3 q)^{2}\)
- Jibu
-
48\(q^{14}\)
\(\left(\frac{1}{3} x^{2}\right)^{2}\left(\frac{1}{2} x\right)^{3}\)
\(\left(\frac{2}{5} m^{2} n\right)^{3}\)
- Jibu
-
\(\frac{8}{125} m^{6} n^{3}\)
Kuzidisha Monomials
Katika mazoezi yafuatayo 8, kuzidisha monomials.
\(\left(-15 x^{2}\right)\left(6 x^{4}\right)\)
\(\left(-9 n^{7}\right)(-16 n)\)
- Jibu
-
144\(n^{8}\)
\(\left(7 p^{5} q^{3}\right)\left(8 p q^{9}\right)\)
\(\left(\frac{5}{9} a b^{2}\right)\left(27 a b^{3}\right)\)
- Jibu
-
15\(a^{2} b^{5}\)
Kuzidisha Polynomials
Kuzidisha Polynomial na Monomial
Katika mazoezi yafuatayo, ongeze.
7 (a+9)
-4 (y+13)
- Jibu
-
-4y-52
-5 (r-1)
p (p+3)
- Jibu
-
\(p^{2}+3 p\)
-m (m+15)
-6u (2u+7)
- Jibu
-
\(-12 u^{2}-42 u\)
9\(\left(b^{2}+6 b+8\right)\)
3\(q^{2}\left(q^{2}-7 q+6\right) 3\)
- Jibu
-
\(3 q^{4}-21 q^{3}+18 q^{2}\)
\((5 z-1) z\)
\((b-4) \cdot 11\)
- Jibu
-
11b-44
Kuzidisha Binomial na Binomial
Katika mazoezi yafuatayo, kuzidisha binomials kutumia:
- Mali ya Kusambaza,
- njia ya FOIL,
- Njia ya Wima.
(x-4) (x+10)
(6y-7) (2y-5)
- Jibu
-
- \(12 y^{2}-44y+35\)
- \(12 y^{2}-44y+35\)
- \(12 y^{2}-44y+35\)
Katika mazoezi yafuatayo, kuzidisha binomials. Tumia njia yoyote.
(x+3) (x+9)
(y-4) (y-8)
- Jibu
-
\(y^{2}-12 y+32\)
(p-7) (p+4)
(q+16) (q-3)
- Jibu
-
\(q^{2}+13 q-48\)
(5m-8) (12m+1)
\(\left(u^{2}+6\right)\left(u^{2}-5\right)\)
- Jibu
-
\(u^{4}+u^{2}-30\)
(9x-y) (6x-5)
(8mn+3) (2mn-1)
- Jibu
-
\(16 m^{2} n^{2}-2 m n-3\)
Kuzidisha Trinomial na Binomial
Katika mazoezi yafuatayo, kuzidisha kutumia
- Mali ya Kusambaza,
- Njia ya Wima.
\((n+1)\left(n^{2}+5 n-2\right)\)
\((3 x-4)\left(6 x^{2}+x-10\right)\)
- Jibu
-
- \(18 x^{3}-21 x^{2}-34 x+40\)
- \(18 x^{3}-21 x^{2}-34 x+40\)
Katika mazoezi yafuatayo, ongeze. Tumia njia yoyote.
\((y-2)\left(y^{2}-8 y+9\right)\)
\((7 m+1)\left(m^{2}-10 m-3\right)\)
- Jibu
-
\(7 m^{3}-69 m^{2}-31 m-3\)
Bidhaa Maalum
Mraba Binomial Kutumia Mipangilio ya Mraba ya Binomial
Katika mazoezi yafuatayo, mraba kila binomial kwa kutumia Pattern ya Mraba ya Binomial.
\((c+11)^{2}\)
\((q-15)^{2}\)
- Jibu
-
\(q^{2}-30 q+225\)
\(\left(x+\frac{1}{3}\right)^{2}\)
\((8 u+1)^{2}\)
- Jibu
-
\(64 u^{2}+16 u+1\)
\(\left(3 n^{3}-2\right)^{2}\)
\((4 a-3 b)^{2}\)
- Jibu
-
\(16 a^{2}-24 a b+9 b^{2}\)
Kuzidisha conjugates Kutumia Bidhaa ya Conjugates Pattern
Katika mazoezi yafuatayo, kuzidisha kila jozi ya conjugates kwa kutumia Bidhaa ya Conjugates Pattern.
(s-7) (s+7)
\(\left(y+\frac{2}{5}\right)\left(y-\frac{2}{5}\right)\)
- Jibu
-
\(y^{2}-\frac{4}{25}\)
\((12 c+13)(12 c-13)\)
(6,1r) (6+r)
- Jibu
-
\(36-r^{2}\)
\(\left(u+\frac{3}{4} v\right)\left(u-\frac{3}{4} v\right)\)
\(\left(5 p^{4}-4 q^{3}\right)\left(5 p^{4}+4 q^{3}\right)\)
- Jibu
-
\(25 p^{8}-16 q^{6}\)
Tambua na Tumia Pattern maalum ya Bidhaa
Katika mazoezi yafuatayo, tafuta kila bidhaa.
\((3 m+10)^{2}\)
(6a+11) (6a-11)
- Jibu
-
\(36 a^{2}-121\)
(5x+y) (x-5y)
\(\left(c^{4}+9 d\right)^{2}\)
- Jibu
-
\(c^{8}+18 c^{4} d+81 d^{2}\)
\(\left(p^{5}+q^{5}\right)\left(p^{5}-q^{5}\right)\)
\(\left(a^{2}+4 b\right)\left(4 a-b^{2}\right)\)
- Jibu
-
\(4 a^{3}+3 a^{2} b-4 b^{3}\)
Kugawanya Monomials
Kurahisisha Maneno Kutumia Mali ya Quotient kwa Watazamaji
Katika mazoezi yafuatayo, kurahisisha.
\(\frac{u^{24}}{u^{6}}\)
\(\frac{10^{25}}{10^{5}}\)
- Jibu
-
\(10^{20}\)
\(\frac{3^{4}}{3^{6}}\)
\(\frac{v^{12}}{v^{48}}\)
- Jibu
-
\(\frac{1}{v^{36}}\)
\(\frac{x}{x^{5}}\)
\(\frac{5}{5^{8}}\)
- Jibu
-
\(\frac{1}{5^{7}}\)
Kurahisisha Maneno na Zero Exponents
Katika mazoezi yafuatayo, kurahisisha.
\(75^{0}\)
\(x^{0}\)
- Jibu
-
1
\(-12^{0}\)
\(\left(-12^{0}\right)(-12)^{0}\)
- Jibu
-
1
25\(x^{0}\)
\((25 x)^{0}\)
- Jibu
-
1
\(19 n^{0}-25 m^{0}\)
\((19 n)^{0}-(25 m)^{0}\)
- Jibu
-
0
Kurahisisha Maneno Kutumia Quotient kwa Mali ya Nguvu
Katika mazoezi yafuatayo, kurahisisha.
\(\left(\frac{2}{5}\right)^{3}\)
\(\left(\frac{m}{3}\right)^{4}\)
- Jibu
-
\(\frac{m^{4}}{81}\)
\(\left(\frac{r}{s}\right)^{8}\)
\(\left(\frac{x}{2 y}\right)^{6}\)
- Jibu
-
\(\frac{x^{6}}{64 y^{6}}\)
Kurahisisha Maneno kwa kutumia Mali kadhaa
Katika mazoezi yafuatayo, kurahisisha.
\(\frac{\left(x^{3}\right)^{5}}{x^{9}}\)
\(\frac{n^{10}}{\left(n^{5}\right)^{2}}\)
- Jibu
-
1
\(\left(\frac{q^{6}}{q^{8}}\right)^{3}\)
\(\left(\frac{r^{8}}{r^{3}}\right)^{4}\)
- Jibu
-
\(r^{20}\)
\(\left(\frac{c^{2}}{d^{5}}\right)^{9}\)
\(\left(\frac{3 x^{4}}{2 y^{2}}\right)^{5}\)
- Jibu
-
\(\frac{343 x^{20}}{32 y^{10}}\)
\(\left(\frac{v^{3} v^{9}}{v^{6}}\right)^{4}\)
\(\frac{\left(3 n^{2}\right)^{4}\left(-5 n^{4}\right)^{3}}{\left(-2 n^{5}\right)^{2}}\)
- Jibu
-
\(-\frac{10,125 n^{10}}{4}\)
Kugawanya Monomials
Katika mazoezi yafuatayo, ugawanye monomials.
\(-65 y^{14} \div 5 y^{2}\)
\(\frac{64 a^{5} b^{9}}{-16 a^{10} b^{3}}\)
- Jibu
-
\(-\frac{4 b^{6}}{a^{5}}\)
\(\frac{144 x^{15} y^{8} z^{3}}{18 x^{10} y^{2} z^{12}}\)
\(\frac{\left(8 p^{6} q^{2}\right)\left(9 p^{3} q^{5}\right)}{16 p^{8} q^{7}}\)
- Jibu
-
\(\frac{9 p}{2}\)
Gawanya Polynomials
Gawanya Polynomial na Monomial
Katika mazoezi yafuatayo, kugawanya kila polynomial na monomial.
\(\frac{42 z^{2}-18 z}{6}\)
\(\left(35 x^{2}-75 x\right) \div 5 x\)
- Jibu
-
7x-15
\(\frac{81 n^{4}+105 n^{2}}{-3}\)
\(\frac{550 p^{6}-300 p^{4}}{10 p^{3}}\)
- Jibu
-
\(55 p^{3}-30 p\)
\(\left(63 x y^{3}+56 x^{2} y^{4}\right) \div(7 x y)\)
\(\frac{96 a^{5} b^{2}-48 a^{4} b^{3}-56 a^{2} b^{4}}{8 a b^{2}}\)
- Jibu
-
\(12 a^{4}-6 a^{3} b-7 a b^{2}\)
\(\frac{57 m^{2}-12 m+1}{-3 m}\)
\(\frac{105 y^{5}+50 y^{3}-5 y}{5 y^{3}}\)
- Jibu
-
\(21 y^{2}+10-\frac{1}{y^{2}}\)
Gawanya Polynomial na Binomial
Katika mazoezi yafuatayo, kugawanya kila polynomial na binomial.
\(\left(k^{2}-2 k-99\right) \div(k+9)\)
\(\left(v^{2}-16 v+64\right) \div(v-8)\)
- Jibu
-
v-8
\(\left(3 x^{2}-8 x-35\right) \div(x-5)\)
\(\left(n^{2}-3 n-14\right) \div(n+3)\)
- Jibu
-
\(n-6+\frac{4}{n+3}\)
\(\left(4 m^{3}+m-5\right) \div(m-1)\)
\(\left(u^{3}-8\right) \div(u-2)\)
- Jibu
-
\(u^{2}+2 u+4\)
Integer Exponents na Nukuu ya kisayansi
Tumia Ufafanuzi wa Mtazamaji Mbaya
Katika mazoezi yafuatayo, kurahisisha.
\(9^{-2}\)
\((-5)^{-3}\)
- Jibu
-
\(-\frac{1}{125}\)
3\(\cdot 4^{-3}\)
\((6 u)^{-3}\)
- Jibu
-
\(\frac{1}{216 u^{3}}\)
\(\left(\frac{2}{5}\right)^{-1}\)
\(\left(\frac{3}{4}\right)^{-2}\)
- Jibu
-
\(\frac{16}{9}\)
Kurahisisha Maneno na Exponents Integer
Katika mazoezi yafuatayo, kurahisisha.
\(p^{-2} \cdot p^{8}\)
\(q^{-6} \cdot q^{-5}\)
- Jibu
-
\(\frac{1}{q^{11}}\)
\(\left(c^{-2} d\right)\left(c^{-3} d^{-2}\right)\)
\(\left(y^{8}\right)^{-1}\)
- Jibu
-
\(\frac{1}{y^{8}}\)
\(\left(q^{-4}\right)^{-3}\)
\(\frac{a^{8}}{a^{12}}\)
- Jibu
-
\(\frac{1}{a^{4}}\)
\(\frac{n^{5}}{n^{-4}}\)
\(\frac{r^{-2}}{r^{-3}}\)
- Jibu
-
r
Badilisha kutoka Nukuu ya Decimal hadi Nukuu ya kisayansi
Katika mazoezi yafuatayo, weka kila nambari katika maelezo ya kisayansi.
8,500,000
0.00429
- Jibu
-
\(4.29 \times 10^{-3}\)
Unene wa dime ni kuhusu inchi 0.053.
Mwaka 2015, idadi ya wakazi duniani ilikuwa watu wapatao 7,200,000,000.
- Jibu
-
\(7.2 \times 10^{9}\)
Badilisha Nukuu ya kisayansi kwa Fomu ya Decima
Katika mazoezi yafuatayo, kubadilisha kila nambari kwa fomu ya decimal.
\(3.8 \times 10^{5}\)
\(1.5 \times 10^{10}\)
- Jibu
-
15,000,000,000
\(9.1 \times 10^{-7}\)
\(5.5 \times 10^{-1}\)
- Jibu
-
0.55
Kuzidisha na Gawanya Kutumia Notation ya
Katika mazoezi yafuatayo, kuzidisha na kuandika jibu lako kwa fomu ya decimal.
\(\left(2 \times 10^{5}\right)\left(4 \times 10^{-3}\right)\)
\(\left(3.5 \times 10^{-2}\right)\left(6.2 \times 10^{-1}\right)\)
- Jibu
-
0.2017
Katika mazoezi yafuatayo, ugawanye na uandike jibu lako kwa fomu ya decimal.
\(\frac{8 \times 10^{5}}{4 \times 10^{-1}}\)
\(\frac{9 \times 10^{-5}}{3 \times 10^{2}}\)
- Jibu
-
0.00003
Sura ya Mazoezi mtihani
Kwa polynomial\(10 x^{4}+9 y^{2}-1\)
ⓐ Je, ni monomial, binomial, au trinomial?
ⓑ Shahada yake ni nini?
Katika mazoezi yafuatayo, kurahisisha kila kujieleza.
\(\left(12 a^{2}-7 a+4\right)+\left(3 a^{2}+8 a-10\right)\)
- Jibu
-
\(15 a^{2}+a-6\)
\(\left(9 p^{2}-5 p+1\right)-\left(2 p^{2}-6\right)\)
\(\left(-\frac{2}{5}\right)^{3}\)
- Jibu
-
\(-\frac{8}{125}\)
\(u \cdot u^{4}\)
\(\left(4 a^{3} b^{5}\right)^{2}\)
- Jibu
-
16\(a^{6} b^{10}\)
\(\left(-9 r^{4} s^{5}\right)\left(4 r s^{7}\right)\)
3\(k\left(k^{2}-7 k+13\right)\)
- Jibu
-
\(3 k^{3}-21 k^{2}+39 k\)
\((m+6)(m+12)\)
(v-9) (9v-5)
- Jibu
-
\(9 v^{2}-86 v+45\)
(4c-11) (3c-8)
\((n-6)\left(n^{2}-5 n+4\right)\)
- Jibu
-
\(n^{3}-11 n^{2}+34 n-24\)
\((2 x-15 y)(5 x+7 y)\)
\((7 p-5)(7 p+5)\)
- Jibu
-
\(49 p^{2}-25\)
\((9 v-2)^{2}\)
\(\frac{3^{8}}{3^{10}}\)
- Jibu
-
\(\frac{1}{9}\)
\(\left(\frac{m^{4} \cdot m}{m^{3}}\right)^{6}\)
\(\left(87 x^{15} y^{3} z^{22}\right)^{0}\)
- Jibu
-
1
\(\frac{80 c^{8} d^{2}}{16 c d^{10}}\)
\(\frac{12 x^{2}+42 x-6}{2 x}\)
- Jibu
-
\(6 x+21-\frac{3}{x}\)
\(\left(70 x y^{4}+95 x^{3} y\right) \div 5 x y\)
\(\frac{64 x^{3}-1}{4 x-1}\)
- Jibu
-
\(16 x^{2}+4 x+1\)
\(\left(y^{2}-5 y-18\right) \div(y+3)\)
\(5^{-2}\)
- Jibu
-
\(\frac{1}{25}\)
\((4 m)^{-3}\)
\(q^{-4} \cdot q^{-5}\)
- Jibu
-
\(\frac{1}{q^{9}}\)
\(\frac{n^{-2}}{n^{-10}}\)
Geuza 83,000,000 kwa nukuu ya kisayansi.
- Jibu
-
\(8.3 \times 10^{7}\)
Badilisha\(6.91 \times 10^{-5}\) kwenye fomu ya decimal.
Katika mazoezi yafuatayo, kurahisisha, na uandike jibu lako kwa fomu ya decimal.
\(\left(3.4 \times 10^{9}\right)\left(2.2 \times 10^{-5}\right)\)
- Jibu
-
74,800
\(\frac{8.4 \times 10^{-3}}{4 \times 10^{3}}\)
Helikopta ya kuruka kwenye urefu wa miguu 1000 hupungua mfuko wa uokoaji. Polynomial\(-16 t^{2}+1000\) inatoa urefu wa mfuko t sekunde baada ya kushuka. Kupata urefu wakati t = 6 sekunde.
- Jibu
-
Futi 424