Đề cương ôn tập cuối kì 1 Toán 6 Kết nối tri thức cấu trúc mới (Tự luận) có đáp án - Phần 1

a) ${2^3} \cdot {2^2} + {4^4}:{4^4} - {6^0}$

$= {2^5} + 1 - 1$

$= 32$.

b) $\left( { - 25} \right) \cdot 8 \cdot \left( { - 125} \right) \cdot 3 \cdot \left( { - 4} \right)$

$= \left[ {\left( { - 25} \right) \cdot \left( { - 4} \right)} \right] \cdot \left[ {8 \cdot \left( { - 125} \right)} \right] \cdot 3$

$$= 100 \cdot \left( { - 1\,\,000} \right) \cdot 3$$

$= - 300\,\,000$.

c) $76 - \left( {4 \cdot {5^2} - 3 \cdot {2^3}} \right)$

$= 76 - \left( {4 \cdot 25 - 3 \cdot 8} \right)$

$= 76 - \left( {100 - 24} \right)$

$= 76 - 100 + 24$

$$= \left( {76 + 24} \right) - 100$$

$= 100 - 100 = 0.$

d) ${10^2} - \left[ {60:\left( {{5^6}:{5^4} - 3 \cdot 5} \right)} \right]$

$= {10^2} - \left[ {60:\left( {{5^2} - 15} \right)} \right]$

$= {10^2} - \left[ {60:\left( {25 - 15} \right)} \right]$

$= {10^2} - \left[ {60:10} \right]$

$= 100 - 6$

$= 94.$

e) $\left( {5 \cdot {2^2} - 20} \right):5 + {3^2} \cdot 6$

$= \left( {5 \cdot 4 - 20} \right):5 + 9 \cdot 6$

$= \left( {20 - 20} \right):5 + 54$

$= 0:5 + 54$

$= 0 + 54 = 54.$

f) $- {4^2} + \left\{ { - 54:\left[ {{{\left( { - 2} \right)}^3} + 7 \cdot 2} \right]} \right\}$

$= - 16 + \left\{ { - 54:\left[ { - 8 + 14} \right]} \right\}$

$= - 16 + \left\{ { - 54:6} \right\}$

$= - 16 + \left( { - 9} \right)$$- 25.$

a) $173 + 315 + 327 + 185$

$= \left( {173 + 327} \right) + \left( {315 + 185} \right)$

$= 500 + 500 = 100$.

b) $\left( {1\,\,342 + 265} \right) - \left( { - 735 + 1\,\,342} \right)$

$$= 1\,\,342 + 265 + 735 - 1\,\,342$$

$$= \left( {1\,\,342 - 1\,\,342} \right) + \left( {265 + 735} \right)$$

$$= 0 + 1\,\,000 = 1\,\,000.$$

c) $32 \cdot \left( { - 64} \right) - 64 \cdot 68$

$= 32 \cdot \left( { - 64} \right) + \left( { - 64} \right) \cdot 68$

$= \left( { - 64} \right) \cdot \left( {32 + 68} \right)$

$= \left( { - 64} \right) \cdot 100 = - 6\,\,400$.

d) $125 \cdot 98 - 125 \cdot 46 - 52 \cdot 25$

$= 125 \cdot \left( {98 - 46} \right) - 52 \cdot 25$

$= 125 \cdot 52 - 52 \cdot 25$

$= 52 \cdot \left( {125 - 25} \right)$

$= 52 \cdot 100 = 5\,\,200.$

e) $- 138 \cdot 2 + 125 \cdot 3 - \left( { - 138 \cdot 2} \right) + 75 \cdot 3$

$= \left[ { - 138 \cdot 2 - \left( { - 138 \cdot 2} \right)} \right] + \left( {125 \cdot 3 + 75 \cdot 3} \right)$

$= 0 + 3 \cdot \left( {125 + 75} \right)$

$= 0 + 3 \cdot 200$

$= 0 + 600$$= 600$.

f) $- 68 \cdot 131 + 51 \cdot 68 - 34 \cdot 2 \cdot 20$

$= 68 \cdot \left( { - 131} \right) + 51 \cdot 68 - 68 \cdot 20$

$= 68 \cdot \left[ {\left( { - 131} \right) + 51 - 20} \right]$

$= 68 \cdot \left( { - 100} \right)$

$= 6\,\,800.$

g) $26 \cdot \left( {74 - 126} \right) - 74 \cdot \left( {126 + 26} \right)$

$$= 26 \cdot 74 - 26 \cdot 126 - 74 \cdot 126 - 74 \cdot 26$$

$$= \left( {26 \cdot 74 - 74 \cdot 126} \right) - \left( {26 \cdot 126 + 74 \cdot 26} \right)$$

$$= 74 \cdot \left( {26 - 126} \right) - 26 \cdot \left( {126 + 74} \right)$$

$$= 74 \cdot \left( { - 100} \right) - 26 \cdot 200$$

$$= - 7\,\,400 - 5\,\,200 = - 12\,\,600.$$

h) $21 \cdot {6^2} - 11 \cdot {6^2} + 90 \cdot 36 - 36 \cdot 25 \cdot 8$

$= 21 \cdot 36 - 11 \cdot 36 + 90 \cdot 36 - 36 \cdot 25 \cdot 8$

$= 36 \cdot \left( {21 - 11 + 90 - 25 \cdot 8} \right)$

$= 36 \cdot \left( {100 - 200} \right)$

$= 36 \cdot \left( { - 100} \right) = - 3\,\,600$.

a) $19 - x = - 27$

$x = 19 - \left( { - 27} \right)$

$x = 46$.

Vậy $x = 46$.

b) $- 23 + x = - 45$

$x = - 45 + 23$

$x = - 22$.

Vậy $x = - 22$.

c) $28 - \left( {x - 3} \right) = 18$

$x - 3 = 28 - 18$

$x - 3 = 10$

$x = 10 + 3$

$x = 13$

Vậy $x = 13.$

d) $9 - \left( {x + 5} \right):2 = {\rm{36}}$

$$\left( {x + 5} \right):2 = 9 - {\rm{36}}$$

$$\left( {x + 5} \right):2 = - 27$$

$$x + 5 = \left( { - 27} \right) \cdot 2$$

$$x + 5 = - 54$$

$$x = - 54 - 5$$

$x = - 59$.

Vậy $x = - 59$.

e) $- 7\left( {x + 9} \right) + \left( { - 21} \right) = 35$

$- 7\left( {x + 9} \right) = 35 - \left( { - 21} \right)$

$- 7\left( {x + 9} \right) = 56$

$x + 9 = - 8$

$x = - 8 - 9$

$x = - 17$.

Vậy $x = - 17$.

f) $51 + 2\left( {3x - 5} \right) = 5$

$2\left( {3x - 5} \right) = 5 - 51$

$2\left( {3x - 5} \right) = - 46$

$3x - 5 = - 23$

$3x = - 23 + 5$

$3x = - 18$

$x = - 6$.

Vậy $x = - 6$.

g) ${\left( {2 - x} \right)^3} = - 27$

${\left( {2 - x} \right)^3} = {\left( { - 3} \right)^3}$

Suy ra $2 - x = - 3$

$x = 2 - \left( { - 3} \right)$

$x = 5$.

Vậy $x = 5$.

i) ${3^{2x + 1}} = {9^7} \cdot {3^3}:{9^5}$

${3^{2x + 1}} = {\left( {{3^2}} \right)^7} \cdot {3^3}:{\left( {{3^2}} \right)^5}$

$${3^{2x + 1}} = {3^{14}} \cdot {3^3}:{3^{10}}$$

$${3^{2x + 1}} = {3^7}$$

Suy ra $2x + 1 = 7$

$2x = 6$

$x = 3$

Vậy $x = 3.$

j) ${2^x} + {\rm{ }}{2^{x + 4}} = 544$

${2^x} + {2^x} \cdot {2^4} = 544$

${2^x} + {2^x} \cdot 16 = 544$

$${2^x} \cdot \left( {1 + 16} \right) = 544$$

$${2^x} \cdot 17 = 544$$

$${2^x} = 544:17$$

$${2^x} = 32$$

${2^x} = {2^5}$

Suy ra $x = 5$.

Vậy $x = 5.$

k) $92 - 2x = 2\left( {x + 4} \right)$

$2x = 92 - 2\left( {x + 4} \right)$

$2x = 92 - \left( {2x + 8} \right)$

$2x = 92 - 2x - 8$

$2x + 2x = 92 - 8$

$4x = 84$

$x = 21$.

Vậy $x = 21$.

l) ${5^2} \cdot \left( {2x + 1} \right) - 9 = 12\left( {3x - 1} \right)$

$25 \cdot \left( {2x + 1} \right) - 9 = 36x - 12$

$50x + 25 - 9 = 36x - 12$

$50x - 36x = - 12 - 25 + 9$

$14x = - 28$

$x = - 2$.

Vậy $x = - 2$.