Question 1

下列何者錯誤？

Accepted Answer

$(-5)^8$ > $(-5)^{10}$ > $(-5)^{12}$

Answer

$(0.5)^{10}$ > $(0.5)^{11}$ > $(0.5)^{12}$

Answer

$(-2)^3$ > $(-2)^5$ > $(-2)^7$

Answer

$4^3$ < $4^4$ < $4^5$

Question 2

計算 $(17-23)^3 \div (13-19)^2 - (2-3)^2 	imes (3^2 - 2^2)$

Accepted Answer

-11

Answer

-1

Answer

7

Answer

5

Question 3

判斷下列乘積中，何者為負數？

Accepted Answer

$(-2^3) 	imes (-4^5) 	imes (-6^7)$

Answer

$(-2)^3 	imes (-3)^4 	imes (-4)^5$

Answer

$(-2^3) 	imes (-3^4) $

Answer

$(-1^3) 	imes (-1)^4 	imes (-1^5)$

Question 4

已知一光年約 $9.5 	imes 10^{15}$ 公尺，則4光年約為多少公里？

Accepted Answer

$3.8 	imes 10^{13}$

Answer

$3.8 	imes 10^{16}$

Answer

$3.8 	imes 10^{12}$

Answer

$3.8 	imes 10^{14}$

Question 5

下列四個選項分別代表甲、乙、丙、丁四個微生物的長度，則那一個微生物的長度介於 $1.5 	imes 10^{-5}$ mm 與 $8 	imes 10^{-6}$ mm 之間？

Accepted Answer

0.000013 mm

Answer

0.000007 mm

Answer

0.0000007 mm

Answer

0.0000013 mm

Question 6

計算 $5^3 \div (2^4 + 3^2) + (2^3)^2 \div (-2^2)$ 之值為何？

Accepted Answer

-11

Answer

1

Answer

21

Answer

-9

Question 7

將 $2.3861 	imes 10^{13}$ 化成整數的形式後，末尾會有連續 a 個 0；將 $4.9507 	imes 10^{-40}$ 化成小數的形式後，數字 5 出現在小數點後第 b 位，則 $2 	imes a - b$ = ？

Accepted Answer

-24

Answer

-22

Answer

-21

Answer

-23

Question 8

下列那一個算式與 $3^4$ 相等？

Accepted Answer

$3 	imes 3 	imes 3 	imes 3$

Answer

$3 	imes 4$

Answer

3 + 3 + 3 + 3

Answer

$4 	imes 4 	imes 4$

Question 9

我們可將 「7個3相乘」記為下列何者？

Accepted Answer

$3^7$

Answer

$7^3$

Answer

$7 	imes 3$

Answer

7 + 3

Question 10

小明拍了一部片酬為七位數字的廣告，則下列何者可能是他的片酬？

Accepted Answer

三百萬元

Answer

二千萬元

Answer

一億元

Answer

七十萬元

Question 11

將 $\frac{1}{25000000}$ 以科學記號表示，則下列何者正確？

Accepted Answer

$4 	imes 10^{-8}$

Answer

$2.5 	imes 10^7$

Answer

$2.5 	imes 10^8$

Answer

$4 	imes 10^{-7}$

Question 12

西遊記的孫悟空翻一個觔斗可行走十萬八千里，以科學記號來表示，則下列何者正確？

Accepted Answer

$1.08 	imes 10^5$ 里

Answer

$1.008 	imes 10^5$ 里

Answer

$1.008 	imes 10^6$ 里

Answer

$1.08 	imes 10^6$ 里

Question 13

若 a = $-2^3$、b = $(-2)^4$、c = $-2020^0$、d = $(-2020)^0$，則此四數中，最小的數為何？

Accepted Answer

a

Answer

d

Answer

b

Answer

c

Question 14

下列那一個數值最大？

Accepted Answer

$6.3 	imes 10^{-7}$

Answer

$3.6 	imes 10^{-8}$

Answer

$6.3 	imes 10^{-8}$

Answer

$3.6 	imes 10^{-7}$

Question 15

舒服牌衛生紙，每一箱中有6袋，有一袋中有6串，有一串中有6包，花媽買了1箱，共有幾包？

Accepted Answer

216

Answer

144

Answer

288

Answer

196

Question 16

下列那一個選項正確？

Accepted Answer

$(-2)^3 - (-2^3) = 0$

Answer

$(-2)^4 - (-2^4) = 0$

Answer

$2^3 - (-2^3) = 0$

Answer

$2^4 - (-2^4) = 0$

Question 17

將一個正數 m 以科學記號表示為 $a 	imes 10^n$，則下列敘述何者正確？

Accepted Answer

若 0 < m < 1，則 n 一定是負整數

Answer

$0 \leqslant a \leqslant 1$

Answer

n 一定是正整數

Answer

a 一定是整數

Question 18

下列那一個選項的數值與其它三者不同？

Accepted Answer

$\frac{58}{100000}$

Answer

$\frac{5800}{1000000000}$

Answer

$5.8 	imes 10^{-6}$

Answer

$58 	imes 10^{-7}$

Question 19

$\frac{1}{1600}$可以用科學記號表示為下列何者？

Accepted Answer

$6.25 	imes 10^{-4}$

Answer

$6.25 	imes 10^{-3}$

Answer

$1.6 	imes 10^{-3}$

Answer

$1.6 	imes 10^{-4}$

Question 20

ppm為濃度的計算單位，表示百萬分之一，則以科學記號表示15ppm之值為何？

Accepted Answer

$1.5 	imes 10^{-5}$

Answer

$1.5 	imes 10^6$

Answer

$1.5 	imes 10^{-6}$

Answer

$1.5 	imes 10^{-7}$

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