Exercise1(level b)
(1) Calculation problem:
( 1)23+(-73)
(2)(-84)+(-49)
(3)7+(-2.04)
(4)4.23+(-7.57)
(5)(-7/3)+(-7/6)
(6)9/4+(-3/2)
(7)3.75+(2.25)+5/4
(8)-3.75+(+5/4)+(- 1.5)
(2) Calculate by a simple method:
( 1)(- 17/4)+(- 10/3)+(+ 13/3)+( 1 1/3)
(2)(- 1.8)+(+0.2)+(- 1.7)+(0. 1)+(+ 1.8)+(+ 1.4)
(3) It is known that X =+ 17 (3/4), Y =-9 (5/ 1 1) and Z =-2.25.
Find the value of: (-x)+(-y)+z.
(4) if "> 0 is used, then a-ba (c) if ba (d) if a.
(2) Fill in the blanks:
(1) zero minus the inverse of a, the result is _ _ _ _ _ _ _ _; ② if a-b >; A, then B is _ _ _ _ _ _ _ _ _ _ _; (3) subtract-π from -3. 14, and the difference should be _ _ _ _ _ _ _ _; (4) The minuend is-12(4/5), with a difference of 4.2, so the minuend should be _ _ _ _ _ _ _ _ _ _ _ _; (5) If B-A
(3) True or false:
(1) When a number subtracts a negative number, the difference is less than the minuend. (2) When a number subtracts a positive number, the difference is less than the minuend. (3) Subtract any number from 0, and the difference is always equal to the reciprocal of this number. (4) If X+(-Y)=Z, then X=Y+Z (5) If 0, b|b|, then a-b >; 0
Exercise 2 (Level B)
(1) calculation:
( 1)(+ 1.3)-(+ 17/7)
(2)(-2)-(+2/3)
(3)|(-7.2)-(-6.3)+( 1. 1)|
(4)|(-5/4)-(-3/4)|-| 1-5/4-|-3/4|)
(2) If |a|=4, |b|=2, and |a+b|=a+b, find the value of a-b. 。
(3) If A and B are rational numbers and | a |
(4) If |X- 1|=4, find x and observe the distance between the point representing the number x and the point representing 1 on the number axis.
Exercise 3 (Level A)
(1) Multiple choice questions:
The correct pronunciation of (1) formula -40-28+ 19-24+32 is ().
(a) minus 40, minus 28, plus 19, minus 24 and 32; (b) minus 40, minus 28 plus 19, minus 24 plus 32; (c) minus 40 minus 28 plus 19 minus 24 plus 32; (d) 40 minus 28 plus 19 minus 24.
(2) If the rational number A+B+C
(a) At least two of the three numbers are negative; (b) There is only one negative number in three numbers; (c) At least one of the three numbers is negative; (d) Two of the three numbers are positive or two are negative.
(3) If M
(A)0 (B) m (c) 2m (d)-2m
(4) In the following categories, the value that is not equal to X-y-Z is ()
(A)X-(Y-Z)(B)X-(Y+Z)(C)(X-Y)+(-Z)(D)(-Y)+(X-Z)
(2) Fill in the blanks:
The general steps of (1) rational number addition and subtraction mixed operation are: (1) _ _ _ _ _ _ _; (2)_________; (3)________ _______; (4) _ _ _ _ _ _ _ _ _ _ _. (2) When b0, (a+b)(a- 1) >; 0, there must be () (A)b with the same number as A (B)a+b with the same number as A-1(c) A > 1 (D)b 1 (6) The product of a rational number and its opposite number () (a) The sign must be positive (b) The sign must be negative (c) It must not be less than zero (d) It must not be greater than zero (7) If | a-1|||.
(2) Fill in the blanks:
The multiplication rule of (1) rational number is: multiply two numbers, Use the same symbol _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _. (4) Calculation: (4a) * (-3b) * (5c) *1/6 = _ _ _ _ _ _ _ _ _ _ _; (5) Error in calculation: (-8) * (1/2-1/4+2) =-4-2+16 =10 is _ _ _ _ _. (6) Calculation: (-1/6) * (-6) * (17) * (-7/10) = [(-16) * (-6)].
(3) True or false:
(1) If the product of two numbers is positive, then both numbers must be positive; (2) If the product of two numbers is negative, then the signs of the two numbers are different; (3) Multiply several rational numbers, and when there are even factors, the product is positive; (4) Multiplying several rational numbers, when the product is negative, there are odd negative factors; (5) The product ratio is greater than each factor.
Exercise (4) (Level B)
(1) Calculation problem:
( 1)(-4)(+6)(-7)
(2)(-27)(-25)(-3)(-4)
(3)0.00 1*(-0. 1)*( 1. 1)
(4)24*(-5/4)*(- 12/ 15)*(-0. 12)
(5)(-3/2)(-4/3)(-5/4)(-6/5)(-7/6)(-8/7)
(6)(-24/7)( 1 1/8+7/3-3.75)*24
(2) Calculate by a simple method:
( 1)(-7 1/8)*(-23)-23*(-73/8)
(2)(-7/ 15)*(- 18)*(-45/ 14)
(3)(-2.2)*(+ 1.5)*(-7/ 1 1)*(-2/7)
(3) When a=-4, b=-3, c=-2, d=- 1, find the value of the algebraic expression (ab+cd)(ab-cd).
(4) Given1+2+3+...+31+32+33 =17 * 33, calculate the following formula.
The value of 1-3+2-6+3-9- 12+ ... +3 1-93+32-96+33-99.
Exercise 5 (Level A)
(1) Multiple choice questions:
(1) It is known that A and B are two rational numbers. If their quotient a/b=0, then ()
(A)a=0 and b≠0 (B)a=0 (C)a=0 or b=0 (D)a=0 or b≠0.
(2) Give the following four groups of numbers 1 and1; -1 and-1; 0 and 0; -2/3 and -3/2, where the reciprocal is ()
Only (a) only (b) only (c) only (d) both.
(3) If a/|b|(b≠0) is a positive integer, then ()
(A)|b| is a divisor of a (B)|b| is a multiple of a (C)a and B are the same symbol (D)a and B are different symbols.
(4) If a>b, then there must be ().
(A)A+b & gt； a(B)a-B & gt； a(C)2a & gt； ab(D)a/b & gt； 1
(2) Fill in the blanks:
(1) When |a|/a= 1, a _ _ _ _ _ _ 0; When |a|/a=- 1, a _ _ _ _ _ _ 0; (fill in > 0, then a _ _ _ _ _ _ 0; (1 1) If ab/c0, then B _ _ _ _ _ _ 0; (12) if a/b >; 0，b/c(-0.3)4 & gt； - 106(B)(-0.3)4 >； - 106 >(-0.2)3(C)- 106 & gt； (-0.2)3 & gt； (-0.3)4(D)(-0.3)4 & gt； (-0.2)3 & gt； -106 (4) If A is a rational number and A2 >；; A, then the value range of A is () (a) A.
(2) Fill in the blanks:
(1)23, 3 is _ _ _ _ _, 2 is _ _ _ _ _ _, and the power is _ _ _ _ _ _ _ _; If 3 is regarded as a power, its cardinal number is _ _ _ _ _ _ _ _,
The index is _ _ _ _ _ _ _ _; (2) According to the meaning of power: (-2)3 stands for _ _ _ _ _ _ _ multiplication; (-3)2v represents _ _ _ _ _ multiplication; -23 means _ _ _ _ _. (3) The rational number whose square equals 36/49 is _ _ _ _ _ _ _; The cubic number equal to -27/64 is _ _ _ _ _ _ _ (4) Write a positive number greater than 10 as a* 10n (n is a positive integer), where the range of a is _ _ _ _ _ _ _ _, where n is an integer.
The number of digits is less than _ _ _ _ _ _, which is called scientific notation; (5) Write down the following numbers by scientific notation: 4000 = _ _ _ _ _ _ _ _ _ _ _ _; 950000=________________; earth
The mass is about 49800 ... 0g (28 bits), which can be recorded as _ _ _ _ _ _ _ _; (6) What are the numbers recorded by scientific notation, namely105 = _ _ _ _ _ _ _ _ _ _ _; 2* 105=______________; 9.7 *107 = _ _ _ _ _ _ 9.756 *103 = _ _ _ _ _ (7) The following numbers are natural numbers. 7* 106 is 3.78* 107 is _ _ _ _ digits; 10 10 is _ _ _ _ _ digits; (8) If rational number m 0, B0 (b) a-| b | > 0 (c) A2+B3 > 0 (d) A <; 0 (6) The minimum value of algebraic expression (a+2)2+5 is () (a) A = 0 (b) A = 2 (c) A =-2 (d) A0 (b) B-A >; 0 (c) A and B are reciprocal; (D)-ab (C)a
(5) The approximate value 1.20 obtained by rounding method represents the range of the exact number a ().
(A) 1. 195≤A & lt； 1.205(B) 1. 15≤a & lt； 1. 18(C) 1. 10≤a & lt； 1.30(D) 1.200≤a & lt； 1.205 (6) The following statements are correct: (a) The accuracy of similarity number 3.80 is the same as that of similarity number 38; (b) The number of significant digits of similarity number 38.0 is the same as that of similarity number 38. (c)3. 14 16 has three significant digits 3, 1 4 after being accurate to the percentile; (d) Write 123* 102 as 1.23* 104 with four significant digits.
(2) Fill in the blanks:
(1) Write the precision and significant figures of the following rounded approximations: (1) Approximate number 85 is accurate to _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ (3) The divisor of 5.2 million is accurate to _ _ _ _ _ _ _ _, and the effective number is _ _ _ _ _ _ _ _; (4) The approximate value of 0.20 is accurate to _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
The divisor 2.7 183 is accurate to _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
(3) True or false:
(1) The approximate value of 25.0 is exactly a dash, and the significant digits are 2,5; (2) Similarity number 4000 is as accurate as similarity number 4000; (3) The divisor 4000 is as accurate as the divisor 4 * 10 3; (4) The approximate value of 9.949 accurate to 0.0 1 is 9.95.
Exercise 8 (Level B)
(1) Use rounding method to approximate the following figures (three significant figures are required): (1) 37.27 (2) 810.9 (3) 0.0045078 (4) 3.079.
(2) Use rounding method to approximate the following numbers (accurate to thousands): (1) 37890.6 (2) 213612.4 (3)1906.57.
(3) Calculation (the result is reserved with two significant figures): (1) 3.14 * 3.42 (2) 972 * 3.14 *14.
Exercise 9
(a) look-up table evaluation:
( 1)7.042 (2)2.482 (3)9.52 (4)2.00 12 (5) 123.42 (6)0. 12342 (7) 1.283 (8)3.4683 (9)(-0.5398)3 ( 10)53.733
(2) Given that 2.4682=6.90 1, we can find the values of 24.682 and 0.024682 without looking up the table.
(3) 5.2633= 145.7 is known, so we don't look it up.
( 1)0.52633 (2)0.05263 (3)52.632 (4)52633
(4) Given 21.762 2 = 473.5, what is the approximate value of 0.002 1762 with three significant digits?
(5) Look-up table calculation: the surface area of a ball with a radius of 77cm (the area of the ball =4π*r2).
References:
For reference only, I wish you progress in your study!