First Semester First Year Maths Paper Fill in the Blanks (2 points per blank, ***30 points)
1, The opposite of 1/2 is _______, the absolute value is ________, and the negative reciprocal is _______. 2, Algebraically, (1) the number that divides 3 to give n is _____; (2) the difference between the squares of two numbers a and b is ________ 3、Compare the size (fill in ">", "<", "=") (1) -2.9___-3.1; 0-(-2)____04, The absolute value of ______ is equal to its opposite.5. If you look up the table and get 2.4682=6.091, if x2=0.06091,then x=_____.6. If you look up the table and get 5.193=139.8, then (-519)3=___________.7. Expressed in scientific notation: 500900000= ______________. 8. Use the rounding method to find the approximate value of the following numbers: (1) 0.7049 (retain two significant figures) for _______. (2) 1.6972 (to the nearest 0.01) is _______. . 9. Calculation: 2.785 × (-3)2 × 0 × 23 = _________. 10. Orange|x+4| = 4, then x = ______. Second, judgment questions (1 point per question, *** 10 points) 1, the number with a negative sign are negative, the square of a negative number are positive.
( ) 2, the sum of a pair of opposite numbers is 0, and the quotient is -1.
( ) 3, the formula for the area of a circle with radius r is s = πr2.
( ) 4, if a is a rational number, then 1/100a<a.
( ) 5, the formula S = V0 + Vt is not an algebraic formula.
( ) 6. If 0<b<a<1,a2>b2>b3.
( ) 7. A three-digit number whose hundredth digit is a, whose tens digit is b, and whose ones digit is c is abc for this three-digit number. ( ) 8. If |a|=-a, then a<0.
( ) 9. If a and b are rational numbers and |a+b|=0, then there must be a=0 and b=0.
( )10. Among the rational numbers, there is no largest integer and no smallest negative number. ( ) Three, multiple choice questions (3 points each, ***30 points) 1, in the following numbers: -(-2), -(-22), -|-2|, (-2)2, -(-2)2, -(-2)2, the number of negative numbers is ( ).
A, 1
B, 2 C, 3 D, 42, If a - b, then there must be ( ).
A, a=0
B, b=0 C, a=0 or b=0 D, a=0 and b=03, The following statement is correct ( ).
A, If |a|=|b|, then a=b B, If 0>a>b, then 1/a>1/b
C, If a>0 and a+b<0, then a-b<0
D, Any even power of any non-zero rational number is greater than 0. 4, If a number m is increased by it's x% to get a number n, then n is equal to ( ). A, m-x%
B, m(1+x%)
C, m+x%
D, m(1+x)%5, The integers **** greater than -3.95 and not greater than 3.95 are ( ).
A, 7
B, 6 C, 5 D, countless 6. The following equations have the same solution as the equation 1/2x-3=3 ( ).
A, x-6=3
B, 2x+6=6 C, 1/3x=1 D, x-6=67, A and B are m kilometers apart, the original plan is for the train to travel x kilometers per hour. If the train travels 50 kilometers per hour, the time required for the train to travel from A to B is less than the original (
).
A, m/50 hours B, m/x hours C, (m/x - m/50) hours D, m/50 - m/x hours 8, If |a|/a + b/|b| = 0, the magnitude relationship between -(b/a) and ab is ( ).
A, -(b/a) is larger B, ab is larger C, equal
D, can not be determined 9, the range of values of the exact number x represented by the approximation 1.30 is ( ).
A, 1.25 ≤ x<1.35
B, 1.20<x<1.30 C, 1.295 ≤ x<1.305 D, 1.300 ≤ x<1.30510, if |a|<1/a is valid, then a satisfies the condition ( ).
A, 0<a<1
B, a>0 C, a<0
D, 0<a<1 or a<-1 IV. Answer the following questions (3 points each, ****6 points) 1. Represent the following numbers on the axis: 4, -1(1/2), 0, |-2|2, Solve the equation: 5/ 2x-3=0 V. Calculation (2 points each for 1 to 4, 3 points each for 5 and 6, ****14 points) (1) 2/5 + (-3/5)
(2) (-5.9) - (-6.1) (3) (1/3 + 1/6 - 1/2) × (-12) (4) -0.25 × (-8/5) ÷ (-2/3) (5) -15.6 ÷ [-28/15 × (-1.75) + 2.75 × (32/15)] (6) -32 ÷ (-3)2 + |-1/6| × (-6)-(2)4 - (-1/2)3 - (-1) VI. Simplify or find the value of 1. If a<0 and ab<0, simplify |b-a+4| - |a-b-7| (3 pts.) 2. If (3x-2y)2 + |x+2| = 0 , find the value of the algebraic formula (x3+y3)/xy-1. (4 points) 3. You know that a, b, and c are rational numbers represented at the points on the number axis shown in the figure: ──┬──┬──┬──→
a c 0
b Find the value of the algebraic formula |ab|/ab+|bc|/bc-|ac|/ac-(|abc|/abc)3. (3 points) Answers and References i. 1, -1/2, 1/2, -2 2, 3n, a2-b2
3, >, > 4, non-negative
5, ±0.2468 6, -139800000 or -1.398 × 108 7, 5.009 × 108
8, 0.70, 1.70 9, 0. 10
10, 0 or -8 II. 1, x 2, x 3, √ 4, x 5, √ 6, √ 7, x 8, x 9, x 10, √ III. 1, B 2, C 3, D 4, B 5, A 6, D 7, C 8, A 9, C 10, A IV. 1, Omitted, 1 point for the axis, 2 points for 4 numbers, 2, x = 6/5 V. 1, -1/5 2, 0.2 3, 0 4, -3/5 5, 6, -4 (give points according to the part, the result 1 point) VI. 1, ∵ a<0,b>0,∴ b-a+4>0,a-b-7<0
(1 points)
Original formula = b-a+4-[-(a-b-7)]
= b-a+4+a-b-7=-3
(2 points)
2. ∵(3x-2y)2≥0,|x+2|≥0
and (3x-2y)2+|x+2|=0
∴3x-2y=0,x+2=0
(1 pts)
∴x=-2,y=-3
(1 pts)
The original equation = ((-2)3+(-3) 3)/(-2)(-3)-1=-8-27/6-1=-7
(2 points)
3. a<0,c<0,b>0,original equation-1-1-1×13=-3
(1 point)
(2 points)