Mathematical Algebraic Formula and Its Addition and Subtraction Problems in the First Volume of Grade One.
First, multiple-choice questions (3 points for each small question ***30 points)
1. Among the following algebraic expressions, () meets the writing requirements.
A.P*A B.n2 C.a？ b D. 2C
2. Among the following types, the algebraic type is ().
a.a2﹣b2=0 b . 4 & gt； 3c a d.5x﹣2？ 0
3. In the following two sets of algebraic expressions, the one that belongs to the same category is ().
A. and B. and ...
4. Polynomial, the following statement is wrong ()
A.this is a quadratic trinomial. B. The coefficient of the quadratic term is 1.
C the coefficient of the linear term is d, and the constant term is.
5. The following operation is correct ()
A.B. C. D。
6. If, then the algebraic value is ().
A.B. C. D。
7. If a single sum is similar, the values of sum are () respectively.
A.，b，
C.，d，
8. Algebraic expression, the number of monomials in 0,,, is ().
a，3 B，4 C，5 D，6
9. If and are similar projects, the value of is ().
A.，b，
C.，d，
10. As shown in the figure, put black pieces of the same size on the edge of a regular polygon and put them down according to this rule, then the number of black pieces required for the first figure is.
Fill in the blanks (3 points for each small question ***24 points)
1 1. A commodity is priced at RMB, and now it is sold at a 10% discount at RMB.
12. The single factor is, and the number is.
13. If yes, then _ _ _ _ _ _ _ _.
14. If sum is similar, then m+n=.
15. Observe the following monomial:, -2. According to the law you found, the sixth formula is.
16. The observation is as follows: (1)42- 12=3? 5; (2)52-22=3? 7; (3)62-32=3? 9; ?
Then the nth equation (n is a positive integer) is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
17. As shown in the figure, it is a pattern made of matchsticks. 1 The pattern needs 3 matchsticks, the second pattern needs 5 matchsticks, the third pattern needs 7 matchsticks, and the fourth pattern needs 1 matchstick.
18. What is a polynomial? According to this rule, the eighth item of this multi-item is _ _ _ _.
Third, answer questions (19, 20 questions, 6 points for each small question; 2 1, 22, 23 is 8 points for each small question; 24 questions 10)
19. Simplification (6 points)
( 1)(2)2(a2 b+ab2)-2(a2 b- 1)+2a B2-2
20. Simplify before evaluating: (-4x2+2x-8)-( x- 1), where x=.
2 1. If 2x| 2a+ 1 |y and xy| b | are similar terms, where a and b are reciprocal, find the value of 2(a-2b2)- (3b2-a).
22.(6 points) Observe the following formula: ① 1? 3- =3-4=- 1; ②2? 4- =8-9=- 1;
③3? 5- = 15- 16=- 1; ④ ;
(1) Please write the fourth formula according to the above rules;
(2) Please use one containing n: =; The formula to express this law;
(3) Do you think the formula written in (2) must be true? Explain why.
23. As shown in the figure, quadrilateral ABCD and quadrilateral CEFG are two squares with side lengths respectively. (8 points)
The area of (1) triangle BGF is expressed by algebraic expression;
(2) When =4cm and =6cm, find the shadow area.
24. (The full mark of this question is 10)
Use black and white square tiles with the same specifications to pave the floor, as shown in the following figure:
(1) Observe the chart and fill in the following table:
Graph (1) (2) (3)
Number of black tiles 4 7
The total number of black and white cards is 15 25.
(2) According to the above speculation, the number of black tiles in the nth graph is: the total number of black and white tiles is (all expressed by algebraic expressions containing n).
(3) Is it possible that there are 20 15 more white cards than black cards? If so, what is the number? If not, please explain why.
Algebraic formula and its reference answers to addition and subtraction questions in the first volume of junior one mathematics
1.D
analyse
Test analysis: according to the requirements of algebra writing, judge each option in turn to answer.
Solution: A, the band score in should be written as a false score;
B, 2 should be written before the letter;
C, should be written in the form of scores;
D, meet the writing requirements.
So choose D.
Comments: This topic mainly examines the writing requirements of algebraic expressions:
The multiplication symbol in (1) algebraic expression is usually abbreviated as? Or omit not to write;
(2) When multiplying numbers and letters, the numbers should be written in front of the letters;
(3) The division operation in algebraic expressions is generally written in the form of fractions. Scores should be written in the form of false scores.
2.C
analyse
Test analysis: According to the definition of algebraic expression, this question can be answered by analyzing each option.
Solution: A: A2-B2 = 0 is an equation, not an algebraic expression, so this term is wrong.
b:4 & gt； 3 is an inequality, so this item is wrong.
c； A is algebra, so this item is correct.
D:5x﹣2？ 0 is an inequality, so this item is wrong.
So choose: C.
Comments: This question examines the definition of algebraic expression and only judges each option. Pay attention to equality, inequality is not an algebraic expression.
3.B
analyse
Test analysis: similar items contain the same letters, and the indicators of the same letters are equal, and all constant items are similar items, so this question chooses B.
Test center: similar projects
4.D
analyse
Test analysis: the polynomial is a quadratic trinomial, the quadratic term coefficient is 1, the linear term coefficient is 3, and the constant term is -2, so this question chooses D.
Test site: related concepts of polynomials
5.B
analyse
Test analysis: because they are not of the same type, they cannot be merged, so A is wrong; Because, so b is correct; Because, so C is wrong; Because, so D is wrong, so choose: B.
Test site: 1. Merge similar projects; 2. idempotent operation.
6.C。
analyse
Test analysis: 5-a=0, b+3=0 can be obtained from, thus: a=5, b=-3.
So:
So choose C.
Test site: 1. Non-negative nature; 2. Algebraic evaluation.
7.A
analyse
Test analysis: If the single sum is similar, we can get: according to the definition of the same type, so, therefore, we choose: A.
Test site: 1. Similar items; 2. equation.
8.C
analyse
Test analysis: the monomial is the product of numbers and letters, or the product of a single number and letters. So there are five monomials, 0,, * *.
So choose C.
Test center: single item
9.B。
analyse
Analysis of test questions: We can get: from the definition of similar terms, and we can get: by solving this set of equations. So we choose B.
Test site: 1. Similar items; 2. Solve binary linear equations.
10.n(n+2)
analyse
Test and analysis: according to the meaning of the question, it can be concluded that the number of black pieces required for the 1 th number is 2? 3-3, the number of black pieces required for the second figure is 3? 4-4, the third number needs to be black. The number of pieces is 4? 5-5, and so on, it can be concluded that the number of black pieces required for the nth number is (n+ 1)(n+2)-(n+2), and the answer can be obtained through calculation.
Problem analysis: 1 The graph is a triangle with three sides, each side has two points, and three points are repeated. It needs a black piece 2? 3-3,
The second figure is a quadrilateral with four sides, each side has three points, and the four points are repeated, which requires a black block 3? 4-4,
The third figure is a Pentagon, with five sides, each side has four points, and repeating five points requires four black pieces. 5-5,
Put it down according to this law,
Then the number of black pieces required for the nth number is (n+ 1)(n+2)-(n+2)=n(n+2).
Test center: regular type: graphic variation type.
1 1.0.9a
analyse
Test and analysis: A commodity is priced at RMB, and now it is sold at a 10% discount at a price of RMB 0.9a.
Test Center: Algebraic Expressions
12. The coefficient is, and the degree is 3.
analyse
Test analysis: answer directly according to the concept of single coefficient and number of times. Attention? As a coefficient.
Problem analysis: the coefficient of single item is, and the number of times is 3.
Test center: single item.
13.6.
analyse
Test analysis: 9-a+2b is transformed into 9-(a-2b), and then substituted into a-2b=3.
Test analysis: 9-a+2b=9-(a-2b)=9-3=6.
Test center: rational number subtraction.
14.- 1.
analyse
Test and analysis: according to the definition of similar term, we can get: m=2, n+7=4, solution: m=2, n=-3, then m+n=- 1.
Test center: definition of similar projects.
15.-32a6
analyse
Problem analysis: According to the law, the sixth formula is -32a6.
Examination center: the law of numbers
16.(n+3)2=3(2n+3)
analyse
Test analysis: longitudinal observation of the following types:
( 1)42- 12=3? 5;
(2)52-22=3? 7;
(3)62-32=3? 9; ?
Because n is a positive integer, the second column is expressed as, the first column as and the fourth column as, so the nth (n is a positive integer) equation is.
Test site: 1. Column algebra; 2. Square difference formula.
17.9，2n+ 1。
analyse
Test and analysis: According to the numerical method, the fourth number needs 9 matchsticks, and the nth number needs 3+2(n- 1)=2n+ 1.
Test center: regular questions.
18. [Constitutes the ancient or Latin modern names of animals and plants]
analyse
Test and analysis: according to the known even term is negative, the eighth term A has 1 time, and B has 7 times.
Test center: regular questions
19.( 1) ;
(2)4ab2
analyse
Test and analysis: remove brackets first, and then merge similar items.
Problem analysis: (1);
(2)2(a2 b+ab2)-2(a2 b- 1)+2ab 2-2 = 2a2b+2ab 2-2a2b+2+2ab 2-2 = 4ab 2
Test center: algebraic expression addition and subtraction.
20.。
analyse
Test and analysis: remove the brackets in the original formula, merge similar items to get the simplest result, and then substitute the value of x for evaluation.
Problem analysis: the original formula =-x2+ x-2- x+ 1.
=-x2- 1
When x=, the original formula =.
Test site: addition and subtraction of algebraic expressions-simplified evaluation.
2 1.-8.
analyse
Test and analysis: according to the definition of similar terms, list the equations: |2a+ 1|= 1, |b|= 1, and solve the equations to get the values of a and b; At the same time, pay attention to the condition that a and b are negative reciprocal; Then the simplified algebraic expressions 2(a-2b2)- (3b2-a) are substituted into the values of A and B. 。
Problem analysis: According to the meaning of the question, |2a+ 1|= 1, |b|= 1,
The solution is a= 1 or 0, and b= 1 or-1.
Because a and b are reciprocal, a=- 1 and b=- 1.
The original formula =2a-8b2- b2+ a=-8.
Test site: 1. Addition and subtraction of algebraic expressions? Simplified assessment; 2. Countdown; 3. Similar projects.
22.( 1)4? 6- =24-25=- 1 1; (2)、n(n+2)-=- 1； (3) See analysis.
analyse
Test and analysis: According to several given formulas, the general law is obtained, and then the correctness is explained according to the multiplication formula of polynomial.
Problem analysis: (1)4? 6- =24-25=- 1
、n(n+2)- =- 1
(3)n(n+2)-=+2n--2n- 1 =- 1。
Test center: regular questions.
23.( 1) (a+b)？ b； (2) 14cm2。
analyse
Test and analysis: (1) According to the area formula of triangle and the side length of each quadrilateral, the area of triangle BGF can be expressed;
(2) The shadow area is equal to the area of square ABCD+the area of square CGFE-Δ -δ-△ADB-Δ -δ-△BFG, and then substitute the values of a and b to get the answer.
Problem analysis: (1) According to the meaning of the question:
△ The area of △BGF is: BG? FG= (a+b)？ b；
(2) Shadow area = area of square ABCD+area of square CGFE-δ-δ ADB-δ-δ BFG.
=a2+b2- a2- (a+b)？ b
= a2+ b2- ab
When a=4cm and b=6cm, the above formula =? 16+ ? 36- ? 4? 6= 14cm2。
Test site: 1. Column algebra; 2. Algebraic evaluation.
24. (1)10,352 points (2) 3N+ 1, 10N+56 points.
(3) 8 points
Answer: n=503
Answer: Figure 503. 10.
analyse
Test analysis: (1) The first figure has 3 black tiles+1 = 4, and the total number of black and white tiles is 3? 5 pieces;
The second figure has a black tile 3? 2+ 1=7 tiles, and the total number of black and white tiles is 5? 5 pieces;
The third figure has a black tile 3? 3+ 1= 10 tiles, the total number of black and white tiles is 7? 5 pieces;
(2) The nth figure needs 3n+ 1 black tiles, and the total number of black and white tiles is (2n+ 1)? 5 pieces;
(3) According to the fact that the white wattage may be 20 15 more than the black wattage, the equation can be listed and solved.
Problem analysis: (1) The first figure has three black cards+1 = 4, and the total number of black and white cards is 3? 5= 15;
The second figure has a black tile 3? 2+ 1=7 tiles, and the total number of black and white tiles is 5? 5=25 pieces;
The third figure has a black tile 3? 3+ 1= 10 tiles, the total number of black and white tiles is 7? 5=35 pieces;
(2) The nth figure needs 3n+ 1 black tiles, and the total number of black and white tiles is (2n+ 1)? 5= 10n+5 blocks;
(3) According to the meaning of the question, we can get:, and the solution is: n=503.
A: The 503rd number.
Test site: 1. Explore the law; 2. Column algebra and its evaluation; 3. The application of one-dimensional linear equation.