EP Grade 6 Mathematics: Algebraic expressions and Like terms a k m

Transcription

1 Name Class Number: _ Date EP Mathematics: Algebraic expressions and Like terms Algebraic and numerical expressions Numerical expressions Numbers and operation signs (eg. +, -, x, ) Algebraic expressions Numbers, operation signs AND variables! (letters) 1. Are these numerical or algebraic expressions? Copy these expressions into the correct column a k m y + a 5w-4 3 y Numerical expressions Algebraic expressions 2. Make your own numerical and algebraic expressions. Algebraic expressions have variables in them. Numerical Expressions Algebraic Expressions Test Math Worksheet 1

2 Like terms Like terms Like Like terms have have the the same same variable (letter), or or they they just just have have a a number only. only. For For example: 5x 5x and and 30x 30x are are like like terms because they they both both have have the the variable x. x. 2y 2y and and y y are are like like terms because they they both both have have the the variable y. y and and are are like like terms because they they are are both both just just numbers they they don t don t have have a a variable with with them. 3. Draw a line to match up the like terms. One has been done already for you. 15x 3b 7 5m 6y 90 k -3y 15k -6 x 8 5b 90m 4. Write your own algebraic expressions. (hint: use numbers and variables) a. b. c. d.

3 Name: Class: Date: Number: Draw a cube. Draw the net of a cube. How many faces, vertices, and edges does it have? Draw a cuboid. Draw the net of a cuboid. How many faces, vertices, and edges does it have? Draw a triangular prism. Draw the net of a triangular prism. How many faces, vertices, and edges does it have? Test Maths Worksheet 10

4 Name: Class: Date: Number: Draw a tetrahedron. Draw the net of a tetrahedron. How many faces, vertices, and edges does it have? Draw a square pyramid. Draw the net of a square pyramid. How many faces, vertices, and edges does it have? Draw an octahedron. Draw the net of an octahedron. How many faces, vertices, and edges does it have?

5 Name Class Number: _ Date EP Mathematics: Writing algebraic expressions Addition and Subtraction Here are some rules to follow when adding and subtracting. You cannot combine the number and the variable if they are not like terms. eg. Add 16 and m. We write this as 16 + m, NOT 16m. When writing an algebraic expression, it does not need an equal sign (=). 1. Write an algebraic expression for each of these questions below. a) Add n and 64 b) Add 5 to n c) Subtract 12 from n d) 5 less than n e) Subtract n from 20 f) Find the sum of n and 18 Test Math Worksheet 2

6 2. Write algebraic expressions for these word problems. a) Danny spent 500 baht on a meal. Anna spent y baht less than that. Express the amount of money that Anna spent in terms of y. b) Tammy is 10 years old. Her sister is x years younger than her. Express Tammy s sister s age in terms of x. c) John weighs 42 kg this month. He was z kg heavier last month. Express his weight last month in terms of z. d) Cathy is m years old now. Express her age 3 years ago in terms of m. e) Cathy is m years old now. Express her age 4 years from now in terms of m. Did you check your answers?

7 Name Class Number: _ Date EP Mathematics: Writing algebraic expressions Multiplication The rules for multiplication: Hide the multiplication sign! eg. 16 x m = 16m = 3 x 6 so g + g + g = 3 x g = 3g For multiplication, the number sits before the variable. eg. m x 16 = 16m, NOT m16. When writing an algebraic expression, it does not need an equals sign (=). 1. Answer these questions for multiplication. a) 3w= x b) 70y = x. c) 4h means groups of. d) 12 times p is. 2. Write an algebraic expression for each of these questions below. a) Multiply 4 and n b) Multiply 5 and n c) n times 6 d) n + n + n e) 14 groups of n f) n + n + n + n + n Test Math Worksheet 3

8 3. Write algebraic expressions for these word problems. a) Sally is 4 times older than her cousin. Her cousin is n years old now. What is Sally s age in terms of n? b) Danny bought 4 boxes of doughnuts. There were p doughnuts in each box. Express the total number of doughnuts Danny bought in terms of p. c) 3 students spent k baht each. How much did they spend altogether? Answer in terms of k.

9 Name Class Number: _ Date EP Mathematics: Writing algebraic expressions Division The rules for division: Write divisions as a fraction. eg. 3 m = m 3 When writing an algebraic expression, it does not need an equals sign (=). 1. Answer these questions for division. 3 x a) =. c) =. y y k 150 b) =. d) =. 6 m 2. Write an algebraic expression for each of these questions below. a) Divide 56 by n. b) n divided by 12. c) n dollars shared amongst 5 people. d) 256 n e) n split into 50 parts Test Math Worksheet 4

10 3. Write algebraic expressions for these word problems. a) There were y students in a class. They were split equally into groups of 6. How many students were in each group? Write your answer in terms of y. b) Alfred had $m. He was able to buy 4 pens with the money, without any change leftover. How much was each pen? Write your answer in terms of m. c) There were b students in a class. In one day, 14 students in the class received Top Boy Tickets. What fraction of the class received a Top Boy Ticket? Answer in terms of b.

11 Name Class Number: _ Date EP Mathematics: Simplifying Algebraic Expressions Mixed Expressions More rules for simplifying! The operation sign (+, -, x, ) belongs to the variable or number that comes after it. eg. 5y y - 2 = + 5y y - 2 = + 5y + 6y = 11 y 5 Which of these is correct when we simplify: 1. 8x - 2y x 9 (a) 13x - 2y - 1 (b) 3x - 2y + 1 (c) 23x 2y - 9 (d) 13x 2y d 3 + 5d + 2f -f (a) 11d + 3f -3 (b) 9d + 4f -3 (c) 17d + f -3 (d) 3d + 3f g 13-5g + 4z -2z (a) 27g + 6z -13 (b) 17g - 2z +13 (c) 12g + 2z -3 (d) 17g + 2z -13 Test Math Worksheet 5

12 4. Simplify these algebraic expressions. a) 5r + 2r + 2 = b) 7s 3s + 3 = c) 5t + 3t + 3 = e) 4v v + 5 = g) x = i) 3 + 6z + 4z = d) 8u + 3u 3 = f) 10w 6 5w = h) 4y y 1= j) 11a 6a + 6 = 5. Simplify these algebraic expressions. a) 8c + 2c + 6s + 4s = c) 14f 2 + 6f 4 = e) 7m + 5 2m + 8 = g) 3 + 2q u = b) 13f 2f + 3g + 7g = d) 9p + 3w 6p + 4 = f) 9h + 6h = h) 7g + 3d 5g + 12d 6 =

13 Name Class Number: _ Date Name ALGEBRA VOCABULARY Word Meaning Example Algebra Variable In algebra, we use letters numbers. We do this because sometimes we don t know a number or the number can change. A variable is the we use. The number of boys who will be in Time Out next Monday will be t boys. Mr. Matt is b years old. Tomorrow the temperature will be x C. Ms. Alyson is x years old. The variable is x. John can hold his breath for y seconds. The variable is y. Value A value is an number. 3 x 2 = 6 the value of the numerical expression is 6. Like terms Like terms have the same 13a and 5a are like terms, or they just because they both have have a number only. the variable a. 15 and 364 are like terms because they are both numbers (or coefficients) they don t have a variable. Numerical Expression A numerical expression has numbers and X 130 Algebraic Expression Simplify Substitute Evaluate An algebraic expression has _, operation signs and variables. When we combine the terms. When we substitute, we the variable to a number. When we evaluate, we find the value of an algebraic expression. We do this by (changing) the variable to get a final answer. 5x + 6y 5x 2 4x 3d + 4d = 7d 5w -2w = 3w If x = 5, 15 + x = If x = 5, 15 + x = = 20 change letter variable like instead of numbers substituting operation signs exact Use these words to fill in the blanks. Test Math Worksheet 6

14 Name Class Number: _ Date EP Mathematics: Base Angles of an Isosceles Triangle Remember: The base angles are the angles opposite the sides of equal length! AB = BC So the base angles are BAC and BCA because they are opposite the sides that are equal in length (AB and BC). So BAC = BCA. 1. Circle the base angles for these isosceles triangles. a) b) A A C B C B c) d) A 5m A 12cm B 5m C 6m 12cm B 14cm C 2. Mark the sides that are equal in length for these isosceles triangles. a) b) A A B C B C Test Math Worksheet 7

15 3. Using your knowledge of the base angles of isosceles triangles, find the missing angles for these triangles. a) Find z. b) Find y. A z y c) Find x. d) Find w. 40 w x e) Find v. f) Find u. 70 v 80 u Test Math Worksheet 7

16 Name Class Number: _ Date EP Mathematics - Exterior Angles of a Triangle. An exterior angle of a triangle is equal to the sum of the twointerior opposite angles. 1. Find the angle of x for each of these questions and show your answer like the example above. a)l x = b) x = c) x = d) x = A C B D J I L K E G F H 2. Write down the two interior opposite angles for these external angles. a. A: and b. D: and c. F: and d. G: and Test Math Worksheet 8

17 Name Class Number: _ Date EP Mathematics - Angles in geometric figures Answer Answer Answer Answer Test Math Worksheet 9

18 5. Answer Test Math Worksheet 9

19 Test Math Worksheet 9