Alameda Unified School District. Grade 7. Benchmark 3 Study Guide

Transcription

1 Alameda Unified School District Grade 7 Benchmark Study Guide

2 1 Simplify: + ( 8 1) 1 Benchmark Study Guide Simplify: 7 + 7( 4) AF 1./6.EE.c Use the distributive property to write an equivalent expression for 8 x + 7 ( ). ( ) ( ) + 8( 7) 8 x x 4x + 6 Use the distributive property to write an 7 x + 8. equivalent expression for ( ) AF 1./6.EE. Simplify the expression by combining like terms. 7b + 6b b + 10b ( ) + 6b + b 7b + 10b ( ) + ( 8 ) Simplify the expression by combining like terms: 6x + x + x 9x 7 b + 9b + AF 1./7.EE.1 Page 1 of 11 MCC@WCCUSD (AUSD) 0/01/1

3 Benchmark Study Guide 4 Find the missing side of the right triangle. 4 4 ft x A flagpole forms a 90 angle with the ground. The flagpole is 1 feet tall and casts an 8 foot shadow on the ground. How far is it from the top of the flagpole to the end of its shadow? ft In a right triangle, a + b c. In the right triangle above, a can be either ft or 4 ft, and b will be the other side length. a + b c ( ) + ( 4) c c c c The missing side of the right triangle is feet. c MG./8.G.7 Find the average: 6,, 4, 7, ( ) ( 1) NS 1./6.SP. Find the average:, 7, 8, 9,, 10 6 Solve: 1x x 1 7 1x x 7 1x x 6 Solve: 8x 1 44 AF 4.1/A.REI. Page of 11 MCC@WCCUSD (AUSD) 0/01/1

4 Benchmark Study Guide 7 What is the prime factorization of 6x y? 6x y x x x y y 7 What is the prime factorization of 4a b c 4? NS 1./N.RN. 8 What is the Least Common Multiple (LCM) of 18 and 4? Use prime factorization: 8 What is the Least Common Multiple of 14 and? 18 4 Use Bubble method: Put first set of factors in the bubble. Put factors from second set in the bubble that are not already in. Multiply prime factors in the bubble to get the LCM. NS./.NF.1 Page of 11 MCC@WCCUSD (AUSD) 0/01/1

5 Benchmark Study Guide 9 Simplify: 7x y z 1xy 4 z 7x y z 1xy 4 z 7 x x y y y z 7 x y y y y z x y 9 Simplify: 1a b c 6a b c AF.1/N.RN. 10 Simplify: Simplify: 7 NS./N.RN. 11 Find the unit rate: apples for $.0 11 $.0 apples $.0 apples $.0 apple The unit rate is $.0 per apple. Find the unit rate: 1 cupcakes for $6.00 MG 1./6.RP.b Page 4 of 11 MCC@WCCUSD (AUSD) 0/01/1

6 1 Solve the equation: x 7 x 7 x 7 x 7 1 Benchmark Study Guide Solve: c x 7 or 1 AF 4.1/6.EE.7 1 Use the circle below and.14 for π. What is the circumference of the circle? C πr ( )(.14)( in. ) ( )( in. )(.14) ( 6 in. )(.14) in. 1 What is the circumference of the circle? Use.14 for π. The circumference of the circle is inches. MG.1/7.G.4 14 What is the m 1 when the m 110? 14 You try: 1 and are supplementary angles, and therefore, their measures add up to 180. Determine the measure of angle x. m 1 ( ) m 1 70 MG.4/7.G. Page of 11 MCC@WCCUSD (AUSD) 0/01/1

7 1 Graph the function: y x 1 Benchmark Study Guide Which function matches the graph below: 1) To graph the function y x, graph the mother function with a vertical phase shift of -. Instead of the vertex at (0,0), the vertex is at (0,-). ) Or choose values for x and solve for y to determine ordered pairs that represent points on the parabola. Plot the points and graph the parabola. x y (x,y) - (-, ) -1-1 (-1, -1) 0 - (0, -) 1-1 (1, -1) (, ) A) y x + 1 B) y x 1 C) y x 1 D) y x + 1 AF.1/F.IF.7 ( ) 4 ( xy) 7 16 Simplify xy 4 7 ( xy) ( xy) 7 1 ( xy) 4 ( xy) 1 7 ( xy) 4 ( xy) ( xy)( xy)( xy)( xy)( xy)( xy)( xy) ( xy)( xy)( xy)( xy) ( xy) x y ( xy) 4 xy ( ) ( ) xy xy x y ( ) 7 16 xy xy Simplify: ( ) ( ) AF./N.RN. Page 6 of 11 MCC@WCCUSD (AUSD) 0/01/1

8 Benchmark Study Guide 17 Solve the percent problem: What is 1% of 60? x x 100 x 17 What is 0% of 10? x 9 1 x 9 1% of 60 is 9. NS 1./7.RP. 18 If $00.00 is invested at 4%simple interest for years, how much interest is earned? I Simple Interest P principal (amount invested or borrowed) r rate (convert to decimal or fraction) t time in years 18 If $ is invested at % simple interest for years, how much interest is earned? I P r t 4 I ( 00) ( ) I 100 I 60 $60.00 is earned in interest. AF 1.7/7.RP. ( ) ( ) ( )( a + b) ( )( a) + ( ) ( b) ( ) + ( b) 19 Simplify: 7 a + b 7 a + b a 7 a b a b ( a + b) ( a) ( b) 7 a b a b Simplify: 4( a b) AF 1./6.EE. End of Study Guide Page 7 of 11 MCC@WCCUSD (AUSD) 0/01/1

9 Benchmark Study Guide 1 You Try Solutions: Simplify: 7 + 7( 4) ( 9 4) ( ) ( ) Use the distributive property to write an 7 x + 8. equivalent expression for ( ) 7 7 ( x + 8) ( x) + 7( 8) 14x + 6 Simplify the expression by combining like terms: 6x + x + x 9x 7 ( 6x 9x ) + ( x + x) + ( 7) 1x + 7x 10 4 A flagpole forms a 90 angle with the ground. The flagpole is 1 feet tall and casts an 8 foot shadow on the ground. How far is it from the top of the flagpole to the end of its shadow? In a right triangle, a + b c. In the right triangle above, a can be either 1 ft or 8 ft, and b will be the other side length. a + b c ( 8) + ( 1) c 64 + c 89 c c The missing side of the right triangle is 17 feet. flagpole 1 ft Find the average:, 7, 8, 9,, 10 + ( 7) ( 9) + + ( 10) ( 6) ? ft 8 ft shadow 6 c Page 8 of 11 MCC@WCCUSD (AUSD) 0/01/1

10 Benchmark Study Guide Solve: 8x x x 6 8x x 7 Simplify: 1a b c 6a b c 1 a a b b b b b c c a a b b b c 1 b b c b c What is the prime factorization of 4a b c 4? 4a b c 4 a a a b b c c c c 10 Simplify: 7 8 What is the Least Common Multiple of 14 and? Use prime factorization: Use Bubble method: Put first set of factors in the bubble. Put factors from second set in the bubble that are not already in. Multiply prime factors in the bubble to get the LCM. LCM Find the unit rate: 1 cupcakes for $6.00 $ cupcakes $ cupcakes $0.0 cupcake 1 1 The unit rate is $0.0 per cupcake. Page 9 of 11 MCC@WCCUSD (AUSD) 0/01/1

11 Benchmark Study Guide 1 1 Solve: c c 1 10 c c or Which function matches the graph below: 1 What is the circumference of the circle? Use.14 for π. A) y x + 1 B) y x 1 C) y x 1 D) y x C πr C C (.14)( 7 feet) ( 6.8)( 7 feet) C 4.96 feet You try: Determine the measure of angle x. 1) The graph is a parabola that is related to the father function. This tells us that it is quadratic and that the leading coefficient of the first term is negative ( y x ). It also has a vertical phase shift of +1, so instead of the vertex being at (0,0) it is now at (0,1). Which means the equation is y x + 1. The answer is D. These angles are complementary angles, and therefore, their measures add up to x x 90 0 x 40 Page 10 of 11 MCC@WCCUSD (AUSD) 0/01/1

12 Benchmark Study Guide xy xy Simplify: ( ) ( ) ( xy) ( xy) 1 ( xy) ( xy) 1 ( xy) ( xy) ( xy)( xy)( xy) ( xy)( xy) xy What is 0% of 10? ( xy) ( xy) + ( xy) 1 ( xy) xy 0 x ( 10) x 100 x x 0 19 If $ is invested at % simple interest for years, how much interest is earned? I Simple Interest P principal (amount invested or borrowed) r rate (convert to decimal or fraction) t time in years I P r t I ( 700) ( ) I 100 I 4 $4.00 is earned in interest. Simplify: 4( a b) ( b) ( 4) ( a + ( b) ) ( 4)( a) + ( 4)( b) ( 8a) + 1b 8a + 1b 8a + 1b + a 4( a b) 4( a) 4( b) 8a + 1b 8a + 1b + Page 11 of 11 MCC@WCCUSD (AUSD) 0/01/1

13 Third Trimester Study Guide Answer Key QUESTION ANSWER STANDARD 1) 168 AF 1./6.EE.c ) 14 x + 6 AF 1./6.EE. ) 1x + 7x 10 AF 1./7.EE.1 4) 17 feet MG./8.G.7 ) NS 1./6.SP. 6) x 7 AF 4.1/A.REI. 7) a a a b b c c c c NS 1./N.RN. 8) 70 NS./.NF.1 9) b c AF.1/N.RN. 10) NS./N.RN. 11) $.0 / cupcake MG 1./6.RP.b 1) c 10 9 or AF 4.1/6.EE.7 1) 4.96 ft MG.1/7.G.4 14) 40 MG.4/7.G. 1) D AF.1/F.IF.7 16) xy AF./N.RN. 17) 0 NS 1.7.RP. 18) $4.00 AF 1.7/7.RP. 19) 8a + 1b + AF 1./6.EE.