Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Survey

Document related concepts

Transcript

Algebra I Remediation PRESENTER: CARLA KIRKLAND NUMBER SENSE and OPERATIONS Objective 1b Use matrices to solve mathematical situations and contextual problems. (DOK 2) Understand the Following: What is a matrix? How to solve word problems How to: Add matrices, Subtract matrices, Perform Scalar Multiplication What is a Matrix? MATRIX: A rectangular arrangement of numbers in rows and columns. The ORDER of a matrix is the number of the rows and columns. The ENTRIES are the numbers in the matrix. The order of this matrix is a 2 × 3. columns rows 6 2 1 2 0 5 Multiplying a Matrix by a Scalar In matrix algebra, a real number is often called a SCALAR. To multiply a matrix by a scalar, you multiply each entry in the matrix by that scalar. 2 0 4(2) 4(0) 8 0 4 4 1 4(4) 4(1) 16 4 1 2 0 2 4 3 6 1 4 = 2 06 5 8 2 5 3 (8) 3 3 = 2 6 5 = 2(3) 2(6) 2(3) 6 6 2(5) 12 10 3. The matrices below show the different numbers of students who participated in three of the sports at two high schools. Which of the following correctly represents the sum of the numbers of students who participated in the three sports at these two high schools? MSATP Alg I, Test 1, 1b Question Number 3 Explanation: Sum of # of students add matrices Calculator Key Strokes: Enter North Brook H.S. into matrix A: x-1 2nd Pulls up matrix A to edit ENTER ENTER Assigns correct dimensions to matrix A: 3×2 ENTER 2 8 ENTER 2 3 ENTER ENTER 2 7 ENTER 1 5 ENTER 3 ENTER 3 1 2 9 2 (Enters in values of North Brook into matrix A) Enter Memorial H.S. into matrix B: 2nd 3 x-1 ENTER 2 2 ENTER Pulls up matrix B to edit Assigns correct dimensions to matrix B: 3×2 (Enters in values of Memorial H.S. into matrix B) Answer: C 2nd MODE 2nd x-1 Returns to main screen 1 + 2nd x-1 2 ENTER 2 9 ENTER 2 7 1 ENTER 5 Question Number 3 (Enters in values of North Brook into matrix A) Alternate Explanation: Enter Memorial H.S. into matrix B: Solve by hand: 2nd x-1 3 ENTER Memorial High School North Brook High School 2 2 ENTER Pulls up matrix B to edit Assigns correct dimensions to matrix B: 3×2 (Enters in values of Memorial H.S. into matrix B) + Answer: C 2nd = MODE 2nd x-1 = Returns to main screen 1 + 2nd ENTER x-1 2 ENTER 15. Matrix B is the result when matrix A is multiplied by a scalar. MSATP Alg I, Test 1, 1b Question Number 15 Explanation: There is a real number x, that when x is multiplied by A, the result is B, So, to find y, use proportions: 6 48 4th entry from A y 4th entry from B 1st entry from B 4 1st entry from A (cross multiply) 6y = -48(-4) 6y 192 6 6 y = 32 Answer: A ×A MSATP Alg I, Test 1, 1b Question Number 32 Explanation: Calculator Key Strokes: 2nd 2 x-1 ENTER Pulls up matrix A to edit ENTER 2 ENTER Assigns 2 × 2 dimensions to A (Enter values from L into A) 2nd 2 x-1 ENTER Pulls up matrix B to edit 2 2 ENTER Assigns 2 × 2 dimensions to B (Enter values from M into B) 2nd MODE 2nd x-1 Answer: D Returns to main screen 1 – 2nd x-1 2 ENTER Computes A-B (or L-M) 2 2 ENTER ENTER Assigns 2 × 2 dimensions to A (Enter values from L into A) Question Number 32 2nd x-1 Alternate Explanation: 2 ENTER Solve by hand: 2 Pulls up matrix B to edit 2 ENTER Assigns 2 × 2 dimensions to B (Enter values from M into B) 2nd 2nd Returns to main screen MODE – x -1 Answer: D = = 1 – 2nd x -1 2 ENTER Computes A-B (or L-M) 43. What values of x, y, z, and w make this matrix equation true? MSATP Alg I, Test 1, 1b Question Number 43 Explanation: The situation is this: A + C = B Which is the same as: A – B = -C Let A = 4 3 -2 7 and B= 5 -2 7 3 Calculator Key Strokes: 2nd 2 x-1 ENTER 2 ENTER Pulls up matrix A to edit ENTER Assigns dimensions to A 2 Pulls up matrix B to edit ENTER Assigns dimensions to B (Enter values for A) 2nd 2 x-1 ENTER 2 (Enter values for B) 2nd MODE 2nd x-1 Returns to main screen 1 -1 5 -9 4 -C = – 2nd 1 -5 C= 9 -4 x = 1, y = -5, z = 9, w = -4 Answer: B x-1 2 ENTER Computes A-B Question Number 43 Alternate Explanation: Solve by Hand: The situation is this: A + C = B Which is the same as: A – B = -C Let A = 4 3 -2 7 4 3 -2 7 -C = = C= Answer: B – and 5 -2 7 3 B= = 5 -2 7 3 -C 6. Matrices A and B are shown below. MSATP, Alg I, Test 2, 1b Question Number 6 Chooses Matrix A to edit Explanation: Calculator Key Strokes: x-1 2nd Enters dimensions for Matrix A 3 ENTER ENTER 3 ENTER (Enter in values for Matrix A) x-1 2nd 3 ENTER Chooses Matrix B to edit 2 3 Enters dimensions for Matrix B ENTER (Enter in values for Matrix B) 2nd 2 Answer: H 2nd MODE x-1 1 + 2nd x-1 2 ENTER Evaluates 2A+B Question Number 6 Alternate Explanation: Solve by hand: + Question Number 6 Chooses Matrix A to edit Explanation: = Calculator Key Strokes: 2nd + x-1 Enters dimensions for Matrix A 3 ENTER ENTER 3 ENTER (Enter in values for Matrix A) x-1 2nd = Chooses Matrix B to edit 2 + 3 ENTER 3 Enters dimensions for Matrix B ENTER (Enter in values for Matrix B) = 2nd 2 Answer: H 2nd MODE x-1 1 + 2nd x-1 2 ENTER Evaluates 2A+B 36. Andrew plans to buy 3 T-shirts and 3 sweaters. The price in dollars, including tax, of each T-shirt and sweater is shown in matrix C. The store is offering a 15% discount on all the items. Andrew determined the sale price of each item as shown in the matrix below. Which operation justifies the sale price of each item he plans to buy? MSATP, Alg I, Test 2,1b Question Number 36 Explanation: Notice there is no need to enter in matrix values, etc., because this is simply a matter of understanding “% discount” Cost is given (c) “15% discount” means: find 15% of cost 0.15C Subtract (15% of cost) from the cost (c) C – 0.15c Answer: H 24 Matrix R is shown below. Which matrix represents -6R? MSATP Alg I, Test 3, 1B Question Number 24 Explanation: Multiply each element in Matrix R by -6. Answer: G Alternate Explanation: Solve by hand: = =Question Number 24 Explanation: Multiply each element in Matrix R by -6. Answer: G