Additional mathematics Form 4
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1 Teaching & learning Additional mathematics Form 4 CHAPTER 4 NAME:. FORM : Date received : Date complete. Marks of the Topical Test :.. Prepared by : Additional Mathematics Department Sek Men Sains Muzaffar Syah Melaka For Internal Circulations Only
2 Additional Mathematics Form 4 Chapter 4 Simultaneous Equations. Solve simultaneous equations in two unknowns: one linear equation and one non-linear equation.. Solve simultaneous equations using the substitution method.. Solve simultaneous equations involving real-life situations.. Simultaneous linear and non-linear equations in two variables Step to solve the simultaneous equations i. Identify the linear equation ii. Make one of the variables the subject of the equation iii. Substitute this variable in the second equation, giving a quadratic equation in one variable. iv. Solve as a quadratic equation. Activity State whether each of the following equation are linear or non-linear equation.. y = y = 49. (y ) = 4. + y = y + y = = 5 y 7. y = 8. y = 4 9. y = + 0. y = Equation Linear/non-linear Eample Eample [ =.9, y = 0.55, = 5.4, y = -. Solve the following simultaneous equations : Solve the following simultaneous equations and give the + y = 6 answer correct to two decimal places. + y = 7 + y = 7 4y = 0
3 Eercise [Ans = - y = 5, =5 y = - ] Eercise [ = -.975, y =.7, = -0.0 y = 0.89 a) Solve the following simultaneous equations : + y = b) Solve the following simultaneous equations and give the answer correct to two decimal places. + y = 9 y = 7 y y = 9 c). + y = = 5 Ans [ y = 5, 6 y =, ] d) y + y = + y = [ ans 9. 6 =, y =, ] Homework : Tet Book Eercise 4.. page 65
4 . Solve simultaneous equations involving real-life situations Real- life problems involving two unknown can be solved as described in the following steps. Identify the two unknowns described in the given problem. Then choose a suitable letter to represent each unknown.. Form two equations using these two letters based on the information described in the problem.. Solve the simultaneous equations accordingly and obtain the final answer as required Eample Eample 4 a) Find the coordinate of the intersection points of the y curve = and the straight line + y = y b) Given that the perimeter of a rectangle is 4 cm and its area is 7 cm. Find the length and the breadth of the rectangle.[ 9 and 8 ] Eercise Eercise 4 The straight line - y = 5 intersects the curve + y + y Given that the perimeter and the area of a rectangular = 9 at point P and point Q. Find the coordinates of P and Q field are 80 m and 96 m respectively. Find the length [ P(4,-), Q (,-4) or P(,-4), Q (4,-) ] and the breadth of the field. [, 8] Homework : Tet Book eercise 4.. Page 66 4
5 SPM 00 [ = - y = 0, = -, y = 4 ] Solve the simultaneous equations 4 + y = - 8 and + y =. SPM Questions SPM 004 [ m=0.606, p =.606 m = p = ] Solve the simultaneous p - m = and p + m = 8 Give your answer correct to three decimal places. SPM 005 Solve the following simultaneous equations: + y =, y = 5 + y ( camb) [ (,-), -7/,4) Homework : Tet Book Review Eercise page 67 5
6 Enrichment eercise Simultaneous Equations (Past years SPM questions). Solve the equations 4 + y + 8 = + y =.. Solve the simultaneous equations + = 4 and + 6y = y. v cm w cm v cm Figure 4 Figure 4 shows the net of the opened bo in the shape of a cuboid. If the perimeter of the net of the bo is 48 cm and the sum of the surface area is 5 cm, find the possible value of v and w. 4. Given the curve y = 8( ) and the straight line y = 4. Without plotting a graph, calculate the intersection points for both graphs. 5. Solve the simultaneous equations + y = 9 and 6y = y y 6. Solve the simultaneous equations + = 0 and 0 + y =. 7. Solve the simultaneous equations 5 = y and y( + y) = ( + y) Given that M = y, N = + and R = y 8. Find the values of and y such that M = N = R. 9. A B E y cm Figure D 7 cm C 6
7 In figure, ABCD is a piece of paper in the shape of a rectangle with its area are 8 cm. ABE with the shape of semicircle is cut from the paper. Perimeter of the left parts are 6 cm. Find the integer values of and y.(used π = 7 ) 0. Solve the simultaneous equations below and give your answers correct to two decimal places, 4y = 9 y = 7 -. Solves the simultaneous equations 4 + y = - 8 and + y =.. Solve the simultaneous equations p m = and p + m = 8. Give your answers correct to three decimals places.. Solve the simultaneous equations + y = and y 0 =. Enrichment - Answer. =, 4 y =, 0. = 0,5 y =,. w = cm, v = 9 cm 4. (, ) and (-, - 4) 5. =, = 8 y =, y = = 9, = - 6 y =, y = 7. =, y = 8. = -, y = = 9, y = 4 9. = 4, y = 9 0. =.56, =.76 y = 0.64, y = -.. = -, - y = 0, 4. m = 0.606, p =.606, =, y = - 4, 7
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Quadratic Applications Name: Block: 3. The product of two consecutive odd integers is equal to 30 more than the first. Find the integers.
Quadratic Applications Name: Block: This problem packet is due before 4pm on Friday, October 26. It is a formative assessment and worth 20 points. Complete the following problems. Circle or box your answer.
Algebra. Topic: Manipulate simple algebraic expressions.
30-4-10 Algebra Days: 1 and 2 Topic: Manipulate simple algebraic expressions. You need to be able to: Use index notation and simple instances of index laws. Collect like terms Multiply a single term over
NATIONAL QUALIFICATIONS
Mathematics Higher Prelim Eamination 04/05 Paper Assessing Units & + Vectors NATIONAL QUALIFICATIONS Time allowed - hour 0 minutes Read carefully Calculators may NOT be used in this paper. Section A -