GRADE 12 FINAL ASSESSMENT PAPER 1 NOVEMBER 2016 TOTAL: 150. TIME: 3 hours

Transcription

1 - - GRADE FINAL ASSESSMENT PAPER NOVEMBER 06 TOTAL: 50 TIME: 3 hours

2 - - INSTRUCTIONS. This question paper consists of 0 questions.. Answer all the questions. 3. Clearly show all calculations used to solve problems. 4. You may use an approved scientific calculator, unless stated otherwise. 5. If necessary, round off answers correct to two decimal places. 6. Diagrams are not necessary drawn to scale. 7. Number the answers according to the questions. 8. Write neatly and legibly.

3 - 3 - QUESTION. Solve for.. ( + 7)( ) = 4 (4) = 0, correct to two decimal places. (4) = (4)..4 3< 0 () 3 ( )...5 = (4). Simplify the following without using a calculator For which value(s) of p will = p + (3) have real roots? (5) [6] QUESTION. If S n = 5n + n calculate the third term in the sequence. (3) 3 +. A series is convergent and the sum to infinity is. Find the value(s) of correct to decimal places. (3) 9 m+ ( ).3 is given. m m= 0.3. How many terms are there in the series? ().3. Calculate the first three terms. () 9 m+ ( ).3.3 Find the value of correct to decimal places. m (3) m= 0.4 Calculate the sum of all the whole numbers from to 00 that will be multiples of 5. (4) [7] QUESTION 3: 3. The sequence 6 ; 7 ; ; 57 ; forms a quadratic pattern. 3. Calculate the value of (3) 3. Determine the nth term in this pattern. (4) [7]

4 - 4 - QUESTION 4: Determine the equation of the function f. (3) 4.. Calculate the coordinates of D, the turning point of f. () 4..3 For which value(s) of p will f ( ) = p have equal roots? (3) 4..4 If the equation of CE is g ( ) = 4+ 8, for which value of will AC have a maimum length? (3) 4. The sketch represents ( ) a and ( ) = ; 0 f = k g. 4.. Calculate the values of a and k. (4) 4.. Find the equation of h if h is a reflection of g in y =. (3)

5 Write down the equation of f in the form =... y () 4.3 A function f ( ) = b +p + 4 goes through the points (;6) and (3;8) Find the values of b, p and q. (4) 4.3. Write down the domain for f. () Determine the range for f ( ) 5. () If g ( ) = a + b+ c goes through the same point with y = 8 the maimum value for g, calculate the values of a, b and c. (4) [3] QUESTION 5: 5 5. Convert a rate of 8% p.a. compounded quarterly to an effective annual rate. (3) 5. An amount of R5 000 is invested on January the first. At the beginning of April, R 000 is added to the investment and another R 000 is deposited at the beginning of October. The interest rate is 4% p.a. compounded monthly. Calculate the value of the investment at the end of the year. (5) 5.3 R4 500 is invested for 0 years. The first two years the interest rate was % p.a. The rate then changes to % p.a. compounded monthly for the net three years and to 4% p.a. compounded quarterly for the final five years. Calculate the final amount paid out at the end of the 0years. (7) [5] QUESTION 6: 6. Find f '( ) using first principles if f ( ) =. (5) 4 6. Calculate D z ( z + ). (3) 4 z 3 dy Find if y=. (4) d [] VRAAG 7: 3 7. The sketch representsf ( ) = m + n+ p.

6 Calculate the values of m, n and p. (4) 7. For which value(s) of will f ( ) < 0? () 7.3 For which value(s) of will f be decreasing? () 7.4 For which value(s) of will f have an point of inflection? (3) [] QUESTION 8: 8. The volume of a cylinder is calculated by V = πr h and the surface area using S = π r( r+ h) If S = 54π, show that V =π (7r r ). (4) 8. For which value of r will the cylinder have a maimum volume? (3) 8.3 Calculate the maimum volume for the cylinder. (3) [0] QUESTION 9: 9. Use the name ANASTASIA to answer the following questions: 9.. How many different ways can the letters in the word ANASTASIA be written? () 9.. How many different ways can the letters in the word ANASTASIA be written if the first letter must be T? () 9..3 How many different ways can the letters in the word ANASTASIA be written if the first letter must be S? () 9. In a bag we have 5 red balls and 8 green balls. A ball is taken from the bag but a second ball is taken without replacing the first ball. Use a tree diagram to determine the probability of getting two red balls. (4) [0 0] QUESTION 0: 0. If for any two events A and B, is given that P(A) = 0,45, P(B) = 50% and P(A B) = 0,5.

7 Draw a Venn diagram to represent the given information. (4) 0. Calculate the following: 0.. P(A B) (4) 0.. P(A B') () [0] TOTAL: 50