(iii) r. (6) (Total 6 marks)

Transcripción

1 TALLER DE REPASO MATEMÁTICAS K11 Importante: Trabaja en forma organizada. Los problemas aparecen en Inglés, pero son de fácil comprensión. Sin embargo, en tu cuaderno tienes suficientes problemas y ejercicios para estudiar. Expresa tus respuestas de manera clara, utilizando tres cifras significativas, siempre que sea posible. No olvides llevar tu calculadora graficadora y baterías con carga suficiente, tu Cuadernillo de Fórmulas del IB, papel milimetrado y los elementos necesarios para trabajar. Recuerda que durante el Examen no se puede consultar material distinto del Examen o del cuadernillo, ni prestar o intercambiar útiles. 1. El siguiente grafico es un diagrama de caja y bigotes. El rango intercuartílico es 20 y el rango es 40. (a) Escriba el valor de la mediana. (b) Encuentre el valor de (i) a; (ii) b. (4) (Total 5 marks) 2. La gràfica de y = p cos qx + r, para 5 x 14, se muestra a continuación. Hay un punto mínimo en (0, 3) y un punto máximo en (4, 7). (a) Encuentre el valor de (i) p; (ii) q; (iii) r. (6) IB Questionbank Maths SL 1

2 3. (a) Factorize the expression 3 sin 2 x 11 sin x + 6. (b) Consider the equation 3 sin 2 x 11 sin x + 6 = 0. (i) Find the two values of sin x which satisfy this equation, (ii) Solve the equation, for 0 x The diagram below shows a quadrilateral ABCD. AB = 4, AD = 8, CD =12, B Ĉ D = 25, B ÂD =. (a) Use the cosine rule to show that BD = 4 5 4cos. (2) Let = 40. (b) (i) Find the value of sin C Bˆ D. (ii) Find the two possible values for the size of C Bˆ D. (iii) Given that C Bˆ D is an acute angle, find the perimeter of ABCD. (12) (c) Find the area of triangle ABD. (2) (Total 16 marks) 5. In a school of 88 boys, 32 study economics (E), 28 study history (H) and 39 do not study either subject. This information is represented in the following Venn diagram. IB Questionbank Maths SL 2

3 U (88) E (32) H (28) a b c 39 (a) Calculate the values a, b, c. (4) (b) A student is selected at random. (i) (ii) Calculate the probability that he studies both economics and history. Given that he studies economics, calculate the probability that he does not study history. (3) (c) A group of three students is selected at random from the school. (i) Calculate the probability that none of these students studies economics. (ii) Calculate the probability that at least one of these students studies economics. (5) (Total 12 marks) 6. The graph of a function of the form y = p cos qx is given in the diagram below y /2 x (a) Write down the value of p. (b) Calculate the value of q. IB Questionbank Maths SL 3

4 7. The following frequency distribution of marks has mean 3.6. Mark Frequency x 8 4 (a) Find the value of x. (4) (b) Write down the standard desviation. (2) 8. Solve the equation 3 sin 2 x = cos 2 x, for 0 x 180. (Total 4 marks) 9. A box contains 100 cards. Each card has a number between one and six written on it. The following table shows the frequencies for each number. Number Frequency k (a) Calculate the value of k. (2) (b) Find (i) the median; (ii) the interquartile range. (5) (Total 7 marks) 10. Given that sin x = 3 1, where x is an acute angle, find the exact value of (a) cos x; (b) cos 2x. 11. A test marked out of 100 is written by 800 students. The cumulative frequency graph for the marks is given below. IB Questionbank Maths SL 4

5 (a) Write down the number of students who scored 40 marks or less on the test. (2) (b) The middle 50 % of test results lie between marks a and b, where a < b. Find a and b. (4) 12. The following diagram shows a triangle ABC, where A ĈB is 90, AB = 3, AC = 2 and B ÂC is. (a) Demuestre que sin = (b) Demuestre que sin 2 = (c) Find the exact value of cos 2. IB Questionbank Maths SL 5

6 13. The following is the cumulative frequency curve for the time, t minutes, spent by 150 people in a store on a particular day cumulative frequency time ( t) (a) (i) How many people spent less than 5 minutes in the store? (ii) Find the number of people who spent between 5 and 7 minutes in the store. (iii) Find the median time spent in the store. (6) (b) Given that 40 of the people spent longer than k minutes, find the value of k. (3) (c) (i) On your answer sheet, copy and complete the following frequency table. t (minutes) 0 t 2 2 t 4 4 t 6 6 t 8 8 t t 12 Frequency (ii) Hence, calculate an estimate for the mean time spent in the store. (5) (Total 14 marks) IB Questionbank Maths SL 6

7 14. The number of hours of sleep of 21 students are shown in the frequency table below. Hours of sleep Number of students Find (a) (b) (c) the median; the lower quartile; the interquartile range. 15. Two fair 4-sided dice, one red and one green, are thrown. For each die, the faces are labelled 1, 2, 3, 4. The score for each die is the number which lands face down. (a) List the pairs of scores that give a sum of 6. (3) The probability distribution for the sum of the scores on the two dice is shown below. Sum Probability p q r 1 16 (b) Find the value of p, of q, and of r. (3) Fred plays a game. He throws two fair 4-sided dice four times. He wins a prize if the sum is 5 on three or more throws. (c) Find the probability that Fred wins a prize. (6) (Total 12 marks) 16. The histogram below represents the ages of 270 people in a village. IB Questionbank Maths SL 7

8 (a) Use the histogram to complete the table below. Age range Frequency Mid-interval value 0 age age age age age 100 (2) (b) Hence, calculate an estimate of the mean age. (4) 17. The diagram below shows the probabilities for events A and B, with P(A ) = p. IB Questionbank Maths SL 8

9 (a) Write down the value of p. (1) (b) Find P(B). (3) (c) Find P(A B). (3) (Total 7 marks) 18. The letters of the word PROBABILITY are written on 11 cards as shown below. Two cards are drawn at random without replacement. Let A be the event the first card drawn is the letter A. Let B be the event the second card drawn is the letter B. (a) Find P(A). (1) (b) Find P(B A). (2) (c) Find P(A B). (3) 19. If A is an obtuse angle in a triangle and sin A = 13 5, calculate the exact value of sin 2A. (Total 4 marks) 20. Two boxes contain numbered cards as shown below. Two cards are drawn at random, one from each box. (a) Copy and complete the table below to show all nine equally likely outcomes. 3, 9 3, 10 3, 10 (2) Let S be the sum of the numbers on the two cards. IB Questionbank Maths SL 9

10 (b) Write down all the possible values of S. (2) (c) Find the probability of each value of S. (2) (d) Find the expected value of S. (3) (e) Anna plays a game where she wins $50 if S is even and loses $30 if S is odd. Anna plays the game 36 times. Find the amount she expects to have at the end of the 36 games. (3) (Total 12 marks) 21. There are 20 students in a classroom. Each student plays only one sport. The table below gives their sport and gender. Football Tennis Hockey Female Male (a) One student is selected at random. (i) (ii) Calculate the probability that the student is a male or is a tennis player. Given that the student selected is female, calculate the probability that the student does not play football. (4) (b) Two students are selected at random. Calculate the probability that neither student plays football. (3) (Total 7 marks) 22. Given that sin θ = 2 1, cos θ = 2 3 and 0 θ 360, (a) find the value of θ; (b) write down the exact value of tan θ. 15. Las calificaciones de diez estudiantes en sus exámenes coordinados de Matemáticas y Biología aparecen en la siguiente tabla: Matemáticas (x) Biología (y) (Total 4 marks) (a) Escriba la recta de regresión lineal de x sobre y. (b) Estime la calificación en Biología de quien haya obtenido 4 en Matemáticas. LAS RESPUESTAS A ESTOS EJERCICIOS SE PUBLICARAN PROXIMAMENTE!!! IB Questionbank Maths SL 10