IB MATH STUDIES. Summer Review Packet for Students. Richard Montgomery High School

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1 IB IB MAH SUDIES Summer Review Packet for Students he problems in the packet are designed to help you review topics from Algebra 2 and Pre-Calculus that are important to your success in IB Math Studies. Please attempt the problems on your own without any notes and SHOW ALL WORK! When you come across topics that require a little review, feel free to look at your old notes, search a website or ask a friend for help. If you want to check your work with a calculator, that is fine also. Bring the finished packet with you to your Math Studies class on the first day of school. You will be assessed on these skills during the first week of school as part of your 1st quarter grade. Enjoy your summer! We are looking forward to seeing you in August. If you have any questions, please contact the math Resource eacher: Laura_D_Goetz@mcpsmd.org Richard Montgomery High School

2 1. Solve the problems below: A girl s height is m. Write her height to the nearest cm. he time taken to fill a tank was 2 hours 43 minutes. Write this time to the nearest 5 minutes. (c) he attendance at a show was 2591 people. How many people, to the nearest 100, were at the show? (d) he mean distance of the Moon from the Earth is approximately km. Write this distance in the form a 10 k where 1 a < 10 and k. 2. he sets A, B and C are subsets of U. hey are defined as follows: U = {positive integers less than 16} A = {prime numbers} B = {factors of 36} C = {multiples of 4} List the elements (if any) of the following: (i) A; (ii) B; (iii) C; (iv) A B C. (i) Draw a Venn diagram showing the relationship between the sets U, A, B and C. (ii) Write the elements of sets U, A, B and C in the appropriate places on the Venn diagram. (c) rom the Venn diagram, list the elements of each of the following (i) (ii) A (B C); (A B) ; (iii) (A B) C.

3 (d) ind the probability that a number chosen at random from the universal set U will be (i) a prime number; (ii) a prime number, but not a factor of 36; (iii) a factor of 36 or a multiple of 4, but not a prime number; (iv) a prime number, given that it is a factor of he perimeter of this rectangular field is 220 m. One side is x m as shown. W m Express the width (W) in terms of x. x m (c) Write an expression, in terms of x only, for the area of the field. If the length (x) is 70 m, find the area. 4. he diagram shows the graph of y = x 2 2x 8. he graph crosses the x-axis at the point A, and has a vertex at B. y A O x B actorize x 2 2x 8. Write down the coordinates of each of these points (i) A; (ii) B.

4 5. Solve the problems below: Solve the equation x 2 5x + 6 = 0. ind the coordinates of the points where the graph of y = x 2 5x + 6 intersects the x- axis. 6. Solve the problems below: Represent the function y = 2x 2 5, where x { 2, 1, 0, 1, 2, 3} by a mapping diagram. x y List the elements of the domain of this function. (c) List the elements of the range of this function. 7. hree propositions are defined as follows: p: he oven is working. q: he food supply is adequate. r: he visitors are hungry. Write one sentence, in words only, for each of the following logic statements. (i) q r p (ii) r (p q) Write the sentence below using only the symbols p, q and logic connectives. "If the oven is working and the food supply is adequate then the oven is working or the food supply is adequate." (c) A tautology is a compound statement which is always true. Use a truth table to determine whether or not your answer to part is a tautology.

5 Hint: Begin by writing the first two columns of your truth table in the following format: p q 8. Consider the following statements: p: Good mathematics students go to good universities q: Good music students are good mathematics students r: Students who go to good universities get good jobs rom these statements, write two valid conclusions. Write in words each of the following (i) q; (ii) p r. 9. [(p q) p] q Complete the truth table below for the compound statement above. p q p q (p q) p [(p q) p] q Explain the significance of your result.

6 10. Consider the statement If a figure is a square, then it is a rhombus. or this statement, write in words (i) its converse; (ii) its inverse; (iii) its contrapositive. Only one of the statements in part is true. Which one is it? 11. Amir needs to construct an isosceles triangle ABC whose area is 100 cm 2. he equal sides, AB and BC, are 20 cm long. Angle ABˆ C is acute. Show that the angle ABˆ C is 30. ind the length of AC. 12. P (4, 1) and Q (0, 5) are points on the coordinate plane. Determine the (i) coordinates of M, the midpoint of P and Q; (ii) gradient of the line drawn through P and Q; (iii) gradient of the line drawn through M, perpendicular to PQ. he perpendicular line drawn through M meets the y-axis at R (0, k). ind k. 13. ABCDV is a solid glass pyramid. he base of the pyramid is a square of side 3.2 cm. he vertical height is 2.8 cm. he vertex V is directly above the centre O of the base. V (c) Calculate the volume of the pyramid. he glass weighs 9.3 grams per cm 3. Calculate the weight of the pyramid. Show that the length of the sloping edge VC of the pyramid is 3.6 cm. (d) Calculate the angle at the vertex, BVˆ C. (e) Calculate the total surface area of the pyramid. (3) (4) (2) A (2) D O B C