Mathematics Conversions/Formula. S.A. 2 r. cylinder. V cone S.A. 4. sphere

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1 Mathematics 1201 Midterm Review 2015 Unit I: Measurement Conversions/Formula 1 ft. = 12 in. 1 in. = 2.5 cm 2 S.A. 2r 2rh cylinder V pyramid 1 (area of base)(height) 1 yd. = ft. 1 mi. = 1.6 km 2 S.A. cone rs r 1 2 V cone rh 1 mi. = 1760 yd. 2 S.A. r r sphere V sphere 1. Which of the following calculations converts yards into centimeters? yd. yd. yd. yd. 2. Tyler s driver s license states that he is 175 cm tall. What is his approximate height in feet and inches? 5 feet 5 inches 5 feet 9 inches 5 feet 6 inches 5 feet 10 inches. On a road trip in Florida, Brady sees a road sign that tells him he is 2 miles from Disney. What is that distance in kilometers? km 2 km.6 km 67.2 km. A cone and a cylinder have the same height and the same base radius. If volume of the cone is 8 cm, what is the volume of the cylinder in cm? 16 cm 2 cm 5 cm 1 cm 5. A square pyramid has a base length of m and has a volume of 80 m, what is the height? m 5 m 15 m 16 m

2 6. A cone has a radius of 7 cm and a slant height of 25 cm. What is its surface area (including the base), to the nearest square centimetre? 15 cm 2 59 cm 2 s=25 cm 70 cm 2 10 cm 2 r = 7 cm 7. What is the slant height of the pyramid below to the nearest meter? 18.8 m 20. m 20. m 77 m 180 m 25 m 269 m 8. What is the volume of the rectangular pyramid below? 2 cm 1 cm 8 cm 656 cm 1 cm 12 cm 8 cm 9. Jack is installing trim around a window that measures 52 in. by 8 in. If the trim is only sold by the foot, how many feet of trim will Jack need to buy? If the trim costs $1.89 per foot, how much will it cost?

3 10. A bowling ball has a surface area of 615. cm 2. Determine the radius of the bowling ball to the nearest centimeter. 11. A picture of an ice cream cone is shown to the right. Ice cream fills the entire cone. How much ice cream is there in total to the nearest tenth of a cm? 2.5 cm 7.5 cm 12. Determine the surface area of the right rectangular pyramid below. 12 cm 10 cm 8 cm Unit II: Roots and Powers 1. Simplify: A) 2 B) 6 C) D) 6 1. What is the LCM of 18 and 2? What is the prime factorization of 60? What is the greatest common factor of 280 and 60?

4 17. Which of the following is a perfect cube? 18. What is the most simplified form of? 19. Which of the following powers below represents the radical? Evaluate: Simplify: 72x 6 72x 6x 6 6x 22. Express as an entire radical. 2. The surface area of a cube is 8 cm 2, what is the volume of the cube, in cm, in its most simplified form? Which is an IRRATIONAL number?

5 25. Simplify using powers with positive exponents 26. Simplify: ( x 2 ) Simplify: 28. Using the Pythagorean theorem, determine the value of x. Express the answer in simplest radical form. x Simplify the following expressions. Express the answer with positive exponents (a) 2 2x y x y (b) 2 2 2x x y 6xy 10 (c) x x 1 y y 1 (d) a b c a b c 9 2 Unit III: Factoring 0. What is the greatest common factor of the terms p q, 6p 2 q 2, 12pq 2? pq 2 pq 2pq 2 2pq 1. What are the correct factors of x 2 x 18? ( x + 6 )( x ) ( x + )( x 6 ) ( x 6 )( x ) ( x 9 )( x + 2 )

6 2. Which factors are represented by the algebra tiles? white tiles: positive grey tiles: negative ( 2x 1 )( 2x + 1 ) ( 2x 2 )( 2x + 2 ) ( x 1 )( x + 1 ) ( x 2 )( x + 2 ). Simplify: ( r 2 ) 2 9r 2 + 9r 2 12r + 9r 2 9r 2 12r. Which expression is represented by the algebra tiles given below? white tiles: positive grey tiles: negative x 2 7x 12 x 2 + 7x 12 x 2 x 12 x 2 + x What value represents in in the expansion ( w 8 )( w ) = w 2 + w + 2? What are the correct factors of 8 + 2x x 2? ( 2 x )( x ) ( 2 + x )( + x ) ( 2 x )( + x ) ( 2 + x )( x ) 7. Which represents a perfect square trinomial? 9x 2 + x + 1 5x 2 2x x 2 0x + 25 x 2 + xy + y 2

7 8. Factor completely each of the following algebraic expressions. (a) 18m 2 2 (b) 0 y y 2 (c) 2m mn + 0n 2 (d) p 2 + 2p 8 (e) 15x 2 9xy 18y 2 (f) 16x 2 0x Multiply the following expressions. ( 2x )( x 2 + 6x + 9 ) 0. Determine the expression (in expanded form) that represents the area of the shaded region. x + 5 2x + x + 1 x + 8 Unit IV: Relations and Functions 1. The amount of sunlight affects the height of the plant. What is the independent variable? The amount of sunlight. The amount of water. The height of the plant. The type of soil. 2. Which ordered pair represents g( 2) = 5? ( 5, 2) ( 2, 5) (2, 5) (5, 2). If, what is h(6)? For the function f(x) = 2x + 10, determine the value of x when f(x) = Express y = x + 7 using function notation. f(y) = x + 7 f(x) = y + 7 f(x) = x + 7 f(y) = y + 7

8 D i s t a n c e ( k m ) A l t i t u d e ( m ) 6. Jane went on a mountain hike. The graph shows her altitude for the duration of the hike. What time interval was she climbing down the mountain? Jane's Mountain Hike 0 1 hours h 1 hours 5 hours hours 7. Students from Eastern High School had a ski trip to White Hills in Clarenville. The graph below represents their trip. Accurately describe the trip, including references to: Time (h) t (i) distance travelled (ie. number of kilometers) (ii) direction of travel (ie. towards White Hills, stopped, heading back) 150 d D E B C A F Time (h) t Trip Distance Travelled Direction of Travel AB BC CD DE EF Answers: 1. C 2. C.D. D 5.C 6. C 7.B 8.B 9.(a) 17 ft. (b) $ cm cm cm 2 1. B 1. C 15. C 16. B 17. B 18. A 19. B 20. C 21. C 22. D 2. A 2. D 25. B 26. D 27. A 28.

9 29. (a) (b) (c) (d) 0. C 1. B 2. A. B. C 5. A 6.D 7. C 8..(a) 2(m )(m + ) (b) (5 y)(8 + y) (c) 2(m + 5n)(m + n) (d) (p )(p + 2) (e) (5x + 2y)(x y) (f) (x 5) x x 2 + 2x A 2. B. B. C 5. C 6. C 7. Trip Distance Travelled Direction of Travel 50 km Towards W.H AB BC CD DE EF 0 km Stopped 100 km Towards W.H. 0 km Stopped 150 km Heading Back