FIRST TERM EXAM REVISION WORKSHEET AY Grade 10 Mathematics. Algebra. Section A: Vocabulary

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1 FIRST TERM EXAM REVISION WORKSHEET AY Grade 0 Mathematics Name: Section: Algebra Section A: Vocabulary Fill in the blanks using the words given in the following table: geometric sequence arithmetic sequence exponential function radicand exponential growth radical expression common ratio decay An expression that is represented by an equation of the form f(x) = ab x is called. A sequence in which each term is found by multiplying or dividing the previous term by a constant is a. This form of functions y = a( - r) t is usually called an exponential function. The ratio of successive terms in a geometric sequence is called. A sequence in which the difference between one term and the next is always the same is called an. The following form of functions y = a( + r) t is known as. The expression written under the radical symbol is called. an expression that contains the radical symbol ( ) is referred as. Page of 5

2 Section B: Mental Math Simplify the following: x y x y = ( ) 3 9 ( x ) x (0, 000). 909 (654) (,000,000x ) Page of 5

3 4 0, 000 y 0, ( x ). 3 3 x x x x Find the common ratio (r) for each geometric sequence and use (r) to find the next three terms. 0, -00, , 4.5, -.5,, , -80, 3, -.8, 3 4 Page 3 of 5

4 -5, 3, -.8,.08, 0.5, 0.05, Section C: Math Drill Write an exponential growth function to model each situation. Determine the domain and range of each function. Then find the value of the function after the given amount of time. A. A new savings account is opened with $500 and gains 3.% yearly for 5 years. B. The population of a town is 4,000 and is increasing at a rate of 6% per year for 3 years. C. The value of a piece of fine jewelry is $80 and decreases at a rate of 3% yearly for 7 years. Page 4 of 5

5 Section D: Critical Thinking and Problem Solving The approximate number of Calories C that an animal needs each day is given byc 7 m 4, where m is the animal s mass in kilograms. Find the number of Calories that a 65 kg bear needs each day. 3 At a factory that makes cylindrical cans, the formula r V is used to find the radius of a can with volume V. What is the radius of a can with a volume of 9 cm3? Graph each function. On your graph, include points to indicate the ordered pairs for x = -, 0,, and.. f ( x) 0.75() x Page 5 of 5

6 . f ( x) 5(4) x Write an equation for the function shown. ) A blood sample has 50,000 bacteria present. A drug fights the bacteria such that every hour the number of bacteria remaining, r(n), decreases by half. If r(n) is an exponential function of the number, n, of hours since the drug was taken, find the bacteria present four hours after administering the drug. ) The height h(n) of a bouncing ball is an exponential function of the number n of bounces. One ball is dropped and on the first bounce reaches a height of 6 feet. On the second bounce it reaches a height of 4 feet. Page 6 of 5

7 3) The NCAA basketball tournament begins with 64 teams, and after each round, half the teams are eliminated. The number of remaining teams t(n) is an exponential function of the number n of rounds already played. State a, b, and the y-intercept then graph the function and describe the end behavior of the graphs. A. ƒ(x) = 3(3) x B. f ( x) 6. x Page 7 of 5

8 C. f(x) 4(0.5) x Make a table of values for each function and graph them together on the same coordinate plane. Find the y-intercepts, and explain how they relate to the translation of the graph. x A. f ( x) 6 and f ( x ) 6 5 x Page 8 of 5

9 Geometry Section A: Vocabulary Match each statement with the correct theorem. SSS Triangle Similarity Theorem AA Triangle Similarity Theorem 3 SAS Triangle Similarity Theorem If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar If two sides of one triangle are proportional to the corresponding sides of another triangle and their included angles are congruent, then the triangles are similar. If the three sides of one triangle are proportional to the corresponding sides of another triangle, then the triangles are similar Choose the correct answer:. Two plane figures are similar if and only if one figure can be mapped to the other through A. Similarity transformation B. Exponential function C. Dilation D. Common ratio. A transformation in which a geometric figure is moved to another location without any change in size or orientation A. Rotation B. Reflection C. Translation D. Dilation 3. A geometric transformation that changes a figure's size A. Reflection B. Dilation C. Translation D. Rotation Page 9 of 5

10 4. A transformation in which each point of a figure has an image that is the same distance from the line of reflection as the original figure A. Rotation B. Dilation C. Translation D. Reflection Rules of transformations: Section B : Mental Math Prove that the figures are similar by describing a series of transformations that maps first figure to the other. A. TUV and XYZ Your answer: Page 0 of 5

11 B. JKLMN to VWXYZ Your answer: Use the tangent to find the unknown side length. Find AB: A B 9 o C Find AB: Find the measure of the angle specified for each triangle. Use the inverse tangent (tan - ) function of your calculator. Round your answer to the nearest degree. Find A and B Page of 5

12 Find the measure of angle D using the tangent formula. Find the unknown length x in each right triangle, to the nearest tenth. Find each acute angle measure, to the nearest degree. Page of 5

13 Section C : Math Drill Check if triangles are similar, state the similarity theorem and find the indicated length, (if possible). Find RT: Find AD: Find QR: Page 3 of 5

14 Find GH: Find the value of x. Determine whether the given segments are parallel. WX and DE PQ and NM Page 4 of 5

15 Section D: Critical Thinking and Problem Solving Find the indicated dimension using the indirect measurements shown in the figure and the properties of similar triangles. A. Mohammed is 80 inches tall. To measure a flagpole, Mohammed stands near the flag. Mohammed s friend John measures the lengths of Mohammed s shadow and the flagpole s shadow. Find the height h of the flagpole. B. A mirror is placed on the ground, shown by point N, so that a person looking at it can see the top of a nearby statue, shown by point P. The figure is not drawn to scale. The mirror is placed 30 feet away from the statue, and Jean stands 5 feet from the mirror. If her eyes are 5 feet, 6 inches above the ground, shown by how tall is the statue? Best of Luck Page 5 of 5