Act exam success_6 ppt

1. How is five hundred twelve and sixteen thousandths written in decimal form? a. 512.016 b. 512.16 c. 512,160 d. 51.216 e. 512.0016 2. 4 ᎏ 1 3 ᎏ − 1 ᎏ 3 4 ᎏ = ? f. 2 ᎏ 1 7 2 ᎏ g. 3 ᎏ 1 5 2 ᎏ h. 3 ᎏ 2 3 ᎏ i. 2 ᎏ 1 5 2 ᎏ j. 1 ᎏ 1 8 ᎏ 3. Simplify |3 − 11| + 4 × 2 3 . a. 24 b. 40 c. 96 d. 520 e. 32 4. The ratio of boys to girls in a kindergarten class is 4 to 5. If there are 18 students in the class, how many are boys? f. 9 g. 8 h. 10 i. 7 j. 12 5. What is the median of 0.024, 0.008, 0.1, 0.024, 0.095, and 0.3? a. 0.119 b. 0.095 c. 0.0595 d. 0.024 e. 0.092 – ACT MATH TEST PRACTICE– 165 6. Which of the following is NOT the graph of a function? f. g. h. i. j. – ACT MATH TEST PRACTICE– 166 7. 4.6 × 10 5 = ? a. 4.60000 b. 0.000046 c. 4,600,000 d. 460,000 e. 0.0000046 8. What is the value of x 5 for x = 3? f. 15 g. 243 h. 125 i. ᎏ 5 3 ᎏ j. 1.6 9. What is the next number in the pattern below? 0,3,8,15,24, a. 35 b. 33 c. 36 d. 41 e. 37 10. What is the prime factorization of 84? f. 42 × 2 g. 7 × 2 × 3 h. 2 2 × 3 × 7 i. 2 × 6 × 7 j. 2 3 × 7 11. Find the slope of the line 7x = 3y − 9. a. 3 b. −9 c. ᎏ 7 3 ᎏ d. −3 e. ᎏ 3 7 ᎏ – ACT MATH TEST PRACTICE– 167 12. The perimeter of a rectangle is 20 cm. If the width is 4 cm, find the length of the rectangle. f. 6 cm g. 16 cm h. 5 cm i. 12 cm j. 24 cm 13. Find the area of the figure below. a. 79 square inches b. 91 square inches c. 70 square inches d. 64 square inches e. 58 square inches 14. Five cans of tomatoes cost $6.50. At this rate, how much will 9 cans of tomatoes cost? f. $13.00 g. $11.70 h. $1.30 i. $11.90 j. $12.40 15. For all x ≠ 0, ᎏ 3 2 x ᎏ + ᎏ 1 5 ᎏ = ? a. ᎏ 1 2 5x ᎏ b. ᎏ 1 1 0 5 + + 3 x x ᎏ c. ᎏ 10 1 + 5x 3x ᎏ d. ᎏ 15 2 + x ᎏ e. ᎏ 5 1 x ᎏ 10 in 7 in 7 in 3 in – ACT MATH TEST PRACTICE– 168 16. Which inequality best represents the graph below? f. −1.5 > x > −1 g. x ≤ 0 h. −0.5 > x > 0 i. −1.5 < x < 0 j. −1.5 ≤ x ≤ 0 17. Simplify −(6x 4 y 3 ) 2 . a. −36x 6 y 5 b. 36x 2 y c. −36x 8 y 6 d. 36x 8 y 4 e. −36xy 18. If 2x + 3y = 55 and 4x = y + 47, find x − y. f. 28 g. 16 h. 5 i. 12 j. 24 19. Which inequality represents the graph below? a. −4x < 0 b. −20x > 5 c. x < −4 d. −x ≤−4 e. −x < 4 20. Simplify ͙ 3 16x 5 y 4 ෆ . f. 2xy͙ 3 2x 2 y ෆ g. 8x 2 y h. 8xy͙ 3 2 ෆ i. 2xy͙ 3 xy ෆ j. 4x 2 y 2 ͙ 3 x ෆ −40 4 −2−3 −10 1 – ACT MATH TEST PRACTICE– 169 21. The formula to convert Celsius to Fahrenheit is F = ᎏ 5 9 ᎏ C + 32, where F is degrees Fahrenheit, and C is degrees Celsius. What Fahrenheit temperature is equivalent to 63° Celsius? a. 32° b. 95° c. 67° d. 83° e. 47° 22. What are the solutions to the equation x 2 + 8x + 15 = 0? f. {8, 15} g. {0} h. {−5, −3} i. no solution j. {2, 4} 23. If 5k = 9m − 18, then m = ? a. 5k + 18 b. ᎏ 5 9 ᎏ k + 2 c. −9 + 5k d. 5k + 9 e. 9k + 18 24. What is the solution set for 5x − 7 = 5(x + 2)? f. {2} g. {7} h. no solution i. all real numbers j. all positive numbers 25. Simplify ᎏ 4x 2 + x + 11 3 x − 3 ᎏ for all x ≠−3. a. 3x 2 + 11 b. 2x + 1 c. 4x 2 + 12x d. 4x 2 + 10x − 6 e. 4x − 1 – ACT MATH TEST PRACTICE– 170 26. If x = [] and y = [] , find x − y. f. [] g. [] h. [] i. [] j. [] 27. If log 3 x = 2, then x = ? a. 6 b. 9 c. ᎏ 2 3 ᎏ d. 4 e. ᎏ 1 2 ᎏ 28. Simplify ᎏ x x 2 − − 3 9 ᎏ . f. x − 12 g. x − 6 h. x + 3 i. −x 2 − 6 j. x − 3 29. The vertices of a triangle are A(−1, 3), B(3, 0), and C(−2, −1). Find the length of side A ෆ C ෆ . a. ͙15 ෆ b. ͙17 ෆ c. 19 d. 17 e. 3͙6 ෆ 61 25 41 28 −50 −6 −6 18 46 50 66 −24 −10 34 56 – ACT MATH TEST PRACTICE– 171 30. Which of the following equations has a graph that has a y-intercept of 4 and is parallel to 3y − 9x = 24? f. −12x + 4y = 16 g. 9x − 3y = −15 h. 2y = 4x + 8 i. 7y = 14x + 7 j. 3x − 9y = 14 31. At what point do the lines x = 9 and 3x + y = 4 intersect? a. (3, 9) b. ( ᎏ 5 3 ᎏ ,9) c. (−20, −9) d. (9, −23) e. (9, 4) 32. Which of the numbers below is the best approximation of (͙37 ෆ )(͙125 ෆ )? f. 52 g. 4,600 h. 150 i. 66 j. 138 33. What is the solution set of the equation x 2 − 4x − 4 = 2x + 23? a. {−4, 4} b. {−4, 23} c. {1, 11.5} d. {−3, 9} e. {5, 6} 34. If a fair coin is flipped and a die is rolled, what is the probability of getting tails and a 3? f. ᎏ 1 2 ᎏ g. ᎏ 1 1 2 ᎏ h. ᎏ 1 6 ᎏ i. ᎏ 1 4 ᎏ j. ᎏ 1 8 ᎏ – ACT MATH TEST PRACTICE– 172 35. What is ᎏ 1 2 ᎏ % of 90? a. 45 b. 0.045 c. 4.5 d. 0.45 e. 450 36. Between which two integers does ͙41 ෆ lie? f. 5 and 6 g. 8 and 9 h. 4 and 5 i. 7 and 8 j. 6 and 7 37. Mike has 12 bags of shredded cheese to use to make pizzas. If he uses ᎏ 3 4 ᎏ of a bag of cheese for each pizza, how many pizzas can he make? a. 12 b. 24 c. 36 d. 9 e. 16 38. Greene ran the 100-meter dash in 9.79 seconds. What was his speed in kilometers per hour (round to the nearest kilometer)? f. 31 km/h g. 37 km/h h. 1 km/h i. 10 km/h j. 25 km/h 39. Larry has 4 blue socks, 6 red socks, and 10 purple socks in his drawer. Without looking, Larry ran- domly pulled out a red sock from the drawer. If Larry does not put the red sock back in the drawer, what is the probability that the next sock he randomly draws will be red? a. ᎏ 1 4 ᎏ b. ᎏ 1 3 0 ᎏ c. ᎏ 1 5 9 ᎏ d. ᎏ 3 7 ᎏ e. ᎏ 1 6 ᎏ – ACT MATH TEST PRACTICE– 173 40. What is the product of 5 × 10 −4 and 6 × 10 8 ? f. 11 × 10 4 g. 3 × 10 4 h. 1.1 × 10 5 i. 3 × 10 5 j. 5.6 × 10 −4 41. What is the sine of angle B in the triangle below? a. ᎏ 3 4 ᎏ b. ᎏ 3 5 ᎏ c. ᎏ 4 3 ᎏ d. ᎏ 4 5 ᎏ e. ᎏ 5 4 ᎏ 42. Find tan x for the right triangle below. f. ᎏ 5 4 ᎏ g. ᎏ 3 4 ᎏ h. ᎏ 4 3 ᎏ i. ᎏ 6 3 ᎏ j. ᎏ 5 3 ᎏ 4 5 3 x° A B 8 6 C – ACT MATH TEST PRACTICE– 174 [...]... F = ᎏ5ᎏ(63) + 32 9 F = 35 + 32 F = 67 The answer is 67°F 187 – ACT MATH TEST PRACTICE – 22 Choice h is correct The equation is quadratic, so there are two ways to solve it First, try to factor the left-hand side of the equation Since it is factorable, solve the equation using factoring x2 + 8x + 15 = 0 (x + 5)(x + 3) = 0 Set each of the factors equal to zero and solve for x x+5=0 x=−5 x+3=0 x = −3 The... there is no solution 25 Choice e is correct Factor the numerator (4x − 1)(x + 3) ᎏᎏ x+3 Use the denominator as a clue when factoring the numerator Most likely, the denominator will be one of the factors in the numerator Cancel the x + 3 in the numerator with the x + 3 in the denominator This leaves 4x − 1 188 – ACT MATH TEST PRACTICE – 26 Choice f is correct Subtract the numbers in y from the corresponding... sixteen ten thousandths.” 2 Choice f is correct First, change the fractional parts of the problem to have the common denominator of 12 4ᎏ4ᎏ − 1ᎏ9ᎏ 12 12 Subtract the numerators Since 4 is less than 9, you must borrow one whole from the whole number 4 12 This means that you are adding ᎏᎏ to the first fraction 12 16 3ᎏᎏ − 1ᎏ9ᎏ 12 12 Subtract the fractional parts then the whole numbers The final answer is 2ᎏ7ᎏ... can eliminate choices f and i because they contain numbers that are not prime Next, use a factor tree to determine the prime factorization 84 2 42 7 6 3 2 The prime factorization of 84 is 2 × 2 × 3 × 7, which can be written in exponential notation as 22 × 3 × 7 The answer is 22 × 3 × 7 185 – ACT MATH TEST PRACTICE – 11 Choice c is correct To easily see the slope, change the equation into the form y... inches ෆ i 6͙3 inches ෆ j 12 inches 181 – ACT MATH TEST PRACTICE – 75 What is the sum of the solutions to the equation 2x2 = 2x + 12? a 4 b 7 c 1 d 9 e −1 76 Find the value of sin A if angle A is acute and cos A = ᎏ9ᎏ 10 f 11 ͙ෆ ᎏ ᎏ 10 g 5 ᎏᎏ 4 10 h ᎏ9ᎏ i 19 ᎏᎏ 100 j 19 ͙ෆ ᎏ ᎏ 10 77 Find the value of x ¯¯¯ √5 45° x a b c d e 2 1 ͙7 ෆ ͙10 ෆ 2͙5 ෆ 182 – ACT MATH TEST PRACTICE – 78 Which equation corresponds... Find a common denominator and add the fractions The common denominator is 15x 4 ᎏᎏ 3x x−1 + ᎏ5ᎏ 20 ᎏᎏ 15x 3x(x − 1) + ᎏᎏ 15 20 + 3x(x − 1) ᎏᎏ 15x 20 + 3x2 − 3x ᎏᎏ 15x 3x2 − 3x + 20 ᎏᎏ 15x 61 Choice b is correct Since the exponent is negative, take the reciprocal of the fraction, then apply the exponent of 3 (ᎏ1ᎏ)−3 2x2 2 2x (ᎏ1ᎏ)3 (2)3(x2)3 8x6 195 – ACT MATH TEST PRACTICE – 62 Choice f is correct Use... Choice j is correct The radius of the large circle is 7 (add the inner radius plus the extra 3 from the ring) Therefore, the area of the large circle is 49π Subtract the area of the inner circle, which is 16π 49π − 16π = 33π 191 – ACT MATH TEST PRACTICE – 45 Choice a is correct Take the square root of the area to find the length of one side ͙100 = 10, so the ෆ length of the sides of the square is 10 centimeters... y ≥ − 3x + 2 y < 3x + 2 y < − 3x + 2 4x ᎏ 80 What is the domain of the function f(x) = ᎏ− 5 4 ? x2 + 3x − f {x | x ≠ 0} g Ø h All real numbers i {x | x ≠ 3} j {x | x ≠ −4 and x ≠ 1} 183 – ACT MATH TEST PRACTICE – Practice Questions Answers and Explanations 1 Choice a is correct The word and indicates a decimal point Therefore, the decimal point should go after five hundred twelve and before sixteen thousandths... centimeters Find the length of diagonal WY in centimeters a 10͙2 cm ෆ b 20 cm c 10 cm d 2͙5 cm ෆ e 10͙5 cm ෆ 46 Find the hypotenuse of the triangle below 4 9 f ͙13 ෆ g ͙5 ෆ h ͙65 ෆ i ͙97 ෆ j 13 175 – ACT MATH TEST PRACTICE – 47 A circular lid to a jar has a radius of 3ᎏ1ᎏ inches Find the area of the lid 2 a b c d e 12 ᎏᎏπ sq in 49 49 ᎏᎏπ sq in 12 49 ᎏᎏπ sq in 4 7 ᎏᎏπ sq in 2 4 ᎏᎏπ sq in 49 48 What is the value... 1 ᎏᎏ 2 51 The formula for the volume of a rectangular solid is V = lwh If each dimension is tripled, how many times the original volume will the new volume be? a 3 b 9 c 1 ᎏᎏ 3 d 27 e 81 176 – ACT MATH TEST PRACTICE – 52 In a right triangle, the two non-right angles measure 7x and 8x What is the measure of the smaller angle? f 15° g 60° h 30° i 48° j 42° 53 What is the length of the missing leg in the . 0.092 – ACT MATH TEST PRACTICE– 165 6. Which of the following is NOT the graph of a function? f. g. h. i. j. – ACT MATH TEST PRACTICE– 166 7. 4 .6 × 10 5 = ? a. 4 .60 000 b. 0.0000 46 c. 4 ,60 0,000 d. 460 ,000 e ? f. ᎏ x 1 + 5x 3 ᎏ g. ᎏ x 8 + x 3 ᎏ h. ᎏ 3 x x + + 3 5 ᎏ i. ᎏ 3x 2 − 1 3 5 x x +20 ᎏ j. ᎏ x 2 + 1 4 5 x x − 1 ᎏ – ACT MATH TEST PRACTICE– 178 61 . Simplify ( ᎏ 2 1 x 2 ᎏ ) −3 . a. 6x 6 b. 8x 6 c. ᎏ 6 1 x 6 ᎏ d. ᎏ 8 3 x 5 ᎏ e. ᎏ 8 1 x 5 ᎏ 62 . If 4x = 3y + 15 and 2y − x = 0, find x. f. 6 g. 3 h. 2 i 3 6 ෆ 61 25 41 28 −50 6 6 18 46 50 66 −24 −10 34 56 – ACT MATH TEST PRACTICE– 171 30. Which of the following equations has a graph that has a y-intercept of 4 and is parallel to 3y − 9x = 24? f. −12x + 4y = 16 g.