PATI Test Math Assessment If You Cannot Complete These Questions You Need To Study Heavily For This Test www.policetestprep.ca
PATI Math Placement Test 1. What is the definition of complementary angles? 2. Solve the equation for x: If y = 7x-1, then x=. 3. If side = 15 and ÐC = 38, what is the length of AC? 4. How would you best describe the transformation between the two graphs below? 5. Find the mean average, median, mode, and range for the following set of numbers: 15, 27, 10, 18, 13, 13, 16, 20, 12, 11, 15 Mean average= Median= Mode= Range= 6. Factor the expression: 9 + 2x + 16
PATI Math Placement Test 7. If =, what can you conclude? 8. What is the value of y in the system of equations: x 2y = 3 and x + y=7? 9. Branson opens a bank account with a starting balance of $40. Each month he adds an additional $10. How much money will Branson have in his account at the end of one year? 10. What angle is complementary to 92? 11. The third, fourth, and fifth numbers of a sequence are 16, 22, and 28. Which of the following functions describes the sequence? a. f(n) 6n + 16 b. f(n) = 6n 2 c. f(x) = 3x + 12 d. f(x) = 12x + 6 c 12. + = a 3 4 13. What is the slope and y-intercept of the equation y = 6x + 8? Provide two answers. 14. A survey was done at school to see how many students struggled the most with each category of math. The results were as follows: Algebra: 67 Functions: 12 Geometry: 6 Trigonometry: 58 What is the population proportion for the easiest category of math?
PATI Math Placement Test 15. A cube has a surface area of 216, what is its volume? 16. If the sixth root is equal to -5, then y =? 17. Solve: 2 ( 23) 18. Multiply the numerator and denominator by -x 2 Then simplify. y+ x 2 +y 2 y- x 2 +y 2 19. The parallelogram shown below has a perimeter of 44 cm and an area of 64 cm2. Find angle T in degrees. 5 x + 4 3 x + 2 T 20. The probability of flipping a head on a coin is 0.5. What is the probability you will flip 12 heads in a row? a. 2.4 x 104 b. 6.0 c. 1.6 x 107 d. 0.5 x 1012
1. What is the definition of complementary angles? Complementary angles are either of two angles whose sum is 90 0. 2. Solve the equation for x: If y = 7x-1, then x=. x = or x = y/7 + 1/7 7 This is a single equation with two variables, and thus you cannot determine unique real number solutions for x and y. However, you can rearrange the equation to express x in terms of y by adding one to both sides of the equation and then dividing each term by seven. 3. If side = 15 and ÐC = 38, what is the length of AC? AC = 19.2 This is a basic trigonometry question, and in order to solve it properly, you will need a scientific or graphing calculator. The first thing you must do is determine which formula to use based on the information that is provided. Begin by finding the names of the two sides we are working on. These two sides are the side we know and the side we are trying to find. In our question, the side we know is called the opposite. The side we are trying to find is the adjacent. Using the acronym SOHCAHTOA, we can determine which formula we need to complete our problem. We know have an opposite side, and we are searching for an adjacent side. Therefore, the formula we need is as follows: tan38 = Opposite/Adjacent=15/x, where x is the length of AC Crossmultiplying, x tan38 o = 15. Dividing both sides by tan38o gives x = 15/tan38o = 19.2. AC =19.2
4. How would you best describe the transformation between the two graphs below? This is a reflection in the yaxis. You can check this by choosing several points on the first graph and reflecting them in the yaxis. For example, (1, 1) on the first graph would become (1, 1) when reflected, (2, 2) would become (2, 2) and so on, producing the second graph. (Note: The same result could be obtained by rotating the first graph 180 o, that is, 180 o clockwise.) 5. Find the mean average, median, mode, and range for the following set of numbers: 15, 27, 10, 18, 13, 13, 16, 20, 12, 11, 15 Mean average= 15.45 Add all values together and divide the total by 11, which is the total number of data points. Median= 15 Arrange values from smallest to largest and choose the middle value. Mode= 13 and 15 These are the most commonly occurring numbers in the data set. Range= 17 This is the difference between the largest value, 27, and the smallest value, 10. 6. Factor the expression: 9 + 2x + 16 This expression is not factorable. 7. If =, what can you conclude? 3m = 2p The crossproducts of equivalent fractions are equal, thus 3m = 2p. It is not possible to find a single, unique solution for m and p. For example, m = 4 and p = 6 is one possible solution, as is m = 20 and p = 30.
8. What is the value of y in the system of equations: x 2y = 3 and x + y=7? y = 10 Notice the coefficients of x in the two equations. This system is most easily solved by elimination. Adding the two equations leaves us with y = 10, thus, y = 10. You could also solve this system by substitution. The first equation may be rearranged to give x = 2y + 3. When this expression is substituted for x in the second equation, we get 2y 3 + y = 7, which gives y = 10 or y = 10. 9. Branson opens a bank account with a starting balance of $40. Each month he adds an additional $10. How much money will Branson have in his account at the end of one year Branson will have $160 in his bank account at the end of one year. $10 per month x 12 months = $120 $120 plus the original balance of $40 = $160 10. What angle is complementary to 92? 2 The student must remember that a pair of complementary angles MUST add up to 90 o. Hence: 92 + 2 = 90 If a student has difficulty comprehending the concept of a negative angle, point out that the negative sign generally suggests clockwise rotation. 11. The third, fourth, and fifth numbers of a sequence are 16, 22, and 28. Which of the following functions describes the sequence? a. f(n) 6n + 16 b. f(n) = 6n 2 c. f(x) = 3x + 12 d. f(x) = 12x + 6 b. f(n) = 6n 2 Evaluating f(n) = 6n 2 at n = 3, 4 and 5 gives 16, 22, and 28 respectively. It may be helpful to the student to clarify that the independent variable in a function may be position of a number in a sequence. Comprehension may be further assessed by having the student generate other terms in the sequence (e.g. 1st term is f(1) = 4, etc.) c 12. + = a ac + 12 4a 3 4 The easiest common denominator to use in adding these fractions is 4a. Multiplying the first fraction by unit fraction 4/4 and the second by unit fraction a/a gives both fractions a denominator of 4a, and ac + 12 a total of 4a when the two fractions are added.13. What is the slope and y-intercept of the equation y = 6x + 8? Provide two answers.
13. What is the slope and y-intercept of the equation y = 6x + 8? Provide two answers. m = 6, y-intercept at (0, 8) The slope of the line is the coefficient of x, which is 6. The yintercept is the point at which x = 0. So, y = 6(0) + 8 = 8 at the yintercept. There are no other answers for the slope and yintercept of this line. 14. A survey was done at school to see how many students struggled the most with each category of math. The results were as follows: Algebra: 67 Functions: 12 Geometry: 6 Trigonometry: 58 What is the population proportion for the easiest category of math? 6/143 (approximately 0.045 or 4.5%) Geometry is the easiest category of math for students in this population, as fewer students struggle with geometry as compared to the other categories. The population proportion of students struggling with geometry is 6 out of a total of 143 students, and 6/143 = 0.045 or 4.5%. 15. A cube has a surface area of 216, what is its volume? 216 cm 3 The volume of a cube is a product of its length, width and height. As all three of these dimensions are equal for a cube, one must find the length of an edge. A cube has six faces, each of equal area. Thus, the area of each face is 216 cm2/6 = 36 cm 2. A square face with an area of 36 cm2 has a side length of 36 cm or 6 cm. So, the length of each edge of the cube is 6 cm. Then, V = lwh = 6 cm x 6 cm x 6 cm = 216 cm 3 16. If the sixth root is equal to 5, then y =? y = 15 625 If = 6 y = -5, then y = (-5) 6 = 15 625. 17. Solve: ( 23) 2-23 By definition, the square root of 23 is a number that, when multiplied by itself, gives 23. Thus the square root of 23, when squared, gives 23. This is true regardless of the fact that no real number, when squared gives a negative quantity. The square root of 23 can be defined using imaginary numbers. 18. Multiply the numerator and denominator by -x 2 Then simplify. y+ x 2 +y 2 y- x 2 +y 2
19. The parallelogram shown below has a perimeter of 44 cm and an area of 64 cm2. Find angle T in degrees. 5 x + 4 3 x + 2 T T = 34.8 o The unknown quantity x can be found using the perimeter of 44cm. 2(3x + 2) + 2(5x + 4) = 44 simplifies to 16x + 12 = 44, giving a value of x = 2. This gives a length of 5(2) + 4 = 14 cm for the base. For a parallelogram A = bh, so h = A/b. Thus we can solve for the height, h, as h = 64 cm2/14 cm = 4.57 cm. Now, consider a right triangle constructed by dropping a line from the top left vertex of the parallelogram perpendicular to the base. That triangle has a height of 4.57 cm which is opposite angle T and a hypotenuse of length 3(2) + 2 = 8 cm. Thus, sint = opposite/hypotenuse = 4.57/8 = 0.571. Using an inverse sine function to find the angle T, we find that sin1(0.571) = 34.8 o. 20. The probability of flipping a head on a coin is 0.5. What is the probability you will flip 12 heads in a row? a. 2.4 x 104 b. 6.0 c. 1.6 x 107 d. 0.5 x 1012 a. 2.4 x 104 Each coin flip is independent, meaning that the outcome of the one coin flip does not affect the probability of the others. The probability of a series of independent events occurring is the product of the probabilities of the individual events. Thus the probability of 12 heads in a row is 0.512 = 2.4 x 104.