Entrance to Grade 9 - Principles/Foundations of Mathematics (MPM1D/MFM1P)

Transcription

1 Entrance to Grade 9 - Principles/Foundations of Mathematics (MPMD/MFMP). Write 8% as a decimal.. Which of the following number lines shows the graph of,, and? [A] [B] [C] [D]. Write each ratio in simplest form. a) b) 4 c) d) 7:9 4. Simplify. a) + ( 4) b) ( ) c) 4 d) ( ) ( ) e) + ( ) f) ( 4)(4 ) ( ) City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

2 Entrance to Grade 9 - Principles/Foundations of Mathematics (MPMD/MFMP) [].8 [] A [] a) 9 b) 4 c) d) : [4] a) b) c) 6 d) 7 e) 6 f) 8 [] B [6] A [7] a) w = 7, = 7, y = 7, z = 7 b) = 6, y = 6 c) = 4, y = 4, z = [8] B City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

3 Entrance to Grade 9 - Essential Mathematics (MATL) [] D [] a), 4,,, b),,,, [] B [4] a) b) c) d) 7 [] [6].87 [7] a) b) c) d) Percent Fraction Out of Decimal 7% % 4% 69% [8] A City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

4 Entrance to Grade 9 - Essential Mathematics (MATL). Subtract. [A] [B] 6 [C] 4 [D] 6. Complete the tables. a) b) a a+ ( ) +. Add. ( ) + (+7) + ( 8) [A] [B] 6 [C] 6 [D] 4 4. Simplify. a) ( )( + 6 ) ( 4) b) 4( + 9) ( 6)( + ) c) ( 7) ( )( + ) d) 9( 7) ( )( + ) City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

5 . Add. ( ) + ( 9) 6. Write 8 % as a decimal Complete the table. Percent Fraction Out of Decimal a) b) 7% % c) 4 d) Which rational number has a numerator less than and a denominator greater than? [A] 9 9 [B] [C] 6 [D] 4 City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

6 Entrance to Grade Applied - Foundations of Mathematics (MPMP) [] 8 7 [] C [] Jacques, by $./h [4] y + 6 = ( ); y = 4 [] 8 [6] D [7] =, = [8] City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

7 Entrance to Grade Academic - Principles of Mathematics (MPMD) [] a). c. c b) w w + 6w 4 4 c) y y [] a). d 6 b) 4. ab 7 c). k 8 d) 8rst [] a) b) c) d) Cost Price Markup Selling Price $. % $4. $. % $. $.7 % $. $4.74 % $6. 9 [4] years and 44 years [] [6] 4, 79, 87 [7] 49 m [8] = 8 City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

8 Entrance to Grade Academic - Principles of Mathematics (MPMD). Epand. a). c. c c. c c b) w + 6w w + 8 c) 6 y y h h h. Simplify. a). d c h b) c. abhcabh c) c. khc kh d) c rst h cr s th. Complete the table. Cost Price Markup Selling Price a) $. % b) $. % c) $.7 % d) $4.74 % 4. The sum of the ages of Petra and her mother is 9. Her mother is 4 years more than twice as old as Petra. How old are Petra and her mother? City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

9 . Find the slope of the line. y 6. Identify the net three terms in the sequence., 9, 7, 8, Find the area of the composite shape. m m 8 m m 8. Find the value of City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

10 Entrance to Grade Applied - Foundations of Mathematics (MPMP). Estimate, then multiply Simplify. 7 7 [A] [B] [C] [D]. Gerrie was paid $68. for 8 h of work. Jacques received $6.6 for 7 h. Who had the higher rate of pay and by how much? 4. Write an equation of the line that passes through the point (, 6) and has slope. Then, rewrite the equation in slope and y-intercept form. City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

11 . Find the mode of the data. 4, 7, 8,, 7, 8, 4,, 8, 6. Solve. 4n n + = 4 [A] [B] [C] 9 [D] 7. Find the measures of and Solve.. 7. = City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

12 Entrance to Grade Foundations for College Mathematics (MBFC). Application Name the type of quadrilateral formed when the lines = 7, + y 7 =, y =, and + y = intersect.. Problem Solving The width of a rectangle is m less than the length. The area of the rectangle is m. Find the dimensions of the rectangle.. State whether each set of ordered pairs represents a function. a) {( ),, ( 4, ), (, ), (, )} b) {(, ), (, ), ( 4, ), (, )} c) {( 7, ), ( 9, ), ( 77, ), ( 97, )} d) {(, ), (, ), (, ), (, )} 4. In the given triangle, name the largest angle. The triangle is not drawn to scale. B cm 4 cm A 7 cm C City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

13 . Epand and simplify. a) ( a 6) + ( a+ ) b) ( 7) + ( )( + ) c) ( t )( t+ ) 4( t ) d) ( d ) ( d) 6. Problem Solving A small park is enclosed by 8 m of fencing. The area of the park is 6 m. What are the dimensions of the park? 7. Factor [A] ( 8 )( 8+ 7) [B] ( 8 )( 8+ 7) [C] 8 ( 9)( + 6) [D] 8( 9)( + 6) 8. State the coordinates of the verte of the parabola. Then, use a graphing calculator or graphing software to determine any -intercepts. Round to the nearest tenth, if necessary. y = 8.( ) + City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

14 Entrance to Grade Foundations for College Mathematics (MBFC) [] trapezoid [] m by m [] a) yes b) yes c) yes d) no [4] B [] a) a a+ 6 b) 4+ 4 c) t + 8t 7 d) 4d 4d 7 [6] 48 m by 4 m [7] C y [8] verte ( ;, ) -intercepts:.7,. City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

15 Entrance to Grade University/College Functions and Applications (MCFM). Factor. + + [A] ( + 4)( ) [B] ( + 4)( + ) [C] ( 4)( ) [D] ( + )( 4). Communication The table gives the area and three side lengths for two similar right triangles. Describe the relationship between the ratio of the lengths of the corresponding sides and the ratio of the areas. Area (m ) Side Side Side Triangle A Triangle B Application The lengths of two similar rectangles are 4 cm and cm. What is the ratio of the corresponding side lengths? the areas? 4. Write the equation of the circle, given its centre and radius. centre (, ), radius 7 [A] + y = 4 [B] + = [C] + y = 7 [D] + y = City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

16 b g and b, g. b g F [C] I HG K J. Find the midpoint of the line segment with endpoints 8, [A] F HG I K J, [B], 8, [D], 4 F HG I K J 6. Factor [A] 9 ( 9)( + 4) [B] ( 9 )( 9+ ) [C] ( 9 )( 9+ ) [D] 9( 9)( + 4) 7. Sketch the graph of each parabola. Determine any intercepts, to the nearest tenth, and find two other points on the graph. a) y = ( ) b) y = ( ) c) y =. ( + ) + d) y = ( ) Solve the system of equations by substitution or elimination. Check the solution. a) y = + y = 6 7 d) y = + y = + b) + y = 4 4+ y = 7 e) = 4 y = 9+ 6y c) + y = y = 9 4 f) y = 6 y 4= City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

17 Entrance to Grade University/College Functions and Applications (MCFM) [] B [] The ratio of the areas of two similar triangles is equivalent to the square of the ratio of the side lengths. If the ratio of the side lengths of triangle A to triangle B is :, then the ratio of the areas is :4. [] 4:; 96: [4] D [] D [6] A a) -intercept ; y-intercept 4; (, ), (, ), (4, 4), (, 9),... b) -intercepts.8 and.; y-intercept ; (, ), (, ), (, ), (, ),... c) -intercepts.4 and.4; y-intercept.; (,.), (,.), (, ), (, ),... d) no -intercept; y-intercept 6; (, 7), (, 4), (, 7), (4, 6),... a) y b) y c) y d) y 6 4 [7] [8] a) (4, F ) b) (4, ) c) ( 4, ) I d) HG K J F, e) (, 9) f), HG I K J City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

18 Entrance to Grade University Functions (MCRU) b g.. Graph y = + 4 [A] y [B] y [C] y [D] y. In the given triangle, name the longest side length. The triangle is not drawn to scale. B 4 c a A 67 b 9 C. Communication ΔPQR and ΔPST are similar. Eplain how to calculate each ratio. a) PR b) ST area of ΔPST c) PT QR area of ΔPQR T R P S Q City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

19 4. Solve each system by elimination. If there is eactly one solution, check the solution. y = 4 + y = [A] b, g [B], 4 b g [C] b, g [D] b, g. Problem Solving The area of a triangle is represented by the polynomial + 8. The base of the triangle is represented by + 6. a) Factor + 8. b) Write a binomial that represents the altitude of the triangle. c) Find the area of the triangle if =. 6. ΔVWX ~ ΔVYZ. Find VY, WY, VZ, and XZ. V 7 cm 8 cm X cm W Z cm Y 7. The diameter of a circle joins the points C(, 7) and D(, ). What are the coordinates of the centre of the circle? 8. Application Write an equation for each function. a) y b) y c) y d) y City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

20 Entrance to Grade University Functions (MCRU) [] D [] a [] a) PR PT PQ 4 = = = PS b) ST QR PS = = PQ c) PS PQ = area of ΔPST so area of ΔPQR = = 4 [4] D [] a) ( + 6)( ) b) 6 c) 6 [6] VY = 4 cm, WY = 6 cm, VZ = cm, and XZ = 4 cm [7] [8] F HG, 4 I K J a) y = + b) y = + 6 c) y = + 7 d) y = + City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

21 Entrance to Grade Foundations for College Mathematics (MAP4C). Application The verte of a parabola is (, ). One -intercept is. What is the other -intercept?. Find the ais of symmetry of the parabola. y = + 6 [A] = [B] = [C] = [D] =. Communication Write the equation that represents the graph. Eplain your reasoning. y 4. Communication None of the following trinomials is a perfect square. Change one term in each trinomial to make a perfect square. Eplain your reasoning. a) a + 7ab+ 6b b) t 8t+ c) 9 + 7y+ y d) c + cd + d. Find the shortest distance from the origin to each line, to the nearest tenth. a) + y = b) y = 6 c) 4 = y+ d) y+ 6= City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

22 6. Application For the equation y = , a) find the ais of symmetry of the graph of the equation b) find the verte of the graph c) graph the equation [A] a) = 7 F 7 b) verte, HG c) y I K J [B] a) = 7 b) verte c) F HG 7, 8 I K J y [C] a) = 7 F 7 b) verte, HG c) y I K J [D] a) = 7 b) verte c) F HG 7, 8 y I K J 7. Triangle XYZ has vertices X(, ), Y(, ), and Z(6, ). Find the midpoints, A and B, of XY and XZ, respectively, and show that AB is parallel to YZ. 8. Problem Solving Find two numbers whose sum is 44 and whose product is a maimum. City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

23 Entrance to Grade Foundations for College Mathematics (MAP4C) [] 7 [] D [] [4] b g, is The verte, which has the form ( h, k ), is b, g. The equation, which has the form y = a h + k y = ( ) +. a) The first and the last terms are perfect squares. Double the product of their square roots, a and 6b, to get ab as the middle term. Check ( a+ 6b). b) Change the last term to 6 to make it a perfect square. Then, check ( t 4). c) The first and last terms are perfect squares. Double the product of their square roots, and y, to get 6y as the middle term. Check ( + y). d) the middle term should be double cd, or cd. Check ( c+ d). [] a).4 b).7 c). d).9 [6] C [7] F I HG K J F H G I K J The slopes of AB and YZ are both. A, B 4,, ; [8] and City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

24 Entrance to Grade Mathematics for College Technology (MCT4C). Mary saved $ from her summer job and invested it at 4% per annum compounded monthly. How much will she have four years later when she attends college?. Solve each of the following: a. + 6 = 87 c. 4 + = 4 c h = d. 6 b. 6 = 8. Simplify each of the following: c h b g c. a. + 4 b. + b + g b + g b gb g d. b+ g b + g 4. State any restrictions on the variable in each of the following: a. + 7 c y y + 7 b. d. y 7y+ y + y City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

25 . Simplify each of the following: y c h a. c. 4y 9 y 4 4y 4 c hc h d. b. y y 4 c hc h y 4 c h y 6. Solve each of the following for. a. + 8 = c. + = b g d. b. = b gb g b g + + = 4 7. Convert the following to radian measure. a. b. 48 c. 8. Simplify each of the following: a. m a m a a a m m + + b. a 4 a a City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

26 Entrance to Grade Mathematics for College Technology (MCT4C) [] b g F HG A= P+ i n I K J 48 = + 4. = 9. Mary will have $9. four years later. [] a. + 6 = 87 = 8 = 4 = 4 c h = b. 6 = = = + c. 4 = = = 4 + = = d. 8 = 6 = 4 = = = 6 [] a = b. + c h c = = c h d c h = = = [4] a. no restrictions c. b. y, 4 d. y, [] a. c yh 8 y 4 = 4y 4y = y b. y y c hc h = 8 y 9 y 8 = 9 y c hc h c h c. 4 4 y 9 y = 6 y y d. y 4 c h = 4 y y = y = 6 y 6 City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

27 [6] a. + 8 = = 8 =± 8 =± 9i b. = c 6+ 9 = 8+ 7= 8+ = b g h 9+ = 9 = ± c. + = = 7 =± 7 =± i b gb g b g d. + + = = 8+ 6 = 6 = [7] a. = π = π b = π = 4 8 π c. = π = 7 π 8 6 a. m a m a a a m m + + m = m a = m a+ a + b. a 4 a a = F HG a 4 a a I KJ F = a H G I 4 K J [8] = a 8 City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

28 Entrance to Grade - Mathematics for Work and Everyday Life (MELE). A rectangular prism is cm long, cm wide, and cm high. Find the surface area of the prism.. The average cost of a computer has decreased since 978. The following table gives the average computer cost, to the nearest five hundred dollars, for selected years. Year Average Computer Cost ($) a) Plot these points on a graph. b) Connect the points using line segments. c) Determine the average yearly decrease in cost between 978 and 98. d) Determine the average yearly decrease in cost between 98 and Evaluate a b for a =.7 and b = Epress the unit rate in the units shown. a) 7 cans of punch for $4.8; /can b) $6.6 for 8 h of work; $/h c) 76 h of sunshine in 8 days; h/day d) $.7 for 8.7 L of gas; /L City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

29 . The table shows the study times and test scores for a number of students. Draw a scatter plot of score versus time. Study Time (min) Test Score Calculate each surface area, to the nearest square unit. a) b) m cm 9 m 7 cm c) mm d) 6. cm 7 mm.9 cm 7. Write two ratios equivalent to 4:6. 8. If 4, 8 8, 9 6, and 7 were placed in order from greatest to least, which would be first? [A] 9 6 [B] 7 [C] 8 8 [D] 4 City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

30 Entrance to Grade - Mathematics for Work and Everyday Life (MELE) [] 77 cm [] a) and b) c) $6 d) $ Cost ($) Year []. [4] a) 69 /can b) $7.7/h c) 9. h/day d) 7. /L Effect of Study Time on Test Score [] Test Score Study Time (min) [6] a) 6 m b) 96 cm c) 48 mm d) 89 cm [7] Eamples: :, 6:9, 8:, : [8] D City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

31 Entrance to Grade University Advanced Functions (MHF4U) or Mathematics of Data Management (MDM4U). Find two integers whose sum is and whose product is 4.. The science class is investigating projectiles and they have built catapults. Margarita s team has built a catapult that throws a table-tennis ball vertically upward. The height of the table-tennis ball in centimetres above the ground is given by the formula h = + t t. a. At what height is the table-tennis ball released? b. What is the ball s maimum height? c. If the ball has to stay in the air for s to qualify for a prize, can Margarita s team win a prize?. Solve each of the following for. a. + = 7 c. 4 b g = b. = d. 8 = 4 4. A mirror frame is 9 cm by cm. The mirror has an area of 88 cm. How wide is the frame? City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

32 . Solve each of the following: a. + 6 = 87 c. 4 + = 4 c h = d. 6 b. 6 = 8 6. Given ΔABC with AB = BC = AC =, B A C a. draw AD BC. b. find DC. c. find AD. d. find the measure of C. e. find the measure of DAC. f. find sin, cos, and tan. g. find sin 6, cos 6, and tan Solve each of the following for. a. + 8 = c. + = b g d. b. = b gb g b g + + = 4 8. From the graph of f() shown a. graph f(). b. graph 4 f(). c. graph f( ). y City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

33 Entrance to Grade University Advanced Functions (MHF4U) or Mathematics of Data Management (MDM4U) [] [] Let the integers be represented by and b g. = 4 b = = = g b gb g =, 6 If =, the second integer is = + = 6. b g 6. If = 6, the second integer is = + = The two consecutive integers are and 6. a. When t =, h=. The ball is released at cm. b. h = + t t c b = t t+ + + g = t + The maimum height is m. c. The ball hits the ground when h =. + t t = t t = t t = h ± + 4 t = ± 4 = = &. 99 or. 99 Time cannot be a negative. The ball stays in the air for. s and Margarita s team can win a prize. City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

34 + a. = 7 + = + = + = b gb g + = =, + c. 4 = = bg b g = = = b gb g + = =, [] b. = 4 + = + = + + = b+ gb+ g= =, d. 8= = = + 4= + = = ± + = ± Let represent the width of the frame. 9 = 88 b gb g = = + = b gb g = =, 9 cm cm 9 [4] If =, the length and width of the mirror would be negative. Therefore, the width of the frame is cm. [] a. + 6= 87 = 8 = 4 = 4 c h = b. 6 = = = + c. 4 = = = 4 + = = d. 8 = 6 = 4 = = = 6 City Adult Learning Centre (CALC) - Mathematics Assessment (vc)

35 [6] a. B A D C b. DC = c. = AD + AD = AD = d. C = 6 e. DAC = f. g. sin = cos = tan = sin 6 = cos6 = tan 6 = = = [7] a. + 8 = = 8 =± 8 =± 9i b. = c 6+ 9 = 8+ 7= 8+ = b g h 9+ = 9 = ± c. + = = 7 =± 7 =± i b gb g b g d. + + = = 8+ 6 = 6 = [8] y f 4 fb fb g g 4 fbg b g City Adult Learning Centre (CALC) - Mathematics Assessment (vc)