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

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City Adult Learning Centre (CALC) - Mathematics Assessment (v1c)

1. Write 82% as a decimal.

2. Which of the following number lines shows the graph of 3, –1, and –5?

[A]–10 –5 0 5 10

[B]–10 –5 0 5 10

[C]–10 –5 0 5 10

[D]–10 –5 0 5 10

3. Write each ratio in simplest form.

a) 2545

b) 2418

c) 1290

d) 57:19

4. Simplify. a) –3 + ( )−4 2

b) ( )2 3 – 5c) −32 × 4d) ( )−2 3 – (–1)e) –2 + ( )−3 2 × 2f) (–4)(4 5)2− – ( )−2 2

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



[1] 0.82

[2] A

[3]a) 5

9 b) 4

3 c) 2

15 d) 3:1

[4] a) 13 b) 3 c) –36 d) –7 e) 16 f) –8

[5] B

[6] A

[7]

a) w = 70°, x = 70°, y = 70°, z = 70°b) x = 60°, y = 60°c) x = 40°, y = 40°, z = 100°

[8] B

Entrance to Grade 9 - Essential Mathematics (MAT1L)



[1] D

[2] a) 5, 4, 3, 2, 1 b) 1, 0, –1, –2, –3

[3] B

[4] a) 3 b) –3 c) 1 d) 7

[5] –22

[6] 0.0875

[7]

a)

b)

c)

d)

Percent Fraction Out of 100 Decimal

700%700100

7.0

225%225100

2.25

154100 1.54154%

3.69369% 369100

[8] A

Entrance to Grade 9 - Essential Mathematics (MAT1L)



1. Subtract. 513

− 2 12

[A] 1112

[B] −116

[C] 4 1112

[D] 2 56

2. Complete the tables.

a)

a a +

−−

321012

b)

( )x x− +

−−

121012

3. Add. (–5) + (+7) + (–8) [A] 20 [B] –6 [C] 6 [D] –4

4. Simplify.

a) ( )( )( )− +−

2 64

b) 4 96 2( )

( )( )+

− + c) (

(−

− +75)

15)( 5) d) 9 7

3 3( )

( )( )−

− +


5. Add. (–3) + (–19)

6. Write 834

% as a decimal.

7. Complete the table.

a)

b)

c)

d)

Percent Fraction Out of 100 Decimal

700%

225%

154100

3.69

8. Which rational number has a numerator less than −1 and a denominator greater than 1?

[A] – 99

[B] – 31

[C] ––

62

[D] −14

Entrance to Grade 10 Applied - Foundations of Mathematics (MPM2P)



[1] 8 710

[2] C

[3] Jacques, by $0.30/h

[4] y x y x + = ( – ); = – 6 25

2 25

345

[5] 18

[6] D

[7] ∠1 = 125°, ∠3 = 55°

[8] 2

Entrance to Grade 10 Academic - Principles of Mathematics (MPM2D)



[1]

a) 15 0152. .c c−b) w w w3 − + − 3 6 42

c) 2 6 43

2 2x y x x y + − +

[2] a) 0 25 6. d b) 5 4 5 7. a b c) −121 8. k d) −108 7 9 8r s t

[3]

a)b)c)d)

$3.50 20%$12.00 25%$11.70 30%$54.74 15%

Cost Price Markup Selling Price $4.$15.$15.$62.

20002195

[4] 15 years and 44 years

[5] −2

11

[6] 243, 729, 2187

[7] 49 m2

[8] x = 128°

Entrance to Grade 10 Academic - Principles of Mathematics (MPM2D)



1. Expand.a) 0 3 5 0 52. .c c−c hb) − − + − +0 5 2 6 12 83 2. w w wc hc) 1

36 18 3 42 2x y x x y + − +c h

2. Simplify. a) 05 3 2. dc h b) 0 2 32 2 3

. a b abc hc h c) − −01 112 3 2. k kc hc h d) − 3 22 3 2 3 2

rst r s tc h c h

3. Complete the table.

a)b)c)d)

Cost Price Markup Selling Price $3.50 20%$12.00 25%$11.70 30%$54.74 15%

4. The sum of the ages of Petra and her mother is 59. Her mother is 14 years more than twice as old asPetra. How old are Petra and her mother?


5. Find the slope of the line.

y

x–10 –5 5 10

–10

–5

5

10

0

6. Identify the next three terms in the sequence. 3, 9, 27, 81, . . .

7. Find the area of the composite shape.

3 m

3 m

5 m

8 m

8. Find the value of x.

x

62° 69°

101°

Entrance to Grade 10 Applied - Foundations of Mathematics (MPM2P)



1. Estimate, then multiply. 456

145

×

2. Simplify. 357

7

5xx−

[A] 5 2x [B] − x2 [C] − 5 2x [D] − 5 12x

3. Gerrie was paid $68.00 for 8 h of work. Jacques received $61.60 for 7 h. Who had the higher rate of payand by how much?

4. Write an equation of the line that passes through the point (2, –6) and has slope 25

. Then, rewrite the

equation in slope and y-intercept form.


5. Find the mode of the data.14, 17, 18, 13, 17, 18, 14, 13, 18, 15

6. Solve. −4 19 2 23 4n n + + + = – [A] 233

[B] 0 [C] −19 [D] 23

7. Find the measures of ∠1 and ∠3.

7

1 3

5 64 2

125°

8. Solve. 33 0 7 0 6 4 7. . . .x x − = +

Entrance to Grade 11 Foundations for College Mathematics (MBF3C)



1. Application Name the type of quadrilateral formed when the lines x = 7, 2x + 3y – 7 = 0, x – 3y = 0, and2x + 3y = –10 intersect.

2. Problem Solving The width of a rectangle is 3 m less than the length. The area of the rectangle is10 m2. Find the dimensions of the rectangle.

3. State whether each set of ordered pairs represents a function.a) { b) { c) { d) {

( , ( , ), ( , ), ( , )} ( , ), ( , ), ( , ), ( , )}( , ), ( , ), ( , ), ( , )} ( , ), ( , ), ( , ), ( , )}0 5), 1 4 2 3 3 2 2 3 3 2 4 1 5 03 7 5 9 7 7 9 7 1 0 1 3 1 0 1 3

− − −− −

4. In the given triangle, name the largest angle. The triangle is not drawn to scale.

A

B

C27 cm

24 cm20 cm


5. Expand and simplify.a) b) c) d)

( ) ( ( ) ( )( )( )( ) ( ) ( ) ( )a a x x xt t t d d− + + − + − +− + − − − − −

6 5) 7 3 33 1 1 4 1 5 3 2 3 3

2 2 2

2 2 2

6. Problem Solving A small park is enclosed by 180 m of fencing. The area of the park is 2016 m2 . Whatare the dimensions of the park?

7. Factor. 8 72 48 4323 2 2x x x x− + −

[A] ( )( )8 10 8 7x x− + [B] x x x( )( )8 10 8 7− + [C] 8 9 6x x x( )( )− + [D] 8 9 6( )( )x x− +

8. State the coordinates of the vertex of the parabola. Then, use a graphing calculator or graphing softwareto determine any x-intercepts. Round to the nearest tenth, if necessary. y x= + − −18 2 32. ( )

Entrance to Grade 11 Foundations for College Mathematics (MBF3C)



[1] trapezoid

[2] 5 m by 2 m

[3] a) yes b) yes c) yes d) no

[4] B

[5]a) b) c) d)

2 2 61 2 14 408 7 42 42 7

2 2

2 2

a a x xt t d d− + − +

− + − − −

[6] 48 m by 42 m

[7] C

[8]

x

y

–10 10

–10

10

0

vertex ( , )2 3 ; x-intercepts: 0.7, 3.3

Entrance to Grade 11 University/College Functions and Applications (MCF3M)



1. Factor. 3 13 122x x+ +

[A] (3 4x + )(x − 3) [B] (3 4x + )(x + 3) [C] (3 4x − )(x − 3) [D] (x + 3)(3 4x − )

2. Communication The table gives the area and three side lengths for two similar right triangles. Describethe relationship between the ratio of the lengths of the corresponding sides and the ratio of the areas.

Area (m Side 1 Side 2 Side 3Triangle A 24 10Triangle B 96 20

2 )6 8

12 16

3. Application The lengths of two similar rectangles are 14 cm and 11 cm. What is the ratio of thecorresponding side lengths? the areas?

4. Write the equation of the circle, given its centre and radius.centre ( , ),0 0 radius 7

[A] x y2 2 14+ = [B] x x2 2

14 141+ = [C] x y2 2 7+ = [D] x y2 2 49+ =


5. Find the midpoint of the line segment with endpoints –8, 5b g and –5, .3b g[A] −FHG

IKJ

32

1, [B] –13, – 8b g [C] − −FHG

IKJ

32

1, [D] −FHGIKJ

132

4,

6. Factor. 9 81 36 3243 2 2x x x x− + −

[A] 9 9 4x x x( )( )− + [B] ( )(9 10 9 5)x x− + [C] x x x( )(9 10 9 5)− + [D] 9 9 4( )( )x x− +

7. Sketch the graph of each parabola. Determine any intercepts, to the nearest tenth, and find two otherpoints on the graph.a) b) c) d)

y x y xy x y x= == + + = +

–( – ) ( – ) ––1. ( ) ( – )

2 3 1 25 1 3 3 2 4

2 2

2 2

8. Solve the system of equations by substitution or elimination. Check the solution.

a)

x yx y− =+ =2 0

3 2 16

b) 2x yx y+ =+ =

3 414 5 71

c) 3x y

x y+ = −+ =

5 374 7 19

d)

y x

y x

= +

= +

75

5

15

2

e)

13 4 35 59 6

= −= +

x yx y

f)

3 45

1

6 5 4 0

y x

x y

= −

− − =

Entrance to Grade 11 University/College Functions and Applications (MCF3M)



[1] B

[2]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 1:2, then the ratio of the areas is 1:4.

[3] 14:11; 196:121

[4] D

[5] D

[6] A

[7]

a) x-intercept 2; y-intercept –4; (1, –1), (3, –1), (4, –4), (5, –9), ...b) x-intercepts 1.8 and 0.2; y-intercept 1; (1, –2), (2, 1), (3, 10), (–1, 10), ...c) x-intercepts –2.4 and 0.4; y-intercept 1.5; (0, 1.5), (–2, 1.5), (1, –3), (–3, –3), ...d) no x-intercept; y-intercept 16; (1, 7), (2, 4), (3, 7), (4, 16), ...a)

2

−2

0 x

y b)

−2 2

2

0 x

y c)

−2 2

2

0 x

y

d)

2

2

4

6

0

y

x

[8]

a) (4, 2) b) (4, 11) c) (– , –4 5)

d) −FHGIKJ

52

32

, e) (–11, –19) f) 12

15

, −FHGIKJ

Entrance to Grade 11 University Functions (MCR3U)



1. Graph y x= + −1 42b g .

[A]

x

y

0 –10 10

–10

10[B]

x

y

0 –10 10

–10

10

[C]

x

y

0 –10 10

–10

10[D]

x

y

0 –10 10

–10

10

2. In the given triangle, name the longest side length. The triangle is not drawn to scale.

A

B

Cb

ac

67°

54°

59°

3. Communication Δ ΔPQR and PST are similar. Explain how to calculate each ratio.

a) PRPT

b) STQR

c) area of PSTarea of PQR

ΔΔ

RT

QSP


4. Solve each system by elimination. If there is exactly one solution, check the solution. 2 45

x yx y

− =+ =

[A] 10 2, b g [B] 0, −4b g [C] 2 0, b g [D] 3 2, b g

5. Problem Solving The area of a triangle is represented by the polynomial x x2 3 18+ − . The base of thetriangle is represented by x + 6.a) Factor x x2 3 18+ − .b) Write a binomial that represents the altitude of the triangle.c) Find the area of the triangle if x = 12.

6. Δ ΔVWX ~ VYZ. Find VY, WY, VZ, and XZ.

V

W

Y

XZ

7 cm

8 cm5 cm 15 cm

7. The diameter of a circle joins the points C(0, 7) and D(5, 1). What are the coordinates of the centre ofthe circle?

8. Application Write an equation for each function.a) x y

0 11 42 73 104 13

b) x y

0 61 42 23 04 2−

c) x y

0 71 52 53 74 11

d) x y

0 21 72 223 474 82

Entrance to Grade 11 University Functions (MCR3U)



[1] D

[2] a

[3]a) PR

PTPQPS

= = =42

21

b) STQR

PSPQ

= =12

c) PSPQ

so=12

area of PSTarea of PQR

ΔΔ

= =12

14

2

2

[4] D

[5]

a) (x + 6)(x − 3)b) 2 6x −c) 162

[6] VY 24 cm, WY 16 cm, VZ 21 cm,= = = and XZ 14 cm=

[7]52

4,FHGIKJ

[8]

a) y x= +3 1b) y x= − +2 6c) y x x= − +2 3 7d) y x= +5 22

Entrance to Grade 12 Foundations for College Mathematics (MAP4C)



1. Application The vertex of a parabola is (2, –5). One x-intercept is –3. What is the other x-intercept?

2. Find the axis of symmetry of the parabola. y x x + −= 2 6

[A] x = –1 [B] x = 12

[C] x = 1 [D] x −= 12

3. Communication Write the equation that represents the graph. Explain your reasoning.

10

10

0 x

y

4. Communication None of the following trinomials is a perfect square. Change one term in eachtrinomial to make a perfect square. Explain your reasoning.a) a ab b2 217 36+ + b) t t2 8 15− + c) 9 72 2x xy y+ + d) c cd d2 2+ +

5. Find the shortest distance from the origin to each line, to the nearest tenth.a) x y+ = −2 b) 3 2 6x y− = c) 4 5 20x y= − + d) y x+ − =3 6 0


6. Application For the equation y x x + += 2 14 242 ,a) find the axis of symmetry of the graph of the equationb) find the vertex of the graphc) graph the equation

[A] a) x = − 72

b) vertex − FHG

IKJ

72

12

,

c)

x

y

0 –10 10

–10

10

[B] a) x = 72

b) vertex 72

58

, FHGIKJ

c)

x

y

0 –10 10

–10

10

[C] a) x = − 72

b) vertex − −FHG

IKJ

72

12

,

c)

x

y

0 –10 10

–10

10

[D] a) x = 72

b) vertex 72

38

, −FHGIKJ

c)

x

y

0 –10 10

–10

10

7. Triangle XYZ has vertices X(2, 1), Y(1, –3), and Z(6, –2). 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 maximum.

Entrance to Grade 12 Foundations for College Mathematics (MAP4C)



[1] 7

[2] D

[3]The vertex, which has the form ( , ),h k is 1 3, b g. The equation, which has the form y a x h k= − +b g2 , isy x= + .( )−1 32

[4]

a) The first and the last terms are perfect squares. Double the product of their square roots, a and 6b, toget 12ab as the middle term. Check ( ) .a b+ 6 2

b) Change the last term to 16 to make it a perfect square. Then, check ( ) .t − 4 2

c) The first and last terms are perfect squares. Double the product of their square roots, 3x and y, to get6xy as the middle term. Check ( ) .3 2x y+d) the middle term should be double cd, or 2cd. Check ( ) .c d+ 2

[5] a) 1.4 b) 1.7 c) 3.1 d) 1.9

[6] C

[7]A 3

2, B 4, – 1

2, – ;1FHGIKJFHGIKJ The slopes of AB and YZ are both 1

5.

[8] 22 and 22

Entrance to Grade 12 Mathematics for College Technology (MCT4C)



1. Mary saved $2500 from her summer job and invested it at 4% per annum compounded monthly. Howmuch will she have four years later when she attends college?

2. Solve each of the following:a. 3 6 87x + = c. 4 22 421x+ − =

b. 5 2 160 0xc h − = d. 36

812

1x−

=

3. Simplify each of the following:a. x x x2 23 4 1+ − − −c h b g c. x x+ − +3 2 12b g b gb. 2 3 1x x+ −b gb g d. 2 3 3 22 2x x+ − +b g b g

4. State any restrictions on the variable in each of the following:

a. 3 77

x + c. 2 5 95

2x xx+ −−

b. 4 57 122y

y y−

− +d. y

y y+

+ −7

2 152


5. Simplify each of the following:

a. 24

2 3

3 4

x yx yc h

c. 4 9212 3 4

12xy x yc h c h

b. 2 32 3 2 4 2x y x yc h c h− d. 3

15

2 4

2 3x yxyc h

6. Solve each of the following for x.a. x2 81 0+ = c. x2 15 12+ = −b. 3 3 32 2x x− = −b g d. x x x+ + = −2 5 4 2b gb g b g

7. Convert the following to radian measure.a. 330° b. 48° c. –510°

8. Simplify each of the following:

a. m mm m

a a

a a

2 3 2

1 1

+ −

+ −

⋅⋅

b. a aa

14

12⋅

Entrance to Grade 12 Mathematics for College Technology (MCT4C)



[1]

A P i n= +

= +FHGIKJ

=

1

2500 1 0 0412

293300

48

b g.

.Mary will have $2933.00 four years later.

[2]

a. 3 6 873 813 3

4

4

x

x

x

x

+ =

=

==

c. 4 22 424 644 4

1 32

1

1

1 3

x

x

x

xx

+

+

+

− =

=

=+ =

=

b. 5 2 160 0

2 32 02 2

5

5

x

x

x

x

c h − =

− =

==

d. 36

812

3 2433 3

1 56

1

1

1 5

x

x

x

xx

−

−

−

=

=

=− =

=

[3]

a. x x x x

x x x xx

2 2

2 2

3 4 2 1

3 4 2 15 5

+ − − − +

= + − − + −= −

c h c. x x xx x

2

2

6 9 2 24 7

+ + − −

= + +

b. 2 3 3

2 4 6

2

2

x x x

x x

− + −

= + −

c h d. 4 12 9 3 4 4

4 12 9 3 12 123

2 2

2 2

2

x x x x

x x x xx

+ + − + +

= + + − − −

= −

c h

[4]a. no restrictions c. x ≠ 5b. y ≠ 3 4, d. y ≠ −5 3,

[5]

a. 24

842

2 3

3 4

6 3

3 4

3

x yx y

x yx yxy

c h=

=

c. 4 9 36

6

212 3 4

12 4 6

12

2 3

xy x y x y

x y

c h c h c h=

=

b. 2 3 8989

2 3 2 4 2 6 3

4 8

2

5

x y x y x yx yxy

c h c h− =

=

d. 315

315

15

2 4

2 3

2 4

3 6

2

x yxy

x yx y

xy

c h=

=


[6]

a. xx

xi

2

2

81 081

819

+ =

= −

= ± −= ±

c. xx

x

i

2

2

15 1227

27

3 3

+ = −

= −

= ± −

= ±

b. 3 3 3

3 6 9 3

3 18 27 32 18 30 0

9 15 0

9 212

2 2

2 2

2 2

2

2

x x

x x x

x x xx x

x x

x

− = −

− + = −

− + = −

− + =

− + =

=±

b gc h

d. x x x

x x x xx

x

+ + = −

+ + = − +=

=

2 5 4

7 10 8 1615 6

25

2

2 2

b gb g b g

[7]a. 330 330

180116

°= ×π

= π b. 48 48180

415

°= ×π

= π c. − °= − ×π

= − π510 510180

176

[8]

a. m mm m

mm

m

a a

a a

a

a

a

2 3 2

1 1

3 1

2

1

+ −

+ −

+

+

⋅⋅

=

=

b. a aa

a a

a

a

a

14

12

14

12

12

12

14

12

18

⋅=

⋅F

HGG

I

KJJ

=FHGIKJ

=

Entrance to Grade 11 - Mathematics for Work and Everyday Life (MEL3E)



1. A rectangular prism is 11 cm long, 11 cm wide, and 12 cm high. Find the surface area of the prism.

2. The average cost of a computer has decreased since 1978. The following table gives the averagecomputer cost, to the nearest five hundred dollars, for selected years.

Year Average Computer Cost ($)1978 1982 2500 1986 2000

1000

5000

1990

a) Plot these points on a graph.b) Connect the points using line segments.c) Determine the average yearly decrease in cost between 1978 and 1982.d) Determine the average yearly decrease in cost between 1982 and 1986.

3. Evaluate a − b for a = 5.7 and b = –4.4.

4. Express the unit rate in the units shown.a) 7 cans of punch for $4.83; ¢/canb) $61.65 for 8 h of work; $/hc) 76 h of sunshine in 8 days; h/dayd) $10.75 for 18.7 L of gas; ¢/L


5. The table shows the study times and test scores for a number of students. Draw a scatter plot of scoreversus time.

Study Time (min) 6 11 15 18 21 24 31 34Test Score 58 62 59 62 66 70 69 69

6. Calculate each surface area, to the nearest square unit.

d)

10.9 cm

6.5 cm

a)3 m

9 m

c)

b)

7 cm

11 cm

17 mm

13 mm

7. Write two ratios equivalent to 4:6.

8. If 104

, −188

, 96

, and −172

were placed in order from greatest to least, which would be first?

[A] 96

[B] −172

[C] −188

[D] 104

Entrance to Grade 11 - Mathematics for Work and Everyday Life (MEL3E)



[1] 770 2 cm

[2]

a) and b)

1978 1982 1986 1990Year

1000

2000

300040005000

Cos

t ($)

0

c) $625d) $125

[3] 10.1

[4] a) 69¢/can b) $7.71/h c) 9.5 h/day d) 57.5¢/L

[5]10 20 30 40

85807570

6560

5550

Study Time (min)

Effect of Study Time on Test Score

0

Test

Sco

re

[6] a) 226 m2 b) 396 cm2 c) 480 mm2 d) 289 cm2

[7] Examples: 2:3, 6:9, 8:12, 10:15

[8] D

Entrance to Grade 12 University Advanced Functions (MHF4U)or Mathematics of Data Management (MDM4U)



1. Find two integers whose sum is –31 and whose product is 240.

2. The science class is investigating projectiles and they have built catapults. Margarita’s team has built acatapult that throws a table-tennis ball vertically upward. The height of the table-tennis ball incentimetres above the ground is given by the formulah t t= + −5 50 5 2.

a. At what height is the table-tennis ball released?b. What is the ball’s maximum height?c. If the ball has to stay in the air for 10 s to qualify for a prize, can Margarita’s team win a prize?

3. Solve each of the following for x.

a. 3 272 2x x+ = c. 1

42 2

2b gx x=

b. 2 2 14

2 3x x× = d. 3 81 35 2x x× = −

4. A mirror frame is 90 cm by 120 cm. The mirror has an area of 8800 cm2. How wide is the frame?


5. Solve each of the following:a. 3 6 87x + = c. 4 22 421x+ − =

b. 5 2 160 0xc h − = d. 36

812

1x−

=

6. Given ΔABC with AB BC AC= = = 2,

B

A

C

2 2

2

a. draw b. find .c. find .d. find the measure of e. find the measure of f. find and g. find and

AD BCDCAD

CDAC

⊥

∠∠

° ° °° ° °

.

..

sin , cos , tan .sin , cos , tan .

30 30 3060 60 60

7. Solve each of the following for x.a. x2 81 0+ = c. x2 15 12+ = −b. 3 3 32 2x x− = −b g d. x x x+ + = −2 5 4 2b gb g b g

8. From the graph of f(x) showna. graph – 2f(x).

b. graph 34

f(x).

c. graph 2f(x – 2).

–6 –5 –4 –3 –2 –1 1 2 3 4 5 6

–4–3–2–1

1234

x

y

Entrance to Grade 12 University Advanced Functions (MHF4U)or Mathematics of Data Management (MDM4U)



[1]

Let the integers be represented by x and − −31 xb g.x x

x xx xx x

x

− − =

− − =

+ + =

+ + =

= − −

31 240

31 24031 240 0

15 16 015 16

2

2

b g

b gb g,

If x = −15, the second integer is − − = − + = −31 31 15 16xb g .If x = −16, the second integer is − − = − + = −31 31 16 15xb g .The two consecutive integers are –15 and –16.

[2]

a. When t h= =0 5, . The ball is released at 5 cm.b. h t t

t t

t

= + −

= − − + + +

= − − +

5 50 5

5 10 25 5 125

5 5 130

2

2

2

c hb g

The maximum height is 130 m.c. The ball hits the ground when

or

ht t

t tt t

t

=+ − =

− − =

− − =

=± +

=±

= −

05 50 5 05 50 5 0

10 1 0

10 100 42

10 1042

10 099 0 099

2

2

2

.

& . .Time cannot be a negative. The ball stays in the air for 10.1 s and Margarita’s team can win a prize.


[3]

a. 3 27

3 32 3

2 3 03 1 0

3 1

2

2

2

2 3

2

2

x x

x x

x xx x

x xx

+

+

=

=

+ =

+ − =

+ − =

= −b gb g

, +

c. 14

2 2

2 2 2

2 222 0

2 1 02 1

2

2

2

2

2

2

2

b gb g

b gb g

x x

x x

x x

x xx x

x xx

=

=

=

− =

− − =

− + =

= −

−

−

,

b. 2 2 14

2 23 2

3 2 02 1 0

2 1

2

2

3

3 2

2

2

x x

x x

x xx x

x xx

× =

=

+ = −

+ + =

+ + =

= − −

+ −

b gb g,

d. 3 81 3

3 3 3

3 34 51 0

1 1 42

1 52

5

4 5

4 5

2

2

2

2

2

x x

x x

x x

x xx x

x

× =

× =

=

+ = −

+ − =

=− ± +

=− ±

−

−

+ −

[4]

Let x represent the width of the frame.90 2 120 2 8800

10 800 180 240 4 88004 420 2000 0

105 500 0100 5 0

100 5

2

2

2

− − =

− − + =

− + =

− + =

− − =

=

x x

x x xx x

x xx x

x

b gb g

b gb g

,

x x

x

x

90 – 2x

120 – 2x

120 cm

90 cm

If x =100, the length and width of the mirror would be negative.Therefore, the width of the frame is 5 cm.

[5]

a. 3 6 873 813 3

4

4

x

x

x

x

+ =

=

==

c. 4 22 424 644 4

1 32

1

1

1 3

x

x

x

xx

+

+

+

− =

=

=+ =

=

b. 5 2 160 0

2 32 02 2

5

5

x

x

x

x

c h − =

− =

==

d. 36

812

3 2433 3

1 56

1

1

1 5

x

x

x

xx

−

−

−

=

=

=− =

=


[6]

a.

B

A

C

2 2

D1 1

b. c.

d. e.

DCAD

AD

ADCDAC

== +

=

=∠ = °∠ = °

12 1

3

360

30

2 2 2

2

f.

= 3

g.

= 3

sin

cos

tan

sin

cos

tan

30 12

30 32

30 13 3

60 32

60 12

60 31

°=

°=

°=

°=

°=

°=

[7]

a. xx

xi

2

2

81 081

819

+ =

= −

= ± −= ±

c. xx

x

i

2

2

15 1227

27

3 3

+ = −

= −

= ± −

= ±

b. 3 3 3

3 6 9 3

3 18 27 32 18 30 0

9 15 0

9 212

2 2

2 2

2 2

2

2

x x

x x x

x x xx x

x x

x

− = −

− + = −

− + = −

− + =

− + =

=±

b gc h

d. x x x

x x x xx

x

+ + = −

+ + = − +=

=

2 5 4

7 10 8 1615 6

25

2

2 2

b gb g b g

[8]

–6 –5 –4 –3 –2 –1 1 2 3 4 5 6

–4–3–2–1

1234

x

y

f xb g

– 2 f xb g

34

f xb g2 – 2f xb g

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