Resources

Resources

Transformations of linear functions

0 . \overline{437}

expressed in the form

\frac{p}{q}

p

q

are integers and

q \neq 0

437

2

. Write down a pair of integers whose:

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2

-13

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5

. difference is

-12

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0

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d. difference is

10

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23

with one number being negative.

x=3+2 \sqrt{2}

, then find whether

x+\frac{1}{x}

is rational or irrational.

18

\frac{6-4 \sqrt{3}}{6+4 \sqrt{3}}

by rationalizing the denominator.

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6

x=3+2 \sqrt{2}

, then find whether

x+\frac{1}{x}

is rational or irrational

2

(Problem Solving)

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8

. Write a negative integer and a positive integer whose

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-9

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-4

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\operatorname{sum} 0

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9

. The sum of two integers is

116

. If one of them is

-79

, find the other integers.

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10

. Write five pair of integers

(m, n)

m \div n=-3

. One of such pair is

(-6,2)

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11

. What number should be added to the sum of

345

67

to make it equal to the smallest

3

Cnoose the best term from the box. Write it on the blank.

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1

. For any numbers

a

b, a \times b=b \times a

a+b=b+a

when applying the

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2

. The the number line. of

-6

6

, because it is

6

units from zero on

1

. On which axis do the following points lie?

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P(5,0)

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\mathrm{Q}(0-2)

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R(-4,0)

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S(0,5)

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2

A B C D

be a square of side

2 a

. Find the coordinates of the vertices of this square when

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(i) A coincides with the origin and

A B

A D

O X

O Y

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(ii) The centre of the square is at the origin and coordinate axes are parallel to the sides

A B

A D

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P(5,0)

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Q(0-2)

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R(-4,0)

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S(0,5)

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2

A B C D

be a square of side

2 a

. Find the coordinates of the vertices of this square when

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(i) A coincides with the origin and

A B

A D

O X

O Y

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(ii) The centre of the square is at the origin and coordinate axes are parallel to the sides

A B

A D

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3

Q(0-2)

2

of two equilateral triangles

Q(0-2)

3

Q(0-2)

4

2 a

Q(0-2)

6

-axis such that the

2

\sqrt{18 x+27}

k \sqrt{2 x+3}

k

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(ii) Hence solve the equation

\sqrt{18 x+27}-\sqrt{2 x+3}=6

1

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9

15

3

019

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Evaluate the iterated integral by converting to polar coordinates.

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\int_{0}^{1} \int_{y}^{\sqrt{2-y^{2}}} 7(x+y) d x d y

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\mathrm{U}=2,5,6,7,12

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B=2,6

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What is the complement of Set B in Set U?

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\{5,7,12\}

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\{2,6,7,12\}

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\{2,6\}

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\{2,5,6,7,12\}

0

99999

\frac{p}{q}

p

q

are integers and

q \neq 0

A four digit number,

n

W X Y Z

W, X, Y, Z

are all different odd digits. Furthermore

n

is divisible by each of

W, X, Y, Z

. What is the largest possible value for

W-X+Y-Z

a

b

are the intercepts made by a line on the co-ordinate axes. If

3a=b

and the line passes through

(1,3)

, then the equation of the line is

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x+3y =10

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3x+y =6

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x-3y+8 =0

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3x-2+3 =0

Mary says that you can find an

x

-intercept by substituting

0

x

, while Michelle says that you need to substitute

0

y

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a. Who, if anyone, is correct and why?

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b. Use the correct approach to find the

x

-4 x+5 y=16

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Find three consecutive integers whose sum is

138

by writing and solving an equation.

P = \{-1\}

Q = \{-7, -5, -3, -1, 1\}

P \cup Q

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\{-7, -5, -3, -1, 1\}

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\{-1\}

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\{-7, -5, -3, 1\}

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\{-5, -3\}

P = \{1, 7, 8\}

Q = \{-10, 7, 8\}

P \cup Q

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\{7\}

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\{7, 8\}

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\{-10, 1\}

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\{-10, 1, 7, 8\}

P = \{1, 7, 8\}

Q = \{-10, 7, 8\}

P \cup Q

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\{7, 8\}

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\{-10, 1\}

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\{7\}

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\{-10, 1, 7, 8\}

\cos A=\frac{\sqrt{12}}{5}

\cos B=\frac{\sqrt{28}}{6}

, and that angles

A

B

are both in Quadrant I, find the exact value of

\cos (A-B)

, in simplest radical form.

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\mathrm{X}

-19

\mathrm{Y}

\mathrm{Z}

8

units away from Point

\mathrm{X}

\mathrm{Y}

\mathrm{Z}

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\mathrm{Y}=\square \quad \mathrm{Z}=\square

a

b

are non-zero integers such that

a^2 + b^2 - 4a - 2b = 0

a^2 - b^2 = 0

, which of the following could be the value of

(a - b)

Two circles meet at points

\mathrm{X}

\mathrm{Y}

[\mathrm{AXB}]

meets one circle at

\mathrm{A}

and the other at

\mathrm{B}

. Line segment [CYD] meets one circle at

C

and the other at

D

[A C]

[B D]

Triangle CDE is dilated by a scale factor of

5

to form triangle C'D'E'. Side EC measures

16

. What is the measure of side

\mathrm{E}^{\prime} \mathrm{C}^{\prime}

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Three consecutive numbers are selected from the set of integers from

1

30

P

is the product of the numbers drawn. Which of the following must be true? [Without calculator]

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P

is an integer multiple of

3

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P

is an integer multiple of

4

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P

is an integer multiple of

6

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(C) Both I and III

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(D) Both II and III

a

b

are non-zero integers such that

a^2+b^2-4a-2b=0

a^2-b^2=0

, which of the following could be the value of

(a-b)

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-3

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2

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3

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6