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	Fairfield Methodist Secondary School
	Secondary 3 Additional Maths Online Test

Question # 1

Find the values of the unknown constants in the following identity:

??x³ + 2x² - 16x - 14 ?/span> Ax²(x - 2) + B(x - 1)²(x - 2) + C(x + 3)

Choices are:

A.		A = -1, B = 2, C = 6
B.		A = 3, B = -2, C = -6
C.		A = 1, B = -1, C = 11
D.		None of the above

Question # 2

Find the value of k for which x³ + 2x² - 5x + k is exactly divisible by x - 2

Choices are:

A.		-6
B.		-10
C.		6
D.		-5

Question # 3

The expression 2x³ + ax² - 72x - 18 leaves a remainder of 17 when divided by

x + 5. Find the value of a.

Choices are:

A.		23
B.		3
C.		-3
D.		5

Question # 4

When the polynomial p(x) is divided by x - 1, the remainder is 5 and when p(x) is divided by x - 2, the remainder is 7. Find the remainder when p(x) is divided

by (x - 1)(x - 2).

Choices are:

2x + 3

5x + 7

Question # 5

f(x) = x⁴ - x³ + bx² + 50x + a?leaves remainder of?(x + 9)?when divided by

(x² - 3x + 2).?Find the value of a and of b.

Choices are:

A.		a = -5,?b = -21
B.		a = 5,?b = 21
C.		a = -21,?b = -19
D.		a = -59,?b = 19

Question # 6

x² + ax?+ b is exactly divisible by x + 1, and is such that the sum of a and b is 2. Find the values of a and b.

Choices are:

A.		a = 3, b = -1
B.		a = -1, b = 3
C.
D.

Question # 7

(x + 2) and (x + 4) are factors of g(x) =?x⁴ + ax³ + 2x² - bx, solve the equation

g(x) = 0.

Choices are:

x = 0, 1, 2, or 3

x = 0, -1, -2, or -3

x = 0, -1, 2, or -4

x = 0, 1, -2, or -4

Question # 8

Find the value of k for which p + 5q is a factor of p⁴ - 23p²q²+ kq⁴. Hence

factorise p⁴ - 23p² q²+ kq⁴completely.

Choices are:

(p + 5q) (p - 5q) (p² + 2q²)

(p² + 23q²)²

(p + 50q) (p² + 2q²) (p² - 10q)

(p² - 5q) (p² - 5q) (p² + 2q²)

	Fairfield Methodist Secondary School
	Secondary 3 Additional Maths Online Test

Question # 1

If R = {x: x is a letter of the word lament} and

? S =? {x: x is a letter of the word elemental}

then R ≠ S

Correct Answer :

Question # 2

In a colony, C is the set of people who travel in the morning by car, B is the set of people who travel in the morning by bus and S is the set of students residing in the colony.

Express in set notation the statement "not all students travel by bus in the morning"

Choices are:

A.		S' ?/span> B ?/span> f
B.		B' ?/span> S ?/span> f
C.		S' ?/span> B ?/span> f
D.		B' ?/span> S ?/span> f

Question # 3

In the above question, make a statement explaining the meaning of

(B ?/span> C)' ?/span> S ?/span> f

Choices are:

A.		There are some students who neither travel by bus nor car
B.		There are some students who travel by bus or car
C.		There are some students who travel by bus and car
D.		None of the above

Question # 4

List the elements of the following set:
B = {x: x is an even integer and x is a factor of 54}

Choices are:

A.		{2, 4, 6, 8, . . .}
B.		{2, 6, 18, 54}
C.		{54, 108, 162, . . .}
D.		None of the above

Question # 5

Express the subset shaded in the Venn diagram in set notation.

Choices are:

A.		Q ?/span> (P ?/span> R)
B.		(P ?/span> R) ?/span> Q
C.		Q ?/span> (P ?/span> R)
D.		(P ?/span> R) ?/span> Q

Question # 6

Given the condition that B and C are disjoint sets, draw a suitable Venn diagram

representing the sets A, B and C.

In the diagram, shade the region representing [A' ?/span> B' ?/span> C] ?/span> [A ?/span> B]

Choices are:

Question # 7

Given that e = { x : x is an positive integer }

M = {x : 3x - 4 < 17}, N = {x : 4x - 5 ≥ 3}

List the elements of the set M ?/span> N

Choices are:

{1, 2, 3, 4, 5, 6}

{1, 2, 3, 4, 5, 6, 7, 8, . . .}

{2, 3, 4, 5, 6}

{2, 3, 4, 5, 6, . . .}

Question # 8

In the Venn diagram, the number of elements of A, B and C are shown.

If e = A ?/span> B ?/span> C and n(e) = 19, find n(C).

Choices are:

A.		5
B.		8
C.		6
D.		None of the above

Question # 9

Given that n (e) = 50, n (P) = 32, n (Q) = 23 and n (P ?/span> Q) = k

Find n (P' ?/span> Q') in terms of k

Choices are:

A.		-5 + k
B.		-5 - k
C.		-10 - k
D.		-10 + k

Question # 10

In the above question, find the largest and smallest possible value of k

Choices are:

A.		32 and 9
B.		50 and 5
C.		23 and 5
D.		50 and 23

Question # 11

A fun club organized a sports event for its 100 members aged above 45.
40 took part in Marathon race, 27 took part in Swimming, 48 took part in Field Game, 6 took part in Marathon and Swimming, 5 took part in Field Games and Marathon and 7 took part in Swimming and Field Games.
If each took part in at least one event, find the number of people who took part in only one event.

Choices are:

A.		61
B.		3
C.		11
D.		None of the above

Question # 12

A business magazine survey gave the following data for subscription.

60% subscribe to 'Business Line', 50% subscribe to 'Business Info' and

50% subscribe to 'Business Today'.

30% subscribe to 'Business Line' and 'Business Info',

20% subscribe to 'Business Info' and 'Business Today'

30% subscribe to 'Business Line' and 'Business Today' and

10% do not subscribe to any magazine.

Use a Venn diagram to find what percent subscribe to just 'Business Line' and

'Business Today'

Choices are:

A.		30
B.		70
C.		40
D.		20

Question # 13

In the above question, what percent subscribe to only 'Business Line'

Choices are:

A.		60
B.		20
C.		10
D.		70

	Fairfield Methodist Secondary School
	Secondary 3 Additional Maths Online Test

Question # 1

Find the values of x and y if possible. Give reason for your answer if not possible.

Choices are:

A.		x = 3, y = 0
B.		Not possible as the two matrices are of different orders.
C.		x = 3, y = - 1
D.		Not possible as the two matrices have the same order.

Question # 2

The book "Mathemagic" is published in both hard cover and paperback. Store A stocks 100 copies of the hard cover and 300 copies of the paperback edition while store B stocks 150 copies of the hardcover and 300 copies of the paperback edition. 200 copies of the paperback and 400 copies of the hardcover edition are available in store C. Represent the above information as a matrix labelling the rows and columns and state the order of this matrix.

Choices are:

Order is 2 ?/span> 3

Order is 3 ?/span> 2?

Order is 2 ?/span> 3??

None of the above

Question # 3

Find the inverse if it exists.

Choices are:

A only??

B only

A and B

?? ??/span>

Neither A nor B

Question # 4

have an inverse?

Choices are:

x = 4

x = 1

x ?/span> 1

x = -4

Question # 5

Find 3A - 5B + 7C.

Choices are:

None of the above

Question # 6

If AB = C, find the values of p, q and r.

Choices are:

A.		p = 6,?q = - 2,?r = 2
B.		p = 4,?q = - 3,?r = -16
C.		p = -12,?q = 1,?r = 5
D.

Question # 7

Use Matrices to solve the equations:
4x + 3y + 7 = 0
7x + 6y + 16 = 0

Choices are:

A.		x = -2, y = -5
B.		No solution
C.		x = -1, y = -1
D.		None of the above

Question # 8

A bag contains 40 coupons worth a total amount of $ 155. Each coupon is

individually worth either $ 2 or $ 5. Use the matrix method to find the number of

coupons of each denomination.

Choices are:

15 coupons of $ 5 and 25 coupons of $2

15 coupons of $ 5 and 30 coupons of $2

15 coupons of?$2 and 25 coupons of $5

None of the above

	Fairfield Methodist Secondary School
	Secondary 3 Additional Maths Online Test

Question # 1

Solve the cubic equation 2x³ - 3x² -11x + 6 = 0.

Choices are:

None of the above

Question # 2

Solve the equation x³ - 2x² - 49x - 82 = 0, expressing non-integer solutions

Choices are:

A.
B.
C.
D.

Question # 3

Find the x coordinate of the points of intersection of the curve

y = x³ + x² + 3x - 3 with the curve y = 2x² + 4x - 4.

Choices are:

A.		x = -1, x = 1
B.		x = -1, x = 0, x = 1
C.		x = 1, x = -2
D.		x = -2, x = -1, x = 0

Question # 4

Using the substitution x = 2y + 1, solve the equation

?? (2y + 1)³ + (2y + 1)² - 10(2y + 1) + 8 = 0

Choices are:

A.		y = -4 , 1 , 2
B.
C.
D.

Question # 5

If (x + 2p) is a factor of f(x) = p²x⁴ - 3px³ + 4px - 7p² + 2,

find the possible values of p.

Choices are:

A.		p = -0.5 , 0.5
B.		p = -2,?0.25
C.
D.		None of the above

	Fairfield Methodist Secondary School
	Secondary 3 Additional Maths Online Test

Question # 1

log₂ (-8) is well defined. Say true or false.

Correct Answer :

Question # 2

Simplify the following:

Choices are:

A.
B.
C.
D.

Question # 3

Evaluate:

Choices are:

A.		0
B.
C.
D.		None of the above

Question # 4

Solve the following equation:

log₃ a = 16 log_a 3

Choices are:

A.		a = 64
B.		a = 4
C.		?/span>
D.		a = -64, 64

Question # 5

Given that 4 log₆ x = log₆ y - 3, express y in terms of x.

Choices are:

A.
B.		y = 216 x⁴
C.
D.		y = 729 x^-4

Question # 6

If 5^2a= x and 2^b = y.

Express 5^{a + 1}?2^-^2b in terms of x and/or y.

Choices are:

A.
B.
C.
D.

Question # 7

Solve for x: 11^x = e^{2x + 3}
(Leave your answer correct to 3 significant figures)

Choices are:

A.		7.53
B.		7.54
C.		-3.12
D.		-3.13

Question # 8

Choices are:

A.
B.
C.
D.

Question # 9

Solve the simultaneous equations:

log₄ (x - 4y) = 2

log₉ (2x + 60) - log₉ (2y + 8) = 1

Choices are:

A.		x = -40??;??y = -14
B.
C.		x = 24???;??y = 2???
D.		x = 6.4?? ;??y = -2.4

Question # 10

Choices are:

A.
B.
C.
D.

	Fairfield Methodist Secondary School
	Secondary 3 Additional Maths Online Test

Question # 1

Solve for x:? log₂x = -1

Choices are:

A.
B.		1
C.
D.		-2

Question # 2

Solve for x:

9^x - 4 (3^{x + 2} ) + 243 = 0

Choices are:

A.		x = 2 or x = 3
B.		x = 9 or x = 27
C.		x = 6
D.		None of the above

Question # 3

Given that y = ax^b + 10, and that y = 26 when x = 2 and y = 64 when x = 3,

find the values of a and of b.

Choices are:

A.		a = 1 ; b = 3
B.		a = 2 ; b = 3
C.		a = 432 ; b = -3
D.		a = 8 ; b = 3

Question # 4

Choices are:

A.		0.151
B.		0.347
C.		0.693
D.		None of the above

Question # 5

Find the value of x in he following equation:

log₂ (x² + 5x - 2) = log₂ (x² + 3x - 6) + log₄ 9

Choices are:

A.		x = -4
B.		x = 2
C.		Both A and B
D.		Neither A nor B

Question # 6

Given that x = lg k is a solution of the equation 10^{2x + 1} - 9(10^x) = 63,
find the value of k.

Choices are:

A.		3
B.
C.
D.		None of the above

Question # 7

Solve the simultaneous equations

ln (6x - y) = 3 ln 3 - ln 9

Choices are:

A.		x = 9 ; y = 36
B.		x = 1.8 ; y = -7.2
C.		x = 2 ; y = 9
D.

Question # 8

positive, express in its simplest form y in terms of x.

Choices are:

A.
B.
C.
D.		None of the above