 WinMaths Choi Wing Lam

S4 Form Test 1 (Full) 

done: 12 / 52
score: 3 / 52

Question 1: 
(4a)3 ⋅ a2 = Answer: C
A. 64a6 . Solution:
B. 4a5 .
(4a)3 ⋅ a2 = 43 a3 ⋅ a2
C. 64a5 . = 64a5
D. 4a6 .

A B C D


Question 2: 
(2x7 )2
= Answer: A
2x5
A. 2x9 . Solution:
B. 4x9 . (2x7 )2 22 x14
=
2x5 2x5
C. 4x70 . = 2x14−5
D. 2x19 . = 2x9

A B C D


Question 3: 
(6x8 )3
= Answer: B
4x2
A. 54x26 . Solution:
B. 54x22 . (6x8 )3 63 x24
=
4x2 4x2
C. 2x26 . = 54x22
D. 2x22 .

A B C D


Question 4: 
2x2 (6x + x) = Answer: D
A. 13x2 . Solution:
B. 14x2 .
2x2 (6x + x) = 2x2 (7x)
C. 13x3 . = 14x3
D. 14x3 .

A B C D


Question 5: 
−4x
= Answer: A
(−2x−5 )−3
A. 32 . Solution:
x14 −4x
B. 32x15 . (−2x−5 )−3
C. 1 x15 . =
−4x
2 (−2)−3 x15
D. 1
. 32
2x14 = 14
x

A B C D


Question 6: 
(2n5 )−6 = Answer: B
A. 1
. Solution:
128n27
B. 1 1
. (2n5 )−6 =
64n30 (2n5 )6
C. 1
. 1
64n34 = 6 30
1 2 n
D. . 1
128n26 =
64n30

A B C D


Question 7: 
(2y 4 )6
= Answer: B
2y 8
A. 32y 3 . Solution:

B. 32y 16 . (2y 4 )6 26 y 24
=
2y 8 2y 8
C. 256y 48 . = 26−1 y 24−8
D. 256y 24 . = 32y 16

A B C D


Question 8: 
82n+2
n+1 2 = Answer: C
(16 )
Solution:
A. 2−n−5
82n+2 82n+2
B. 2−5n−4 2 = 162n+2
n+1
(16 )
C. 2−2n−2 2n+2
(23 )
D. 2−3n−1 =
(24 )2n+2
26n+6
= 8n+8
2
= 26n+6−(8n+8)
= 2−2n−2

A B C D


Question 9: 
2566n+5
= Answer: D
165n+9
A. 424n+18 . Solution:
B. 4n+10 . 2566n+5 44(6n+5)
= 2(5n+9)
C. 420n+2 . 165n+9 4
424n+20
= 10n+18
D. 414n+2 . 4
= 4(24n+20)−(10n+18)
= 414n+2

A B C D


Question 10: 
(24n )(82n )
= Answer: A
42n
A. 43n . Solution:
B. 46n . (24n )(82n )
42n
C. 4n . (24n )((23 )2n )
=
D. 4−3n . (22 )2n
(24n )(26n )
=
24n
= 24n+6n−4n
= 26n
= (22 )3n
= 43n

A B C D


Question 11: 
(27 ⋅ 9n+3 )3 = Answer: A
A. 36n+27 . Solution:
B. 36n+18 .
(27 ⋅ 9n+3 )3 = (33 ⋅ 32(n+3) )3
C. 36n+36 . = (33+2n+6 )3
D. 39n+18 . = (32n+9 )3
= 36n+27

A B C D


Question 12: 
4222 ⋅ 12444 = Answer: D
A. 24666 . Solution:
B. 48666 . 4222 ⋅ 12444 = (22 )222 ⋅ 12444
C. 48444 . = 2444 ⋅ 12444
D. 24444 . = (2 ⋅ 12)444
= 24444

A B C D


Question 13: 
1
( 181
) 796 =
49
A. 1
.
7266
B. 1
.
7373
C. 0.
D. 1
.
785

A B C D

Question 14: 
(a − b)(a2 − ab + b2 ) =

A. a3 + 2a2 b + 2ab2 − b3 .
B. a3 + 2a2 b − 2ab2 − b3 .
C. a3 − 2a2 b + 2ab2 − b3 .
D. a3 − 2a2 b − 2ab2 − b3 .

A B C D

Question 15: 
(h − k)(h + k)(h − 9) =

A. h3 − 9h2 + hk2 − 9k2 .

B. h3 − 9h2 − hk2 + 9k2 .
C. h3 − 9h2 − hk2 − 9k2 .
D. h3 + 9h2 + hk2 + 9k2 .

A B C D

Question 16: 
(x + 2)(x2 + 6x + 4) =

A. x3 + 10x2 + 20x + 8.
B. x3 + 8x2 + 16x + 8.
C. (x + 2)3 .
D. x3 + 4.

A B C D

Question 17: 
3
If 3h = 5 + , then k =
k+2
A. 13 − 6h
.
3h − 5
B. 13 + 6h
.
3h + 5
C. 13 − 6h
.
5 − 3h
D. 13 + 6h
.
3h − 5

A B C D

Question 18: 
5 2
If + = 4 , then u =
u v
A. 5v
4v − 2
B. 2v
4v − 5
C. 5v
2 − 4v
D. 2v
5 − 4v

A B C D

Question 19: 
If 3 − 8m = 5n , then m =

A. n.
B. 5n − 3
.
8
C. 3 − 5n
.
8
D. 3 + 5n
.
8

A B C D

Question 20: 
If a(a + b) = −4(b − a), then b =

A. −a2 + a
.
1+a
B. −a2 − a
.
1−a
C. −a2 + 4a
.
4+a
D. −a2 − 4a
.
4−a

A B C D

Question 21: 
If 9a + 2 = 5(b − 3) , then b =

A. 9a − 17
.
2
B. 9a − 17
.
5
C. 9a + 17
.
5
D. 9a + 17
.
2

A B C D

Question 22: 
a b
If + = 3 , then x =
5x 6y
A. 5ay
.
90y − 6b
B. 6ay
.
5y − 90b
C. 6ay
.
90y − 5b
D. 5ay
.
6b − 90y

A B C D

Question 23: 
If −6m(−9m + n) = n(2 − 6m), then n =

A. 27m2 .
B. −6m.
C. 27m.
D. 54m2 + m
.
27

A B C D

Question 24: 
y−5 y−2
If = , then y =
c d
A. −2c + 5d
.
d−c
B. −2c + 5d
.
c−d
C. −2d + 5c
.
d−c
D. −2c + 5d
.
c+d

A B C D

Question 25: 
a b
If = , then x =
8+x 4x
A. 8b
.
4a − b
B. 8a
.
4a + b
C. 8a
.
4a − b
D. 4b
.
8a + b

A B C D

Question 26: 
8a + 8b b
If = 5 + , then a =
5a a
A. 17b .
3
B. 17b .
13
C. 13b .
17
D. 3b .
17

A B C D

Question 27: 
2 4
− =
n+2 n−4
A. −2n + 16
.
(n + 2)(n − 4)
B. −2n + 16
.
(n + 2)(−4 − n)
C. −2n − 16
.
(n + 2)(−4 − n)
D. −2n − 16
.
(n + 2)(n − 4)

A B C D

Question 28: 
1 x−3
+ =
6 − x (x − 6)2
A. 9 − 6x
.
(6 − x)2
B. 6x − 9
.
(6 − x)2
C. 9
.
(6 − x)2
D. 3
.
(6 − x)2

A B C D

Question 29: 
1 1
− =
3x + 7 3x − 7
A. 14
.
9x2 − 49
B. 6
.
9x2 − 49
C. 14
.
49 − 9x2
D. 6
.
49 − 9x2

A B C D

Question 30: 
1 1
− =
x2 + 6x + 9 x2 + 5x + 6
A. −1
.
(x + 3)2 (x + 2)
B. 1
.
(x + 3)(x + 2)
C. 5
.
(x + 3)2 (x + 2)
D. 2x + 5
.
(x + 3)2 (x + 2)

A B C D

Question 31: 
4 3
− =
6k + 2 6k − 2
A. 6k + 2
.
36k2 − 4
B. 3k − 14
.
36k2 − 4
C. 6k − 14
.
36k2 − 4
D. 3k + 2
.
36k2 − 4

A B C D

Question 32: 
(3a + 2b)(5a + 4b) − a(18a + 12b) =

A. (3a + 2b)(−a + 4b).

B. (3a + 2b)(11a + 4b).
C. (3a − 2b)(11a + 4b).
D. (3a − 2b)(−a + 4b).

A B C D

Question 33: 
hl + kl + hm + km − hn − kn =

A. (h − k)(l − m + n).
B. (h + k)(l − m − n).
C. (h − k)(l + m + n).
D. (h + k)(l + m − n).

A B C D

Question 34: 
(5x − 9y)2 − (5x + 9y)2 =

A. 50x2 .
B. 0.
C. −90xy .
D. −180xy .

A B C D

Question 35: 
36h2 − k2 + 6k − 9 =

A. (6h + k + 3)(6h − k − 3).

B. (6h + k − 3)(6h − k + 3).
C. (6h + k − 3)(6h − k − 3).
D. (6h + k + 3)(6h − k + 3).

A B C D

Question 36: 
4x2 + 14x − 9y 2 − 21y =

A. (2x + 3y)(2x − 3y − 7).

B. (2x − 3y)(2x + 3y − 7).
C. (2x + 3y)(2x − 3y + 7).
D. (2x − 3y)(2x + 3y + 7).

A B C D

Question 37: 
α2 + α − β 2 + β

A. (α − β ) (α + β − 1)
B. (α + β ) (α + β − 1)
C. (α + β ) (α − β + 1)
D. (α − β ) (α − β + 1)

A B C D

Question 38: 
x2 − y 2 − 5x − 5y =

A. (x + y)(x − y + 5).
B. (x − y)(x + y − 5).
C. (x + y)(x − y − 5).
D. (x − y)(x + y + 5).

A B C D

Question 39: 
u2 − v 2 + u − v =

A. (u + v)(u − v + 1).
B. (u − v)(u + v − 1).
C. (u − v)(u + v + 1).
D. (u + v)(u − v − 1).

A B C D

Question 40: 
81 − (5x + 8y)2 =

A. (9 + 5x − 8y)(9 − 5x − 8y).
B. (9 + 5x + 8y)(9 − 5x − 8y).
C. (9 + 5x + 8y)(9 − 5x + 8y).
D. (9 + 5x − 8y)(9 − 5x + 8y).

A B C D

Question 41: 
3r2 + rs − 4s2 + 3r − 3s

A. (r − s)(3r + 4s − 3).
B. (r − s)(3r + 4s + 3).
C. (r + s)(3r − 4s + 3).
D. (r + s)(3r − 4s − 3).

A B C D

Question 42: 
If a and b are constants such that (x − 3)(x + a) − 9 ≡ (x − 8)2 + b, then b =

A. −34.
B. −16.
C. −32.
D. −13.

A B C D

Question 43: 
Let m and n be constants. If m(x − 3)2 + n(x − 2)2 ≡ x2 − 14x + 29 , then m =

A. 5.
B. 7.
C. −4.
D. −1.

A B C D

Question 44: 
If p and q are constants such that x2 + p ≡ (x + 1)(x + q) + 5 , then p =

A. −1.
B. −2.
C. 4.
D. 3.

A B C D

Question 45: 
If p and q are constants such that px(x + 8) + x2 ≡ qx(x + 5) − 2x , then p =

A. 3.
B. 2.
C. 1.
D. 4.

A B C D

Question 46: 
If a, b and c are non-zero constants such that a(x + 9) + b(5x + 4) ≡ c(x + 2), then a : b =