Free Printable Intermediate compilation

1.

What are the Highest Common Factor and Lowest Common Multiple of 64 and 72?

a)

A 4 and 1152

b)

B 8 and 576

c)

C 36 and 144

d)

D 8 and 512

e)

E 16 and 288

2.

By continual summing the digits of a number, you arrive at the digital root. What is the digital root of 23648157185?

a)

1

b)

3

c)

5

d)

7

e)

9

3.

The number, $4\overline{24}30\overline{73}$ , has four vinculum digits. What is the correct number when the digits are expressed as positive integers?

a)

A 3752927

b)

B 3862937

c)

C 4862037

d)

D 4753126

e)

E 3762927

4.

In using Nikhilam multiplication, which of the following is correct?

a)

A

b)

B

c)

C

d)

D

e)

E

5.

What are the final three digits of 9999996?

a)

A 992

b)

B 016

c)

C 486

d)

D 996

e)

E 136

6.

How many zeros come after the decimal point in the calculation, (0.00000075)²?

a)

A 6

b)

B 8

c)

C 10

d)

D 12

e)

E 14

7.

What are the vinculum digits in the calculation, 1023 × 991?

a)

023

b)

008

c)

207

d)

219

e)

703

8.

When using Vertically and crosswise to calculate 2361 × 4215, what is the result of the fourth step before any carry digits are included?

a)

29

b)

16

c)

31

d)

32

e)

23

9.

12121212121 × 11

a)

13333333331

b)

133333333331

c)

1333333333331

d)

13333333333331

e)

133333333333331

10.

Which fraction is the smallest?

a)

1/2000000008

b)

2/4000000015

c)

4/8000000036

d)

8/16000000056

e)

2/4000000017

11.

When using a working base of 250 and a real base of 1000 to work out 251 × 257, what operation is needed for the left-hand part of the calculation?

a)

×2.5

b)

÷2.5

c)

×4

d)

÷4

e)

×8

12.

The product of two prime numbers is 2021, which can be worked out using the rule, When the final digits add to 10. What are the two prime numbers?

a)

79 × 61

b)

83 × 17

c)

37 × 23

d)

53 × 67

e)

43 × 47

13.

A bottling factory produces 19,866 bottles in 42 hours. In using straight division to find how many bottles are produced each hour, what is the second to last step?

a)

(38 – 26) ÷ 4

b)

(26 – 14) ÷ 4

c)

(32 – 20) ÷ 4

d)

(14 – 2) ÷ 4

e)

(86 – 74) ÷ 4

14.

What is the integer remainder when 1245003411 is divided by 9999998?

a)

9510

b)

5901

c)

1059

d)

5190

e)

1095

15.

1000004 × 1214623

a)

1214627858492

b)

1214628858492

c)

1214627868492

d)

1214627859492

e)

1214627858482

16.

What are the last four digits in the recurring pattern in the decimal equivalent of 1/19?

a)

6667

b)

0526

c)

8421

d)

9991

e)

3829

17.

In calculating 31³, which partial sum is correct?

a)

A

b)

B

c)

C

d)

D

e)

E

18.

What is the sum of the first twenty odd numbers?

a)

200

b)

300

c)

400

d)

500

e)

600

19.

How many lines of symmetry does a regular dodecagon (12 sides) have?

a)

A 8

b)

B 12

c)

C 16

d)

D 24

e)

E 36

20.

What is the total area of the shaded regions?

a)

A 28

b)

B 35

c)

C 70

d)

D 42

e)

E Not enough information

21.

Lisa Doolittle converted the partly recurring decimal into a fraction. In which step did she make a mistake?

a)

A

b)

B

c)

C

d)

D

e)

E

22.

There are 100 students in a class. Exactly 99% of them have their books. How many students with books must leave the room to bring down the percentage with books to 98%?

a)

A 1

b)

B 2

c)

C 10

d)

D 49

e)

E 50

23.

A waiter’s pay consists of tips and a salary. During one month, his tips were 5/4 of his salary. What fraction of his pay came from tips?

a)

A 4/9

b)

B 5/9

c)

C 4/5

d)

D 9/5

e)

E 9/4

24.

Harry the hedgehog was timed walking from one end of the garden to the other. He covered 11 metres in 19.6 seconds. Approximately, how fast is this in km per hour?

a)

0.5

b)

1

c)

2

d)

4

e)

8

25.

The perimeter of a right-angled triangle is 72 cm. The lengths of the sides are in the ratio 3 : 4 : 5. What is the area of the triangle in cm²?

a)

A 144

b)

B 216

c)

C 270

d)

D 360

e)

E 1620

26.

A box contains red, blue and yellow counters. The ratio of red to blue is 3 : 5 and the ratio of blue to yellow is 7 : 9. There are 90 yellow counters in the box. How many red counters are there?

a)

A 21

b)

B 35

c)

C 42

d)

D 45

e)

E 63

27.

The cross in the diagram has one vertical line of symmetry. All measurements are in centimetres. What is the perimeter?

a)

A 24.4

b)

B 45.2

c)

C 52

d)

D 60

e)

E 76

28.

Which of the following is a possible solution to the equation, x + 1/x = 26/5?

a)

3

b)

5

c)

7

d)

9

e)

11

29.

Two similar cylinders, A and B, have surface areas 350 cm² and 5600 cm², respectively. If the volume of cylinder A is 500 cm³, what is the volume of cylinder B in cm³?

a)

8000

b)

16,000

c)

24,000

d)

32,000

e)

128,000

30.

The first five terms of a sequence are 0, 3, 8, 15, 24, ... What is the 98th term?

a)

A 9409

b)

B 9506

c)

C 9603

d)

D 9605

e)

E 9801

31.

What is the factorised form of, (x + y)² + (x + y)

a)

(x + y + 1)²

b)

(x + y)³

c)

x² + 2xy + y² + x + y

d)

(x² + y²)(x + y)

e)

(x + y)(x + y + 1)

32.

x³- 4x² - 20x + 3 ÷ (x + 3)

a)

A x² - 7x + 1

b)

B x² + 9x - 3

c)

C x² + 7x - 1

d)

D x² - 9x + 1

e)

E x² - 9x + 3

33.

Expand (3x² - 2x + 1)(4x² + 3x - 7)

a)

12x⁴ + 3x³ + 27x² - 17x - 7

b)

12x⁴ - 2x³ + 14x² + 12x - 7

c)

12x⁴ + x³ - 27x² + 19x - 7

d)

12x⁴ + x³ - 23x² + 17x - 7

e)

12x⁴ + 2x³ - 23x² + 17x - 7

34.

Which of the following is the equation of the straight line that passes through the points (3, 7) and (1, 5)?

a)

A x + 3y = 5

b)

B x - y = -4

c)

C 3x - 2y = 4

d)

D x + y = 8

e)

E x - y = -3

35.

What is the equation of the line which is perpendicular to the line 5x - 2y = 38 and which passes through the point (-3, 14)?

a)

A 2x + 5y = 76

b)

B 5x + 2y = 64

c)

C 2x - 5y = -76

d)

D 2x + 5y = 64

e)

E 5x + 2y = 13

36.

The equations of two lines are x + y = 14, and x - y = 2. What are the coordinates of the point of intersection?

a)

A (4, 10)

b)

B (10, 4)

c)

C (7, 7)

d)

D (6, 8)

e)

E (8, 6)

37.

What is the equation of the line with gradient 2 and which passes through the point (7, 4)?

a)

A 2x + y = 4

b)

B 2x - y = 10

c)

C 2x + y = 10

d)

D x - 2y = 10

e)

E x + 2y = 3

38.

A square is drawn inside a semicircle. If the radius of the semicircle is 1, what is the area of the square?

a)

4/5

b)

√3/2

c)

2/3

d)

√2/3

e)

√5+1/2

39.

The two roots of the quadratic equation, x² - 85x + k = 0 are both prime numbers. What is the sum of the digits of k?

a)

A 12

b)

B 13

c)

C 15

d)

D 18

e)

E 22

40.

What is exact solution to this equation, xˣ = (3/4)√6

a)

3/2

b)

√2/3

c)

√3/2

d)

3√3/2√2

e)

2/3

41.

How many two-digit numbers can be written as the sum of six different powers of 2, including 2^0?

a)

0

b)

1

c)

2

d)

3

e)

4

42.

Which of the following is neither a square nor a cube?

a)

$2^9$

b)

$3^{10}$

c)

$4^{11}$

d)

$5^{12}$

e)

$6^{13}$

43.

Four straight lines intersect as shown. What is the value of a + b + c + d?

a)

180°

b)

360°

c)

540°

d)

720°

e)

900°

44.

A nine-digit number is randomly composed using the digits from 1 to 9. What is the probability that it is divisible by 18?

a)

1/3

b)

4/9

c)

1/2

d)

3/4

e)

5/9

45.

If 5x - y = 18 and 5y - x = 12, what is the value of x - y?

a)

0

b)

1

c)

3

d)

6

e)

9

46.

If a and b are non-zero numbers, simplify, $(a + \frac{1}{a})^2 + (b + \frac{1}{b})^2 + (ab + \frac{1}{ab})^2 - (a + \frac{1}{a})(b + \frac{1}{b})(ab + \frac{1}{ab})$

a)

0

b)

1

c)

2

d)

3

e)

4

47.

What is the maximum possible area of the rectangle shown?

a)

A 28

b)

B 45

c)

C 48

d)

D 49

e)

E 120

48.

Triangle ABC is equilateral. The side AB is the diameter of a circle of area 49π cm². In cm², what is the area of the triangle?

a)

49√3

b)

98√2

c)

49√2

d)

7√3

e)

14√3

49.

The figure contains a rectangle, with height 1 unit, a quadrant and a semicircle. Given that the two shaded parts have equal areas, find the length of PQ.

a)

√2

b)

2√2

c)

3√2

d)

4√2

e)

5√2

50.

Following the pattern in the first three figures below, how many small triangles are there in the 7th figure?

a)

A 244

b)

B 294

c)

C 352

d)

D 414

e)

E 480

51.

10.01 - 1.1

a)

A 8.91

b)

B 9.01

c)

C 9.1

d)

D 9.9

e)

E 9.91

52.

Which of the following is not divisible by 9?

a)

2772772722772

b)

1234545678

c)

432234432234

d)

90817263542

e)

623637613683

53.

When using Vertically and crosswise to calculate 367 × 482, what is the result of the third step before any carry digits are included?

a)

76

b)

80

c)

82

d)

87

e)

92

54.

Given that 3×37=111, calculate 999999 ÷ 37.

a)

54054

b)

45045

c)

36036

d)

27027

e)

18018

55.

What is the square root of 5625?

a)

45

b)

55

c)

65

d)

75

e)

85

56.

One of the following shows the correct working for 329×989 using Nikhilam multiplication. Which one?

a)

A

b)

B

c)

C

d)

D

e)

E

57.

The devinculated form of $6\overline{2}$ is 58. What is the devinculated form of $7\overline{3}2\overline{14}0\overline{3}$ ?

a)

6718597

b)

6728607

c)

6619697

d)

6718607

e)

6718507

58.

83% of $25.00

a)

$20.75

b)

$20.50

c)

$20.15

d)

$19.75

e)

$19.35

59.

Using Nikhilam division for 24219 ÷ 897, some workings are shown below. What are the three missing digits for A, B and C?

a)

A 328

b)

B 283

c)

C 206

d)

D 308

e)

E 204

60.

0.000125²

a)

0.000625

b)

0.00015625

c)

0.00000015625

d)

0.000000015625

e)

0.000000000625

61.

What are the final three digits of the answer to 9999997²?

a)

009

b)

049

c)

014

d)

019

e)

409

62.

Which fraction is the largest?

a)

24/2972

b)

12/1483

c)

6/745

d)

3/373

e)

1/124

63.

What is the whole number remainder for 57499 ÷ 312?

a)

A 61

b)

B 81

c)

C 82

d)

D 91

e)

E 92

64.

49³

a)

103619

b)

117649

c)

195319

d)

159319

e)

207379

65.

How many factors does 360 have?

a)

A 16

b)

B 18

c)

C 22

d)

D 24

e)

E 26

66.

x and y are two quantities. Rishi calculates that 80% of 50% of x is equal to 40% of 30% of y. Which of the following is true?

a)

y = x/2

b)

y = x/3

c)

y = 4x

d)

y = 8/3 x

e)

y = 10/3 x

67.

How many of the following statements are true?
A multiple of 4 is always a multiple of 8

A multiple of 9 always has the sum of its digits equal to a multiple of 9

The square of an odd nnumber is always an odd number

All prime numbers are odd

a)

A 0

b)

B 1

c)

C 2

d)

D 3

e)

E 4

68.

A sequence begins, 2, 9, 18, 29, 42, ... What is the 98th term of this sequence?

a)

A 8947

b)

B 9123

c)

C 9395

d)

D 9827

e)

E 9993

69.

Simplify, $(x + 2y + 1)^2 - (x - 2y - 1)^2$

a)

A 8xy + 4x

b)

B $x^2 + 8xy + 8y$

c)

C 4xy + 8x

d)

D $5x^2 + 8y^2 + 2$

e)

$2x^2 + 4xy + 8y^2$

70.

Convert, the partially recurring decimal, 0.1636363636363...., to a fraction in lowest terms.

a)

9/55

b)

17/111

c)

81/495

d)

147/900

e)

163/990

71.

Simplify, $8c^2d \times (4cd)^2$

a)

144c⁴d³

b)

128c³d²

c)

32c⁴d³

d)

128c⁴d³

e)

32c³d³

72.

Solve the equation to find the value of x.
$\frac{7x}{2}-\frac{x-1}{8}=-1$

a)

-1/3

b)

1/3

c)

-7/27

d)

-2/27

e)

1/54

73.

What is the Lowest Common Multiple (LCM) of 38808 and 1320?

a)

64 680

b)

194 040

c)

582 120

d)

1 552 320

e)

2 134 440

74.

The total takings from tickets sales at a cricket match in Kolkata are INR 11028864. Each ticket costs INR 112. How many spectators are there?

a)

98472

b)

96582

c)

94647

d)

92886

e)

97452

75.

Solve, $12x^2 + 13x - 14 = 0$

a)

1/2, -7/4

b)

3/2, 6/7

c)

-1/2, 4/7

d)

-3/2, 7/4

e)

2/3, -7/4

76.

What is the square root of, $x^4 - 6x^3 + 17x^2 - 24x + 16$ ?

a)

$x^2 - 4x + 16$

b)

$x^2 + 4x + 4$

c)

$x^2 - 3x - 4$

d)

$x^2 - 3x + 4$

e)

$x^2 + 3x - 4$

77.

What is the remainder when $3x^4 - 7x^3 + 15x^2 - 23x - 5$ is divided by $(x - 2)$ ?

a)

0

b)

1

c)

2

d)

3

e)

4

78.

Sruti buys 4 cups of coffee and 3 cups of tea for $18.95. In the same cafe, Wajma buys 2 cups of

coffee and 5 cups of tea and the total comes to $13.85. What is the cost of one cup of coffee?

a)

$3.20

b)

$3.40

c)

$3.60

d)

$3.80

e)

$4.00

79.

This irregular pentagram has angles as shown. What is the size of x?

a)

31°

b)

33°

c)

38°

d)

43°

e)

Not enough information

80.

What is the equation of the line which is perpendicular to 3x + 2y = 7 and which passes through the point with coordinates, (4, 3)?

a)

3x + 2y = 18

b)

3x - 2y = 6

c)

2x - 3y = -1

d)

2x + 3y = 29

e)

2x + 3y = 7

81.

What is the maximum value of y, given that y = $12x - x^2 - 29$ ?

a)

A 7

b)

B 8

c)

C 9

d)

D 10

e)

E 11

82.

Six semicircles are arranged around a regular hexagon. The distance from the centre of the hexagon to the centre of each semicircle is 1 cm. What is the total shaded area?

a)

$(\frac{3}{2})\pi$ cm^2

b)

π cm^2

c)

$(9/4)\pi cm^2$

d)

$4\pi cm^2$

e)

9 $\pi$ cm^2

83.

A long line AB is divided at point C so that the ratio of lengths AC : CB is 5 : 3. CB is then divided at D in the ratio 5 : 3. DB is similarly divided at E in the same ratio and EB is again divided at F in the ratio 5 : 3. FB is 3 cm. How long is AB?

a)

(64/27) cm

b)

(256/27) cm

c)

(512/27) cm

d)

(1012/27) cm

e)

(4096/27) cm

84.

Two squares of side length 2 units and 6 units touch a circle as shown. What is the radius of the circle?

a)

A 3 - √2

b)

B 6 - 2√2

c)

C 6 - √2

d)

D 1 + √2

e)

E 8 - 4√2

85.

Two identical triangles overlap. The area of the overlapping region, B, is one sixth the area of the whole shaded region. What fraction of the area of one triangle is the area B?

a)

2/5

b)

1/6

c)

2/7

d)

3/8

e)

2/9

86.

In how many ways can 96 be expressed as the difference of two square integers?

a)

0

b)

1

c)

2

d)

3

e)

4

87.

Two congruent isosceles triangles overlap producing a hexagon in the middle. The areas of the smaller triangles are 4 and the larger triangles, 36, as shown. What is the area of the hexagon?

a)

A 44

b)

B 48

c)

C 56

d)

D 64

e)

E 72

88.

Simplify, $\left(1+\frac{1}{x}\right)\left(1-\frac{1}{x}\right)\left(\frac{1}{x+1}+\frac{1}{x-1}\right)$

a)

2/x

b)

$\frac{2}{x^2}$

c)

$\frac{2}{x^2-1}$

d)

2/((x+1)(x-1))

e)

$\frac{2}{x^2(x+1)(x-1)}$

89.

An open wooden box is a cube with edge length x cm. The sides and base have thickness d cm. Which expression shows the total surface area?

a)

$5x^2 + 8dx + 4d^2$

b)

$9x^2 - 6dx + d^2$

c)

$10x^2 - 12dx + 8d^2$

d)

$10x^2 - 6dx + d^2$

e)

$10x^2 - 4dx + 8d^2$

90.

How many rectangles of all types are there?

a)

A 34

b)

B 56

c)

C 289

d)

D 324

e)

E 360

91.

2(1 + 2(1 + 2(1 + 2(1 + 2(1 + 2(1 + 2))))))

a)

63

b)

126

c)

127

d)

254

e)

274

92.

0.0000426 × 0.005

a)

0.00213

b)

0.000213

c)

0.0000213

d)

0.00000213

e)

0.000000213

93.

From the prime numbers less than 20, what is the difference between the squares of the highest and lowest?

a)

357

b)

289

c)

285

d)

352

e)

360

94.

7946 × 9992

a)

72986452

b)

783816432

c)

79396432

d)

74493272

e)

79466342

95.

Which of the following is not a multiple of 9?

a)

768321

b)

224433

c)

891548

d)

243756

e)

830106

96.

What is 36.4% of $25 ?

a)

$9.10

b)

$16.92

c)

$18.20

d)

$12.64

e)

$8.30

97.

What is the whole number remainder when 242871 is divided by 897?

a)

487

b)

851

c)

475

d)

206

e)

681

98.

2023 has a square factor whose square root ends in 7. What is that square root?

a)

7

b)

17

c)

27

d)

37

e)

47

99.

The One Day International World Cup Final took place at Narendra Modi Stadium in Ahmedabad on 19th November 2023. It was a sell-out event. The stadium is the largest in the world and can seat 132000 people. The total takings from sale of tickets was $46 596 000. What was the mean price of each ticket?

a)

$343

b)

$283

c)

$353

d)

$348

e)

$348

100.

79³

a)

493039

b)

627429

c)

534149

d)

467229

e)

510239

101.

11. 992²

a)

978464

b)

987664

c)

976764

d)

984064

e)

988264

102.

When placed in order of size, which fraction is in the middle?

a)

9/11

b)

12/13

c)

18/23

d)

36/43

e)

72/89

103.

A, B and C are three digits. B and C add up to 10. What is the value of A?

a)

2

b)

3

c)

4

d)

5

e)

6

104.

Callisto and Europa are two moons of Jupiter with orbital periods of 408 hours and 84 hours. If they start in line, after how many hours will they be in the same position again?

a)

2040 hrs

b)

2856 hrs

c)

6582 hrs

d)

3108 hrs

e)

8568 hrs

105.

What are the vinculum digits in the Nikhilam multiplication of 524 X 492 when using a working base of 500 and a real base of 1000?

a)

A 144

b)

B 192

c)

C 326

d)

D 808

e)

E 162

106.

Triangle ABC is equilateral and D is the midpoint of BC. Triangle AEF is right-angled and isosceles. What is the size of angle x?

a)

A 65°

b)

B 70°

c)

C 75°

d)

D 80°

e)

E 85°

107.

Three spheres, A, B and C, are such that the volume of B is 50% more than A and the volume of C is 60% more than B. What fraction is the volume of A of the volume of C?

a)

A 3/10

b)

B 2/5

c)

C 4/11

d)

D 4/9

e)

E 5/12

108.

Simplify 3√3 / (3 - √3)

a)

A √3 + 1

b)

B 12√3 / (9 - √3)

c)

C (3√3 + 3) / 2

d)

D 9 / (3 - √3)

e)

E 3 / (1 - √3)

109.

A sequence starts, 4, 5, 8, 13, 20,... What is the 98th term in this sequence?

a)

A 9511

b)

B 9413

c)

C 9697

d)

D 9707

e)

E 9805

110.

When converted into a decimal, the fraction 10/89, has 44 digits in its recurring pattern. What are the first seven decimal digits?

a)

0.1123595

b)

0.0123595

c)

0.1285135

d)

0.1153485

e)

0.1132575

111.

Which of the following is the correct fraction equivalent to the partly recurring decimal, 0.327 (= 0.3272727...)?

a)

A 109/330

b)

B 12/37

c)

C 36/101

d)

D 18/55

e)

E 109/333

112.

A regular octagon (8 sides) and a regular dodecagon (12 sides) share a common edge, AB. Vertices D and C are joined with a line. What is the size of angle DCB?

a)

A 37.5°

b)

B 45.5°

c)

C 57.5°

d)

D 55.5°

e)

E 52.5°

113.

At the Rio Cafe in Alexandria, Anthony buys three cups of coffee and four cups of mint tea for a total of $15.70. Meanwhile, Cleopatra buys two cups of coffee and five cups of mint tea for $14.90. What is the cost of a cup of coffee at the cafe?

a)

$1.90

b)

$2.20

c)

$2.70

d)

$2.90

e)

$3.10

114.

Which of the following is an equation of the straight line which passes through the point (-3, 2) and that is perpendicular to the line with equation, 5s – 3y = 19?

a)

A 3x + 5y = –9

b)

B 3x + 5y = 1

c)

C y = –(5/3)x – 3

d)

D y = –(3/5)x – 9/5

e)

E 5y = 3x + 19

115.

Four of the following points are vertices of the same kite. Which point is not a vertex of this kite?

a)

A (–2, –1)

b)

B (–1, 6)

c)

C (2, 7)

d)

D (1, 2)

e)

E (3, 4)

116.

When the denominator of (3√3)/(3–√3) is rationalised, the answer is,

a)

(√3+1)/1

b)

(3√3–3)/4

c)

(3√3+3)/2

d)

(√3+3)/2

e)

(3√3–1)/9

117.

Which of the following is a factor of 3x³+11x²+30x+72?

a)

(x+1)

b)

(x+2)

c)

(x+3)

d)

(x+4)

e)

(x+6)

118.

After the decimal point, how many non-recurring digits are there in the decimal equivalent for 17/384?

a)

A 3

b)

B 4

c)

C 5

d)

D 6

e)

E 7

119.

SPT is tangent to the circle with centre O. Points Q and R lie on the circumference. Angle TPQ = 64° and angle RQO = 28°. What is the size of angle RPO?

a)

32°

b)

46°

c)

36°

d)

26°

e)

28°

120.

The men’s world record for a 100 metre sprint is 9.58 seconds, set by Usain Bolt in 2009. How fast is this in kilometres per hour? (Answer to the nearest whole number)

a)

A 35 km/h

b)

B 36 km/h

c)

C 37 km/h

d)

D 38 km/h

e)

E 39 km/h

121.

What is the value of x for which, $2^x \times 8^{(x−1)} = 16^{(x^3)}$ ?

a)

A 0

b)

B 9

c)

C 15

d)

D 16

e)

E 48

122.

A, B, C and D are points on a straight line. The ratio AB : BD = 2 : 5. The ratio AC : CD = 7 : 3. What is the ratio, AB : BC : CD?

a)

A 16 : 21 : 28

b)

B 7 : 10 : 17

c)

C 21 : 30 : 25

d)

D 20 : 29 : 21

e)

E 60 : 85 : 69

123.

Each square in this grid has side length one unit. Two circles, each with diameter one unit are placed in two opposite squares. What is the shortest distance between the two circles?

a)

3

b)

2

c)

2√2

d)

√2 + 1

e)

2√2 - 1

124.

What is the simplified form of, $(2x^2 + 3x + 1)^2 − (x^2 − 3x − 1)^2$ ?

a)

$3x^2(x^2 + 6x + 2)$

b)

$3x^2(x^2 + 6)$

c)

$3x^4 + 20x^2 + 12x$

d)

$3x^4 + 20x^2 - 1$

e)

$3x^2(x^2 − 6x − 2)$

125.

The graph of a parabola has y-intercept at (0, 13) and turning point at (-4, -3). Which of the following is the equation for the parabola?

a)

$y = 2x^2 - 4x + 13$

b)

$y = x^2 + 7x + 9$

c)

$y = 3x^2 + 16x + 13$

d)

$y = x^2 + 8x + 13$

e)

$y = 4x^2 + 48x - 13$

126.

What is the value of p, given that, $(4x^2 - 3px + 2)(x^2 + px + 1) = 4x^4 + px^3 - 7px^2 - px + 2$

a)

1

b)

3

c)

5

d)

7

e)

9

127.

How many three-digit numbers can be written as the sum of five different powers of 3, including $3^0$ ?

a)

6

b)

7

c)

8

d)

9

e)

10

128.

In this magic square, the products of numbers in each row, each column and each diagonal are all the same. The missing numbers are 2, 4, 5, 10, 25, 50 and 100. Which number must be placed in the square labelled M?

a)

2

b)

4

c)

5

d)

10

e)

25

129.

A rectangular piece of card is 3 cm longer than its width. It has 3 cm by 3 cm squares cut away from each corner. The area of the resulting shape is numerically the same as the perimeter. What is the area?

a)

34 cm^2

b)

36 cm^2

c)

38 cm^2

d)

40 $cm^2$

e)

42 $cm^2$

130.

Three circles, each with a radius of one unit, are set out as shown with the circumference of the middle circle passing through the centers of the outer two circles. What is the area of the shaded region in terms of π?

a)

2√3 - 2π/3

b)

2√3 - π/6

c)

√3 - π/3

d)

4π/3 - √3

e)

2π/3 - √3

131.

1 - 0.2 + 0.03 - 0.004 + 0.0005

a)

0.9235

b)

0.7365

c)

0.8265

d)

0.8345

e)

0.9685

132.

101214 ÷ 9

a)

11324

b)

15247

c)

11246

d)

11072

e)

13142

133.

9876 × 9993

a)

9875868

b)

98760868

c)

98760768

d)

98731828

e)

98690868

134.

Which of the following is a multiple of 11?

a)

5151515

b)

6161616

c)

7171717

d)

8181818

e)

9191919

135.

What is the value of the digit, A, in the calculation, 83 × 87 = 7A21?

a)

1

b)

2

c)

3

d)

4

e)

5

136.

Including repetitions, how many prime factors does 2024 have?

a)

3

b)

4

c)

5

d)

6

e)

7

137.

What is the remainder for 256379 ÷ 12101?

a)

A 2258

b)

B 3644

c)

C 2735

d)

D 6434

e)

E 5363

138.

Which is the most suitable sutra for the calculation in the previous question? "What is the remainder for 256379 ÷ 12101?"

a)

All from 9 and the last from 10

b)

By the last digits

c)

Vertically and crosswise

d)

Transpose and Apply

e)

By Addition and Subtraction

139.

9988²

a)

99880284

b)

99891164

c)

99760144

d)

99440164

e)

99844154

140.

One sheet of A4 paper has an area of 1/16 m². A4 paper has a mass of 80 g per m². What is the total mass of 320 sheets of A4 paper?

a)

800 g

b)

1200 g

c)

1600 g

d)

2400 g

e)

3200 g

141.

49³

a)

116759

b)

117649

c)

132589

d)

172639

e)

125459

142.

What is the remainder when 2² × 4⁴ × 6⁶ × 8⁸ is divided by 9?

a)

0

b)

2

c)

4

d)

6

e)

8

143.

What is the mean value of the five answers to 91×89, 94×86, 95×85, 92×88 and 93×87?

a)

8086

b)

8089

c)

8090

d)

8091

e)

8093

144.

After the decimal point, how many digits are in the decimal equivalent of 1/6250?

a)

A 4

b)

B 5

c)

C 6

d)

D 7

e)

E 8

145.

Three numbers are in the ratio, 4/5 : 5/6 : 9/10. The difference between the largest and smallest is 12. What is the value of the number that is neither the smallest nor the largest?

a)

A 92

b)

B 96

c)

C 100

d)

D 104

e)

E 108

146.

A sequence begins, 0 3 10 21 36 What is the 25th term in the sequence?

a)

406

b)

551

c)

1073

d)

1176

e)

1326

147.

When using the Vertically and crosswise method to multiply 6734 × 2963 what is the result of the fouth step before any carry digits have been added?

a)

65

b)

75

c)

85

d)

95

e)

105

148.

Each shape is made of four identical right-angled isosceles triangles. Which shape has the smallest perimeter?

a)

Shape A

b)

Shape B

c)

Shape C

d)

Shape D

e)

Shape E

149.

Which of the following is the equation of the straight line which passes through the point (7,–10) and has gradient –2?

a)

2x + y = 24

b)

2x + y = 4

c)

2x – y = 4

d)

2x + y = –24

e)

2x – y = 24

150.

How many of the following points lie on the line with equation 3x – 2y = 14?
(4,−2) (10,8) (16,18) (18,20) (32,41)

a)

1

b)

2

c)

3

d)

4

e)

5

151.

Tile P has an area of 504 cm². Tile Q has an area of 2352 cm². A floor is to made with P tiles and another floor with Q tiles. What is the smallest area, in m², that can be made so that both floors have the same area?

a)

0.1512 m²

b)

0.7056 m²

c)

1.0584 m²

d)

3.2928 m²

e)

4.2336 m²

152.

Due to lack of babies being born, the population of South Korea is predicted to fall by 60% by the end of the century. The current population is 52 million. To the nearest million, what is the predicted population for 2100?

a)

21m

b)

23m

c)

26m

d)

28m

e)

31m

153.

What is the common solution to the equations, $x^2 - 10x - 24 = 0$ and $x^2 - 8x - 48 = 0$ ?

a)

-2

b)

-4

c)

6

d)

8

e)

12

154.

Two ice-cream cones, A and B, are mathematically similar. The surface areas are 16 square inches and 25 square inches, respectively. The volume of cone A is 6.4 cubic inches. What is the volume of cone B?

a)

8 cu.in.

b)

10 cu.in.

c)

12.5 cu.in.

d)

25 cu.in.

e)

125 cu.in.

155.

An equilateral triangle, a square and a regular heptagon are placed together as shown. What is the sum of the interior angles of the resulting shape?

a)

1260°

b)

1440°

c)

1620°

d)

1800°

e)

1980°

156.

Which of the following is a factor of 6x^3 + 7x^2 + x - 28?

a)

$x^2 - 3x + 7$

b)

$2x^2 - 11x + 4$

c)

$6x^2 + x - 4$

d)

$3x^2 - 8x - 7$

e)

$2x^2 + 5x + 7$

157.

When $0.\overline{15}+0.2\overline{27}$ is written as the fraction the answer is m/66. What is the value of m?

a)

7

b)

10

c)

25

d)

225

e)

377

158.

Given that a year is 365.24 days long, and a month, from new moon to new moon, is 29.53 days long, how many months will there be in 19 years?

a)

235

b)

275

c)

281

d)

296

e)

305

159.

A truncated icosahedron has 12 pentagon faces and 20 hexagon faces. Faces are joined along their edges. How many edges are there?

a)

20

b)

32

c)

60

d)

90

e)

120

160.

In the figure, QP and QRS are tangents to the circle with centre O. PQR = 58° and TRS = 68°. What is the size of OPT?

a)

39°

b)

48°

c)

58°

d)

61°

e)

63°

161.

An irregular quadrilateral, has vertices A (2, 2), B (10, 0), C (12, 8) and D (6, 10). Midpoints of each side are joined to make quadrilateral PQRS. What shape is PQRS?

a)

Square

b)

Rectangle

c)

Parallelogram

d)

Rhombus

e)

Kite

162.

$2^a=\frac{2^n}{\sqrt[3]{2}}$ $2^b = (\sqrt{2})^5$ $a + b = 8$ What is the value of n?

a)

2 2/3

b)

3 3/4

c)

4 4/5

d)

5 5/6

e)

6 6/7

163.

In the figure, AB = 5 cm, BC = 2 cm, AD = 8 cm and ED = 7 cm. What is the length of EC?

a)

A 6√5

b)

B 7√6

c)

C 8√7

d)

D 9√8

e)

E 10√9

164.

What is the 11th digit, after the decimal point in the recurring decimal equivalent for 4/39?

a)

A 4

b)

B 5

c)

C 6

d)

D 7

e)

E 8

165.

A regular p-sided polygon has exterior angle q° and a regular q-sided polygon has exterior angle p°. For how many possible pairs of numbers (p, q) is this possible?

a)

A 12

b)

B 16

c)

C 18

d)

D 20

e)

E 24

166.

ABC is a right-angled triangle. AB is parallel to ED. The area of triangle EDC is 24 cm² and the area of triangle BED is 72 cm². What is the area of triangle ABE?

a)

96 cm²

b)

120 cm²

c)

180 cm²

d)

216 cm²

e)

288 cm²

167.

What is the minimum value of x² + y² + 2xy + 8x + 8y + 12?

a)

A -8

b)

B -6

c)

C -4

d)

D -2

e)

E 0

168.

A square has side length 4. Four arcs have their centres at the midpoints of the sides of the square. What is the shaded area?

a)

A 4π - 2

b)

B 4π - 6

c)

C 6π - 8

d)

D 8π - 12

e)

E 8π - 16

169.

Points are placed one third of the way along each edge of a triangle as shown. What fraction of the whole triangle is shaded?

a)

1/2

b)

5/9

c)

2/3

d)

7/12

e)

3/4

170.

ABCD is a square with a quarter-circle centred at B and passing through A and C. The rectangle EFGD measures 9 units by 2 units. What is the edge length of the square?

a)

A 15

b)

B 17

c)

C 21

d)

D 25

e)

E 27

Intermediate compilation

Total questions: 170

Worksheet time: 4hrs 0mins

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