Sec 2 Maths End-of-year exam Paper 1: free PDF with answers

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Mathematics

Sec 2 Maths · End-of-year exam Paper 1

Primes, HCF and LCM + Integers, rational and real numbers + Approximation and estimation + Basic algebra + Linear equations + Coordinates and linear graphs + Number sequences and patterns + Percentage + Ratio, rate and speed + Angles and parallel lines + Triangles, quadrilaterals and polygons + Perimeter and area + Volume and surface area + Statistics (Sec 1) + Direct and inverse proportion + Linear equations, inequalities and simultaneous equations + Expansion and factorisation of quadratic expressions + Algebraic fractions and formulae + Quadratic equations and graphs + Congruence and similarity + Pythagoras' theorem + Trigonometric ratios + Pyramids, cones and spheres + Statistics (Sec 2) + Probability

Practice paper in the same style as the school and national exam papers. Not a copy of any past year paper.

1 hour 15 minutes

Name

Class

Index number

Candidates answer on the Question Paper.

Read these instructions first

Write your name, class and index number in the spaces at the top of this page.

Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs.

Do not use staples, paper clips, glue or correction fluid.

Answer all questions.

If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks.

The use of an approved scientific calculator is expected, where appropriate.

If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.

For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π.

The number of marks is given in brackets [ ] at the end of each question or part question.

The total of the marks for this paper is 50.

For Examiner's Use

/ 50

Daniel says, "

71

is not a prime number." Is Daniel correct? Choose the answer with its reason.

Answer[2]

(a)Calculate

-20 + (-4) - (-16)

Answer (a)[2]

(b)Nur Aisyah estimates the value of

\dfrac{48.7}{3.12}

by writing each number correct to 1 significant figure. Without finding the exact value, explain whether the estimate is greater than or less than the exact value.

Answer (b)[1]

Express

\dfrac{3x + 4}{3} - \dfrac{4x - 3}{5}

as a single fraction in its simplest form.

Answer[2]

(a)A tin has some 20-cent coins and

8

more 50-cent coins than 20-cent coins. The coins are worth $12.40 altogether. Find the number of 20-cent coins.

Answer (a)[2]

(b)The graph shows the length,

y

cm, of a spring when a mass of

x

kg hangs from it. Use the graph to find the length of the spring when a mass of

2

kg hangs from it.

Answer (b)[1]

Write down the next term of the sequence

14, \ 15, \ 17, \ 20, \ \ldots

Answer[3]

Shop	Offer
A	12% off, then a further 5% off the reduced price for members
B	15% off, then $50 cashback

A air purifier has a marked price of $2,400 at two shops. The table shows each shop's offer. Ravi is a member of Shop A. Find how much less Ravi pays at the cheaper shop.

Answer$[3]

(a)A car travels 12 km on each litre of petrol. Find the number of litres of petrol it needs to travel 240 km.

Answer (a)[2]

(b)Nur is constructing triangle

ABC

with

AB = 6

cm,

\angle BAC = 65^\circ

and

\angle ABC = 55^\circ

. The diagram shows the construction so far. Which of the following is the next step?

Answer (b)[2]

The diagram shows a hexagon made of two identical trapeziums joined along their longer parallel sides (the dashed line). The parallel sides of each trapezium are

4

cm and

12

cm. The area of the hexagon is

80

cm². Find the value of

h

Answercm[3]

A closed cylinder has a radius of

3

cm and a total surface area of

48\pi

cm². Find its height,

h

cm.

Answercm[3]

The bar graph shows the cars passing a junction. Express the number of cars for 8 am as a percentage of the total number of cars.

Answer%[2]

y

is directly proportional to

x

. Complete the table of values.

Answer[3]

ABCD

is a parallelogram with

\angle DAB = (3x + 2y - 1)^\circ

\angle BCD = (5x + 9)^\circ

and

\angle ABC = (5x + 2y + 5)^\circ

. Form two equations in

x

and

y

and solve them. Hence find

\angle ABC

Answer°[3]

The sides of a right-angled triangle are

x

cm,

(x + 5)

cm and

(x + 10)

cm. Find the length of the hypotenuse of the triangle.

Answer[3]

In the diagram, the lines

AD

and

BC

meet at

X

, and

AB

is parallel to

DC

. Find

DC

Answercm[3]

From a point

A

on level ground

40

m from the foot of a lamp post, the angle of elevation of the top

T

22^\circ

. Find the height of the lamp post,

h

m, correct to 3 significant figures.

Answerm[2]

A solid metal cylinder of radius

3

cm and height

7

cm is melted down and recast into a prism of length

15

cm, with no metal lost. The cross-section of the prism is a sector of a circle with radius

R

cm and angle

90^\circ

, as shown. Find

R

, correct to 3 significant figures.

Answercm[3]

The heights, in cm, of 5 seedlings are

17,\ 28,\ x,\ 15,\ 26

. The mean is

19

cm. Find

x

Answer[3]

Cards numbered

1

30

are shuffled and one is drawn at random. Find the probability that the number is an even number.

Answer[2]

END OF PAPER

Answers and worked solutions

Question 1

Answer: PRIME[2]

A prime number has exactly

2

factors:

1

and itself.

\sqrt{71} = 8.42\ldots

, so test

2, 3, 5, 7

: none of them divides

71

exactly.

71

is a prime number, so Daniel is not correct.

Question 2

(a)Answer:

= -8

[2]

-20 + (-4) - (-16)

= -20 - 4 + 16

= -8

(b)Answer: OVER[1]

48.7 \rightarrow 50

is rounded up;

3.12 \rightarrow 3

is rounded down.The top was rounded up and the bottom down, so the estimate is greater than the exact value.

Question 3

Answer:

= \dfrac{3x + 29}{15}

[2]

\text{LCM of } 3 \text{ and } 5 =

15

\dfrac{3x + 4}{3} - \dfrac{4x - 3}{5} = \dfrac{5(3x + 4) - 3(4x - 3)}{15}

= \dfrac{15x + 20 - 12x + 9}{15}

= \dfrac{3x + 29}{15}

Question 4

(a)Answer:

x = 12

[2]

20x + 50(x + 8) = 1240

70x + 400 = 1240

70x = 840

x = 12

(b)Answer: Length:

16

cm[1]

Length:

16

Question 5

Answer:

\mathstrut 20 + 4 =

24

[3]

\mathstrut 15 - 14 =

1

\mathstrut 17 - 15 =

2

\mathstrut 20 - 17 =

3

\mathstrut 2 - 1 =

1

\mathstrut 3 + 1 =

4

\mathstrut 20 + 4 =

24

Question 6

Answer: Shop B is cheaper, by $16.40.[3]

\dfrac{88}{100} \times 2400 = 2112

\dfrac{95}{100} \times 2112 = 2006.40

\dfrac{85}{100} \times 2400 = 2040

2040 - 50 = 1990

2006.40 - 1990 = 16.40

Shop B is cheaper, by $16.40.

Question 7

(a)Answer:

20

litres[2]

\dfrac{240}{12}

= 20

20

litres

(b)Answer: mark C[2]

Done: draw AB, angle at A, angle at B.1. Draw

AB = 6

cm with a ruler. (done)2. At

A

, measure

\angle BAC = 65^\circ

with a protractor and draw a ray. (done)3. At

B

, measure

\angle ABC = 55^\circ

with a protractor and draw a ray. (done)4. Mark

C

where the two rays cross. (next)

Question 8

Answer:

h = 5

cm[3]

\text{One trapezium} = \dfrac{80}{2}

\phantom{\text{One trapezium}} = 40

cm²

\dfrac{1}{2} \times (4 + 12) \times h = 40

8h = 40

h = \dfrac{40}{8}

h = 5

Question 9

Answer: The height is

5

cm.[3]

2\pi r^2 + 2\pi rh = 48\pi

2\pi(3)^2 + 2\pi(3)h = 48\pi

18 + 6h = 48

6h = 30

h = \dfrac{30}{6}

h = 5

The height is

5

cm.

Question 10

Answer:

= 10\%

[2]

\text{Total} = 19 + 8 + 16 + 15 + 22

= 80

\dfrac{8}{80} \times 100\%

= 10\%

Question 11

Answer:

= 42

[3]

k = \dfrac{36}{6}

= 6

When

x = 1

y = 6 \times 1

= 6

When

x = 3

y = 6 \times 3

= 18

When

x = 7

y = 6 \times 7

= 42

Question 12

Answer:

\angle ABC = 106^\circ

°[3]

3x + 2y - 1 = 5x + 9

x - y = -5

... (1)

(3x + 2y - 1) + (5x + 2y + 5) = 180

2x + y = 44

... (2)The

y

-terms have opposite signs, so add.

(1) + (2)

3x = 39

x = \dfrac{39}{3}

= 13

13 - y = -5

-y = -18

y = 18

Check in (2):

2(13) + (18)

= 44

, the right-hand side of (2).

\angle ABC = 106^\circ

Question 13

Answer:

= 25

cm[3]

The hypotenuse is the longest side,

x + 10

.hypotenuse² = sum of the squares of the other two sides

x^2 + (x + 5)^2 = (x + 10)^2

x^2 + x^{2} + 10x + 25 = x^{2} + 20x + 100

x^{2} - 10x - 75 = 0

(x - 15)(x + 5) = 0

x - 15 = 0

x + 5 = 0

x = 15

x = -5

x = -5

is rejected because a length cannot be negative. So

x = 15

.Hypotenuse

= 15 + 10

= 25

Question 14

Answer:

DC = 14

cm[3]

\angle XAB = \angle XDC

(alternate angles)

\angle AXB = \angle DXC

(vertically opposite angles)

\dfrac{DC}{AB} = \dfrac{XD}{XA}

\mathstrut \dfrac{DC}{7} = \dfrac{10}{5}

DC = \dfrac{10}{5} \times 7

DC = 14

Question 15

Answer:

= 16.2

m (3 s.f.)[2]

From the angle of elevation: the height

h

m is the opposite and the distance

40

m along the ground is the adjacent.

\tan 22^\circ = \dfrac{h}{40}

h = 40 \tan 22^\circ

= 16.1610\ldots

= 16.2

m (3 s.f.)

Question 16

Answer:

= 4.10

cm (3 s.f.)[3]

V = \pi \times 3^2 \times 7

\phantom{V} = 63\pi

cm³

\dfrac{90}{360} \times \pi R^2 \times 15 = 63\pi

R^2 = \dfrac{63 \times 360}{90 \times 15}

\phantom{R^2} = 16.8

= 4.0987\ldots

= 4.10

cm (3 s.f.)

Question 17

Answer:

= 9

[3]

Total

= 19 \times 5

= 95

Sum of the others

= 17 + 28 + 15 + 26

= 86

x = 95 - 86

= 9

Question 18

Answer:

P = \dfrac{1}{2}

[2]

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30

That is

15

numbers out of

30

\mathstrut P = \dfrac{15}{30}

P = \dfrac{1}{2}

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Sec 2 Maths End-of-year exam Paper 1: free PDF with answers

In the print window, choose Save as PDF to download it.

MugCornerT-Leng Tuition · mugcornersg.com

Mathematics

Sec 2 Maths · End-of-year exam Paper 1

Practice paper in the same style as the school and national exam papers. Not a copy of any past year paper.

1 hour 15 minutes

Name

Class

Index number

Candidates answer on the Question Paper.

Read these instructions first

Write your name, class and index number in the spaces at the top of this page.

Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs.

Do not use staples, paper clips, glue or correction fluid.

Answer all questions.

If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks.

The use of an approved scientific calculator is expected, where appropriate.

If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place.

For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π.

The number of marks is given in brackets [ ] at the end of each question or part question.

The total of the marks for this paper is 50.

For Examiner's Use

/ 50

Daniel says, "

71

is not a prime number." Is Daniel correct? Choose the answer with its reason.

Answer[2]

(a)Calculate

-20 + (-4) - (-16)

Answer (a)[2]

(b)Nur Aisyah estimates the value of

\dfrac{48.7}{3.12}

by writing each number correct to 1 significant figure. Without finding the exact value, explain whether the estimate is greater than or less than the exact value.

Answer (b)[1]

Express

\dfrac{3x + 4}{3} - \dfrac{4x - 3}{5}

as a single fraction in its simplest form.

Answer[2]

(a)A tin has some 20-cent coins and

8

more 50-cent coins than 20-cent coins. The coins are worth $12.40 altogether. Find the number of 20-cent coins.

Answer (a)[2]

(b)The graph shows the length,

y

cm, of a spring when a mass of

x

kg hangs from it. Use the graph to find the length of the spring when a mass of

2

kg hangs from it.

Answer (b)[1]

Write down the next term of the sequence

14, \ 15, \ 17, \ 20, \ \ldots

Answer[3]

Shop	Offer
A	12% off, then a further 5% off the reduced price for members
B	15% off, then $50 cashback

A air purifier has a marked price of $2,400 at two shops. The table shows each shop's offer. Ravi is a member of Shop A. Find how much less Ravi pays at the cheaper shop.

Answer$[3]

(a)A car travels 12 km on each litre of petrol. Find the number of litres of petrol it needs to travel 240 km.

Answer (a)[2]

(b)Nur is constructing triangle

ABC

with

AB = 6

cm,

\angle BAC = 65^\circ

and

\angle ABC = 55^\circ

. The diagram shows the construction so far. Which of the following is the next step?

Answer (b)[2]

The diagram shows a hexagon made of two identical trapeziums joined along their longer parallel sides (the dashed line). The parallel sides of each trapezium are

4

cm and

12

cm. The area of the hexagon is

80

cm². Find the value of

h

Answercm[3]

A closed cylinder has a radius of

3

cm and a total surface area of

48\pi

cm². Find its height,

h

cm.

Answercm[3]

The bar graph shows the cars passing a junction. Express the number of cars for 8 am as a percentage of the total number of cars.

Answer%[2]

y

is directly proportional to

x

. Complete the table of values.

Answer[3]

ABCD

is a parallelogram with

\angle DAB = (3x + 2y - 1)^\circ

\angle BCD = (5x + 9)^\circ

and

\angle ABC = (5x + 2y + 5)^\circ

. Form two equations in

x

and

y

and solve them. Hence find

\angle ABC

Answer°[3]

The sides of a right-angled triangle are

x

cm,

(x + 5)

cm and

(x + 10)

cm. Find the length of the hypotenuse of the triangle.

Answer[3]

In the diagram, the lines

AD

and

BC

meet at

X

, and

AB

is parallel to

DC

. Find

DC

Answercm[3]

From a point

A

on level ground

40

m from the foot of a lamp post, the angle of elevation of the top

T

22^\circ

. Find the height of the lamp post,

h

m, correct to 3 significant figures.

Answerm[2]

A solid metal cylinder of radius

3

cm and height

7

cm is melted down and recast into a prism of length

15

cm, with no metal lost. The cross-section of the prism is a sector of a circle with radius

R

cm and angle

90^\circ

, as shown. Find

R

, correct to 3 significant figures.

Answercm[3]

The heights, in cm, of 5 seedlings are

17,\ 28,\ x,\ 15,\ 26

. The mean is

19

cm. Find

x

Answer[3]

Cards numbered

1

30

are shuffled and one is drawn at random. Find the probability that the number is an even number.

Answer[2]

END OF PAPER

Answers and worked solutions

Question 1

Answer: PRIME[2]

A prime number has exactly

2

factors:

1

and itself.

\sqrt{71} = 8.42\ldots

, so test

2, 3, 5, 7

: none of them divides

71

exactly.

71

is a prime number, so Daniel is not correct.

Question 2

(a)Answer:

= -8

[2]

-20 + (-4) - (-16)

= -20 - 4 + 16

= -8

(b)Answer: OVER[1]

48.7 \rightarrow 50

is rounded up;

3.12 \rightarrow 3

is rounded down.The top was rounded up and the bottom down, so the estimate is greater than the exact value.

Question 3

Answer:

= \dfrac{3x + 29}{15}

[2]

\text{LCM of } 3 \text{ and } 5 =

15

\dfrac{3x + 4}{3} - \dfrac{4x - 3}{5} = \dfrac{5(3x + 4) - 3(4x - 3)}{15}

= \dfrac{15x + 20 - 12x + 9}{15}

= \dfrac{3x + 29}{15}

Question 4

(a)Answer:

x = 12

[2]

20x + 50(x + 8) = 1240

70x + 400 = 1240

70x = 840

x = 12

(b)Answer: Length:

16

cm[1]

Length:

16

Question 5

Answer:

\mathstrut 20 + 4 =

24

[3]

\mathstrut 15 - 14 =

1

\mathstrut 17 - 15 =

2

\mathstrut 20 - 17 =

3

\mathstrut 2 - 1 =

1

\mathstrut 3 + 1 =

4

\mathstrut 20 + 4 =

24

Question 6

Answer: Shop B is cheaper, by $16.40.[3]

\dfrac{88}{100} \times 2400 = 2112

\dfrac{95}{100} \times 2112 = 2006.40

\dfrac{85}{100} \times 2400 = 2040

2040 - 50 = 1990

2006.40 - 1990 = 16.40

Shop B is cheaper, by $16.40.

Question 7

(a)Answer:

20

litres[2]

\dfrac{240}{12}

= 20

20

litres

(b)Answer: mark C[2]

Done: draw AB, angle at A, angle at B.1. Draw

AB = 6

cm with a ruler. (done)2. At

A

, measure

\angle BAC = 65^\circ

with a protractor and draw a ray. (done)3. At

B

, measure

\angle ABC = 55^\circ

with a protractor and draw a ray. (done)4. Mark

C

where the two rays cross. (next)

Question 8

Answer:

h = 5

cm[3]

\text{One trapezium} = \dfrac{80}{2}

\phantom{\text{One trapezium}} = 40

cm²

\dfrac{1}{2} \times (4 + 12) \times h = 40

8h = 40

h = \dfrac{40}{8}

h = 5

Question 9

Answer: The height is

5

cm.[3]

2\pi r^2 + 2\pi rh = 48\pi

2\pi(3)^2 + 2\pi(3)h = 48\pi

18 + 6h = 48

6h = 30

h = \dfrac{30}{6}

h = 5

The height is

5

cm.

Question 10

Answer:

= 10\%

[2]

\text{Total} = 19 + 8 + 16 + 15 + 22

= 80

\dfrac{8}{80} \times 100\%

= 10\%

Question 11

Answer:

= 42

[3]

k = \dfrac{36}{6}

= 6

When

x = 1

y = 6 \times 1

= 6

When

x = 3

y = 6 \times 3

= 18

When

x = 7

y = 6 \times 7

= 42

Question 12

Answer:

\angle ABC = 106^\circ

°[3]

3x + 2y - 1 = 5x + 9

x - y = -5

... (1)

(3x + 2y - 1) + (5x + 2y + 5) = 180

2x + y = 44

... (2)The

y

-terms have opposite signs, so add.

(1) + (2)

3x = 39

x = \dfrac{39}{3}

= 13

13 - y = -5

-y = -18

y = 18

Check in (2):

2(13) + (18)

= 44

, the right-hand side of (2).

\angle ABC = 106^\circ

Question 13

Answer:

= 25

cm[3]

The hypotenuse is the longest side,

x + 10

.hypotenuse² = sum of the squares of the other two sides

x^2 + (x + 5)^2 = (x + 10)^2

x^2 + x^{2} + 10x + 25 = x^{2} + 20x + 100

x^{2} - 10x - 75 = 0

(x - 15)(x + 5) = 0

x - 15 = 0

x + 5 = 0

x = 15

x = -5

x = -5

is rejected because a length cannot be negative. So

x = 15

.Hypotenuse

= 15 + 10

= 25

Question 14

Answer:

DC = 14

cm[3]

\angle XAB = \angle XDC

(alternate angles)

\angle AXB = \angle DXC

(vertically opposite angles)

\dfrac{DC}{AB} = \dfrac{XD}{XA}

\mathstrut \dfrac{DC}{7} = \dfrac{10}{5}

DC = \dfrac{10}{5} \times 7

DC = 14

Question 15

Answer:

= 16.2

m (3 s.f.)[2]

From the angle of elevation: the height

h

m is the opposite and the distance

40

m along the ground is the adjacent.

\tan 22^\circ = \dfrac{h}{40}

h = 40 \tan 22^\circ

= 16.1610\ldots

= 16.2

m (3 s.f.)

Question 16

Answer:

= 4.10

cm (3 s.f.)[3]

V = \pi \times 3^2 \times 7

\phantom{V} = 63\pi

cm³

\dfrac{90}{360} \times \pi R^2 \times 15 = 63\pi

R^2 = \dfrac{63 \times 360}{90 \times 15}

\phantom{R^2} = 16.8

= 4.0987\ldots

= 4.10

cm (3 s.f.)

Question 17

Answer:

= 9

[3]

Total

= 19 \times 5

= 95

Sum of the others

= 17 + 28 + 15 + 26

= 86

x = 95 - 86

= 9

Question 18

Answer:

P = \dfrac{1}{2}

[2]

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30

That is

15

numbers out of

30

\mathstrut P = \dfrac{15}{30}

P = \dfrac{1}{2}

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