FOREST SCHOOL 13+ Paper 2 SMOOTHMATHS

Welcome to your Forest School 13+Entrance Examination Sample Paper 2

1. Calculate the following:

(a) 9876 + 6789

Answer:

1666516655165551555515665

(b) 987 x 14

Answer:

1381812598135981281813718

(c) 30485 ÷ 13

Answer:

23453254342524352543

(d) 1.7 x 2.1

Answer:

3.572.571.574.75None of the Above

(e) 7.45 — 2.61

Answer:

4.845.844.245.243.84

(f) 0.4 ÷ 0.002

Answer:

200200.20.02All of the Above

2. Calculate the following:

(a) 22 — (-67) =

89-45-8945None of the Above

(b) \[(-3)^{4}\] =

81927-81All of the Above except 'c'

(c) -8 — 17 =

-2525-1111None of the Above

(d) 27 ÷ -3 =

-9973None of the Above

3. If x = -5, y = -10 and z = -15 calculate the following:

(a) x — y + z

Answer:

-10-5010None of the Above

(b) \[2x^{2}\]

Answers:

502512.5100All of the Above

4. (a) Round the following to 2 decimal places:

(i) 1.2468

Answer:

1.251.241.231.26All of the Above

(ii) 1.8989

Answers:

1.91.881.891.8None of the Above

(b) Sana says that x = 7.3 to 1 decimal place.

(i) What is the least possible value of x?

Answer:

7.257.57.27.357.15

(ii) What is the largest possible value of \[\frac{29}{x}\] ?

Answer:

2.742.732.643.545.64

(iii) Charlie says that the largest x can be is 7.34.
Is he right?
Explain clearly your reasoning.

Charlie is wrongCharlie is rightBoth a & bAll of the AboveNone of the Above

5. Molly draws 5 straight lines.
What is the most number of different intersection points she can make?

Answer:

10731215

6. The area of a circle is \[πr^{2}\] and the circumference (perimeter) is 2πr where π= 3.141 5

Estimate the area and the perimeter of this semicircle. where AB = 10 cm.

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Area:

Area= 39.3\[cm^{2}\]Area= 7.8\[cm^{2}\]Area= 19.3\[cm^{2}\]Area= 9.3\[cm^{2}\]None of the Above

Perimeter:

Perimeter= 25.7cmPerimeter= 15.7cmPerimeter= 22.7cmPerimeter= 12.7cmNone of the Above

7. What fraction is halfway between one third and one quarter?
You should show your working clearly.

Answer:

7/241/47/123/4All of the Above

8. Fill in the gaps. Put your fractions in their lowest terms.

Percentage	Fraction
55%
	\[\frac{1}{8}\]
2%
	\[\frac{3}{20}\]

9. A rectangle has width x cm and its length is 4 cm longer than its width. Its
perimeter is 50 + x cm.
Find an equation which x must satisfy and hence find the length of the rectangle.

Length =

18cm14cm16cm12cm24cm

10. In a farmyard the ratio of peacocks to ducks is 2:3 and the ratio of ducks to hens is 4:5.
What is the ratio of peacocks to hens?

Answer:

8:158:124:53:4None of the Above

11. (a) Faizan buys a car ror £200o.
Its value depreciates (goes down) by 2% each year.
How much is it worth after 1 year?

Answer:

£1960£1260£1060£1860£1460

b) How much is it worth after 2 years?

Answer:

£1920.8£1260.4£1060£1860.5£1460.2

12. Liverchester United are playing 2 matches against their arch rivals. Manpool City. They have won 6 out of their last 10 matches against Manpool City.

(a) Based on these results, what is the probability that Liverchester beat Manpool in the first match?

Answer:

0.50.10.20.40.8

(b) What is the probability they win both matches?

Answer:

1/41/21/31/6None of the Above

(c) Having won the last 6 out of 1 0 matches, how many games would Liverchester then have to win in a row so that their probability of winning is \[\frac{3}{4}\] ?

Answer:

6 games4 games3 games2 games8 games

13. The scattergram shows how some pupils at Forest did in a maths test against their height.

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Hibban says “Being tall makes a pupil better at maths”

Do you agree?

YesNoYesNoNone of the Above

Explain your reasoning clearly:

Yes Because the height of students increasesNo Because the height of students increasesYes Because the height of students decreasesNo Because the height of students increasesNone of the Above

14. Andreas wants to estimate how many fish there are in a lake.
One day he catches 20 fish, marks them, and returns them to the lake.
The next day he catches 10 fish. of which 4 are marked.
Use this information to estimate the number ot‘ fish in the lake.

Answer:

262014104

15. Remove the brackets and simplify these expressions fully:

(a ) 4{f - g ) + 5(2f + g ) =

=

14f+g14f+9g14f-g6f+gNone of the Above

(b) 7(2e + 8) — 3(3e — 5) =

=

5E+711.9E+725E-415E-71None of the Above

(c) w(2w + 5v) -3v (5w - 2v) =

=

2\[w^{2}\] - 10wv +6\[v^{2}\]2\[w^{2}\] + 10wv +6\[v^{2}\]2\[w^{2}\] -15wv +6\[v^{2}\]2 \[w^{2}\]-10wv -6\[v^{2}\]2w -10wv -6v

16. Factorise the following expressions fully:

(a) 15a + 27b

Answer:

3(5a + 9b)3(5a-9b)3(5a+8b)5(5a+3b)None of the Above

(b) \[27c^{2}\]\[d^{2}\] — \[36c^{5}\]d

Answer:

\[9c^{2}\]d(3d-\[4c^{3}\])\[3c^{2}\]d(3d-\[4c^{3}\])\[9c^{2}\]d(3d+\[4c^{3}\])\[9c^{2}\]d(\[3d^{2}\]-\[4c^{3}\])None of the Above

17. Find the three missing angles in the diagram below, you must give the full reasoning for each answer. ABC is an isosceles triangle, the lines with arrows are parallel.

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x=

x=94ox=104ox=84ox=74oNone of the Above

Reasons:

y=

y=94oy=101oy=104oy=114oNone of the Above

Reasons:

z=

z=137oz=120oz=117oz=127oNone of the Above

Reasons:

18. Class A has 10 pupils and achieved a mean of 40% in a maths test.
Class B has 15 pupils and achieved a mean of 80% in the same test.
What is the overall mean for both classes?

Answer:

64%120%60%80%50%

19. Draw all the lines of symmetry on these shapes:

(a) An equilateral triangle

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(b) A rectangle

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20. (i) Label the lines with their equations.

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Line A:

Line A: y =xLine A: x =yLine A: y =3Line A: y =2Line A: y = 4

Line B:

Line B: x=4Line B: x=5Line B: x=-4Line B: x=3Line B: x=2

(ii) A triangle has its vertices (corners) at (-2. -2), (-2, 1 ) and (-3. 1 ).
Plot these points, and draw the triangle on the diagram.
Reflect the triangle in Line A.

21. The Fibonacci sequence is formed by adding the previous two numbers to get the next:

1, 1, 2, 3, 5, 8, 13 ,...

What are the next three numbers in this sequence?

The Lucas Sequence has the same rule but starts with 1 and 3.
(i) Write out the first 7 terms of the Lucas sequence.

1,3,4,7,11,18,291,2,4,6,8,10,121,3,4,7,11,18,241,3,4,7,11,14,18None of the Above

(ii) Write down the first 7 terms, in terms off and J, for the sequence with the same rule whose first terms are x and y.

x, y, x+y, x+2y, 2x+3y, 3x+5y, 5x+8yx, y, x+y, x+2y, x+3y, x+5y, x+8yx, y, x+y, x+2y, x+2y, x+2y, x+2yx, y, x+y, 2x+2y, 2x+3y, 2x+5y, 2x+8yNone of the Above

(iii) Mia says: “If x is a multiple of 5 then the 6th term of the sequence is also a multiple of 5 whatever y is”.

Do you agree? Explain your reasoning carefully.

5, y, 5+y, 5+2y, 10+3y, 15+5y5, y, 5+y, 5+2y, 10+2y, 15+2y5, y, 5+y, 5+2y, 10+3y, 15+4y5, y, 5+y, 6+y, 10+y, 15+yNone of the Above

(iv) Steph says: “Every 5” term of the Fibonacci sequence is a multiple of 5”.

Do you agree? Explain your reasoning carefully.

Evey 5th term of Fibbonacci sequence is a multiple of 5Every 5th term Fibbonacci sequence is not a multiple of 5Evey 3rd term of Fibbonacci sequence is a multiple of 3Evey 5th term of Fibbonacci sequence is a multiple of 8Evey 5th term of Fibbonacci sequence is a multiple of 6

22. (i) Show that the interior angle of a regular pentagon is 108 degrees.

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Interior Angle of a regular Pentagon is 108 degreesInterior Angle of a regular Pentagon is 180 degreesInterior Angle of a regular Pentagon is 160 degreesInterior Angle of a regular Pentagon is 270 degreesInterior Angle of a regular Pentagon is 360 degrees

(ii) A regular pentagon and a regular hexagon overlap as shown.
Find the angle x. Show your reasoning clearly.

ADHGIAHEG

84o72o108o120o60o

FOREST SCHOOL 13+ Paper 2

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