FOREST SCHOOL 13+ Paper 2

Welcome to your FOREST SCHOOL 13+ Paper 2

1. Calculate the following:

(a) 9876 + 6789

Answer:

(b) 987 x 14

Answer:

(c) 30485 ÷ 13

Answer:

(d) 1.7 x 2.1

Answer:

(e) 7.45 — 2.61

Answer:

(f) 0.4 ÷ 0.002

Answer:

2. Calculate the following:

(a) 22 — (-67) =

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

(c) -8 — 17 =

(d) 27 ÷ -3 =

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

(a) x — y + z

Answer:

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

Answers:

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

(i) 1.2468

Answer:

(ii) 1.8989

Answers:

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

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

Answer:

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

Answer:

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

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

Answer:

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.

Area:

Perimeter:

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

Answer:

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 =

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:

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:

b) How much is it worth after 2 years?

Answer:

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:

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

Answer:

(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:

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

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

Do you agree?

Explain your reasoning clearly:

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:

15. Remove the brackets and simplify these expressions fully:

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

=

(b) 7(2e + 8) — 3(3e — 5) =

=

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

=

16. Factorise the following expressions fully:

(a) 15a + 27b

Answer:

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

Answer:

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.

x=

Reasons:

y=

Reasons:

z=

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:

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

(a) An equilateral triangle

(b) A rectangle

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

Line A:

Line B:

(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.

(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.

(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.

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

Do you agree? Explain your reasoning carefully.

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