SmoothMaths - Aldenham School 13Plus Paper 1

Welcome to your ALDENHAM SCHOOL 13+ Paper 1

1. Work out the following calculations.

(a) (24 – 10) x 2

16 20 48 28 14

1. Work out the following calculations.
(b) 12 + 3 x 8

24 None of the above 36 120 12

2. Owen buy some cricket pads for £19.56 and a helmet for £24.38.

(a) How much does Owen spend in total?

£19.56 £29.20 £24.38 £43.98 None of the above

2. Owen buy some cricket pads for £19.56 and a helmet for £24.38.
(b) He wishes to buy a cricket bat costing £148
He has £30 saved already and his parents say they will pay half of the cost.

He can save £10 per month. How many months will he have to wait until he can afford the bat?

6 months 3 months 5 months 4 months 7 months

3. Circle the number which is not a multiple of 3?

None of the above 201 180 301 24

4. Mr Collins bought 24 packs of biscuits each containing 15 biscuits.

How many biscuits did he buy in total?

360 Biscuits 288 Biscuits 160 Biscuits 264 Biscuits None of the above

5. Write down a number which is a multiple of 8 and a multiple of 12.

12 6 4 8 24

6. Write the numbers below in order, starting with the smallest.

(a) -3, 3.5, 0, -14, 25, 4

25, 4, 3.5, 0 , -3,-14 -14, -3, 0, 3.5, 4, 25 -3, -14, 0, 3.5, 4, 25 None of the above 0, -3, -14, 3.5, 4, 25

6. Write the numbers below in order, starting with the smallest.
(b) 5m 240cm 80cm 4500mm

None of the above 4500mm, 80cm, 240cm, 5m 5m, 240cm, 80cm, 4500mm 80cm, 240cm, 4500mm, 5m 5m, 4500mm, 240cm, 80cm

7. You start at (7, 3) and move 6 squares left and 4 units up. Where do you end up?

Screenshot 1 39

(1,3) (1,7) (2,6) (7,3) (3,7)

8. Izzy has a new necklace. 12 of the 60 beads are blue.

What percentage of the beads are blue?

0.5 0.2 0.25 0.35 0.45

9. Draw an accurate net of this shape.

Screenshot 2 43

10. A crate can hold 12 glasses.

What is the smallest number of crates needed for 100 glasses?

12 crates 7 crates 8 crates 9 crates 10 crates

11. Simplify the expressions below. (x means multiply)

(a) c + 4m - 7m

c - 11m c - 4m c - 3m c + 4m c + 3m

11. Simplify the expressions below. (x means multiply)
(b) 2t x 5t

\[10t^{3}\] \[10t^{2}\] \[5t^{2}\] \[10t^{4}\] 10t

11. Simplify the expressions below. (x means multiply)
(c) 3a + 5(4a – 2)

10a + 23 3a + 2 20a + 10 3a + 10 23a + 10

12. 6 litres of water is to be shared equally between 15 bottles. How much water will there be in each bottle?

1 liter 0.4 liers 1.5 liter 4 liters 2.5 liter

13(a) Look at the following 10 numbers

7 5 7 6 6 4 5 3 4 4

How would the mode change if one of the 6s was changed to a 4?
Circle your answer.

Increase Decrease No change None of the above a & b both

13 .(b) Look at the following 10 numbers

88 59 80 77 56 85 64 66 76 59

How would the median change if the number 64 was added to the list?
Circle your answer.

None of the above Both a & c Increase Decrease No change

14. Find the volume of the solid below.

Include the units in your answer.

Screenshot 3 51

120m³ 45m³ 30m³ 360³ 180m³

15. The volume of this cube is 729 cubic metres. What is the value of u?
Circle your answer.

Screenshot 4 49

None of above 7m 13m 8m 9m

16.(a) Work out:

\[2\frac{3}{4}+1\frac{2}{5}=\]

4\[\frac{3}{20}\] 3\[\frac{5}{9}\] Both a & b \[\frac{83}{20}\] \[\frac{14}{20}\]

16. (b) Work out and simplify fully.

\[\frac{4}{5} ÷ \frac{2}{3}=\]

1\[\frac{1}{5}\] Both a & b \[\frac{6}{5}\] \[\frac{4}{5}\] \[\frac{2}{5}\]

17. Write 60 as the product of its prime factors.

4 x 3 x 5 2 x 2 x 1 x 5 None of the above 2 x2 x 3 x 5 4 x 15

18. Solve the following equations:

(a) 4n - 8 = 32

4 28 8 32 6

18. Solve the following equations
(b) 6p + 5 = 40 - p

28 None of the above 5 35 6

18. Solve the following equations:

6 or -6 4 or -4 None of the above 5 or -5 9 or -9

19. A store owner bought a bag for £120 and sold it for £150.

What percentage profit is this?

80% 40% 25% 35% 20%

20. Factorise the expression 12 – 4x

4(3 - x) 8 - 4x 12 4x None of the above

21.(a) In a bag there are blue and yellow marbles.

There are 20 marbles in total and 12 are blue.

If a marble is picked out of the bag at random, what is the probability that it is yellow?

\[\frac{3}{5}\] 1 \[\frac{4}{5}\] \[\frac{1}{4}\] \[\frac{1}{5}\]

21.(b) In a bag there are blue and yellow marbles.
There are 20 marbles in total and 12 are blue.
If experiment is repeated 50 times what is the expected number of yellow marbles which would be chosen?

5 20 8 4 12

21.(c) In a bag there are blue and yellow marbles.
There are 20 marbles in total and 12 are blue.
If you were to pick a marble, replace it, then pick another, what is the probability both marbles would be yellow?

\[\frac{4}{25}\] None of the above \[\frac{5}{4}\] \[\frac{1}{5}\] \[\frac{4}{5}\]

22. Look at the scattergraph below linking maths and science test scores.

Screenshot 5 43

(a) What type of correlation does the graph show.

Positive correlation None of the above Negative correlation All of the above except c No correlation

22. Look at the scattergraph below linking maths and science test scores.

Screenshot 5 43
(b) By drawing a line of best fit, predict the value for a maths score for a student whose
science score was 38.

43 marks 45 marks 50 marks 40 marks 38 marks

23. P = 2( a + b )

(a) Work out the value of P when a = 4 and b = 12

20 8 16 32 24

23. P = 2( a + b )
(b) Work out the value of a if P = 16 and b = 3

10 13 11 8 5

24. Here are the ingredients for fudge.

Screenshot 6 52

Work out how much condensed milk is needed to make fudge for 10 people.

None of the above 800g 4800g 600g 580g

25. Mika can eat 21 hot dogs in 6 minutes.

How many minutes would it take her to eat 35 hot dogs if she can keep up the same pace?

You must show your working

10 minutes 12 minutes 15 minutes 6 minutes 8 minutes

26. A box contains counters that are red, blue, yellow or green.

The table shows some information about picking a counter at random.

	red	blue	yellow	green
Probability	x	0.25	0.35	3x

Work out the value of x, the probability of choosing a red counter.

0.3 0.5 0.1 0.7 0.2

27.

Screenshot 7 55

(a) Measure and write down the bearing of B from A.

\[330^{o}\] \[160^{o}\] \[60^{o}\] \[270^{o}\] \[110^{o}\]

(b) Estimate on the diagram, the position of a line on a bearing of 110° from A.

28.(a) Complete the table of values for the graph y = 2x - 4

Screenshot 8 50

28. (b) On the grid, draw the graph of y = 2x - 4 for values of x from -2 to 2

Screenshot 9 49

28. (c) Draw the line y = x on the axes above.

29.

Screenshot 10 41

a Rotate shape P 90° clockwise about the point (0,2). Label the new shape Q

29.

(b) Translate triangle Q by \[\frac{3}{-6}\]

Label your answer R.

30.

Screenshot 11 49

Reflect the shape in the line x= -1

31. The table shows the goals scored scored goals for the school hockey team last month.

Goals scored	Number of students
1	9
2	3
3	5
4	3

(a) What was the modal number of goals scored?

5 4 9 1 3

31. The table shows the goals scored scored goals for the school hockey team last month.

Goals scored	Number of students
1	9
2	3
3	5
4	3

(b) How many students were there in total?

9 None of the above 12 8 20

31. The table shows the goals scored scored goals for the school hockey team last month.

Goals scored	Number of students
1	9
2	3
3	5
4	3

1.5 2.5 1.2 2.1 None of the above

32. Work out the size of angles a and b.

Screenshot 12 43

a = \[20^{o}\] , b = \[120^{o}\] a = \[60^{o}\] , b = \[100^{o}\] a = \[40^{o}\] , b =\[120^{o}\] a = \[70^{o}\] , b =\[80^{o}\] a = \[45^{o}\] , b = \[71^{o}\]

33. (a) Write down the 8th term in this sequence.

4, 10, 16, 22, 28

52 34 40 46 58

33.(b) Write down the formula for the nth term of the following sequence.

-4, 2, 8, 14, 20

4n - 6 6n - 4 6n - 6 10n - 6 6n - 10

33.(c) Which term in the sequence is 62?

\[9^{th}\] term \[12^{th}\] term \[11^{th}\] term \[15^{th}\] term \[10^{th}\] term

34. 40% of people left the party before it ended. 10% of those who left were men.

The ratio of the number of men who left to those who did not was 2 : 5.

If there were 105 men at the party when it started, how many women were at the party when it started?

550 645 750 600 720

35. (a) Simplify \[5^{4}\ × 5^{6}\]

\[5c^{6}\] \[25^{10}\] \[5^{4}\] \[5^{24}\] \[5^{10}\]

35.(b) Simplify \[7^{5}\ ÷ 7^{2}\]

\[7^{1}\] \[7^{4}\] \[7^{5}\] \[7^{2}\] \[7^{3}\]

36. Mrs Green’s garden is in the shape of a rectangle.
Part of the garden is a patio in the shape of a triangle.
The rest of the garden is grass.

Screenshot 1 40

Mrs Green wants to spread fertiliser over all her grass.

One box of fertiliser is enough for 32m² of grass.

How many boxes of fertiliser will she need?
You must show your working.

4 boxes 5 boxes 3 boxes 6 boxes 2 boxes

37. Andrew paid £12 for 4 cups of coffee and 4 cups of tea.

3 cups of coffee cost as much as 2 cups of tea.

What was the total cost of 5 cups of tea and 5 cups of coffee.

£12 £6 £13 £9 £15

38. Roy gets 10% extra time in school exams.

If Roy gets 1 hour, 33 minutes and 30 seconds to complete his maths exam, how long do most students get?

80 minutes 63 minutes 85 minutes 90 minutes 78 minutes

Time's up