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

48 28 16 14 20

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

12 120 36 24 None of the above

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 None of the above £43.98 £29.20 £24.38

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?

3 months 5 months 7 months 4 months 6 months

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

301 None of the above 201 24 180

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

How many biscuits did he buy in total?

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

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

24 4 6 8 12

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

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

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

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

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

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

Screenshot 1 39

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

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

What percentage of the beads are blue?

0.25 0.5 0.45 0.2 0.35

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?

10 crates 12 crates 8 crates 7 crates 9 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

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

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

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

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

2.5 liter 0.4 liers 1.5 liter 1 liter 4 liters

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 None of the above a & b both No change

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.

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

14. Find the volume of the solid below.

Include the units in your answer.

Screenshot 3 51

360³ 45m³ 120m³ 180m³ 30m³

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

Screenshot 4 49

9m 8m 13m 7m None of above

16.(a) Work out:

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

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

16. (b) Work out and simplify fully.

\[\frac{4}{5} ÷ \frac{2}{3}=\]

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

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

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

18. Solve the following equations:

(a) 4n - 8 = 32

28 32 8 4 6

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

28 6 5 35 None of the above

18. Solve the following equations:

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

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

What percentage profit is this?

40% 80% 25% 35% 20%

20. Factorise the expression 12 – 4x

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

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?

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

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?

8 4 12 20 5

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?

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

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

Screenshot 5 43

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

None of the above All of the above except c Negative correlation Positive correlation 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.

50 marks 45 marks 43 marks 38 marks 40 marks

23. P = 2( a + b )

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

16 32 24 20 8

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

13 10 8 5 11

24. Here are the ingredients for fudge.

Screenshot 6 52

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

800g 4800g None of the above 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 6 minutes 8 minutes 15 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.

0.1 0.2 0.7 0.3 0.5

27.

Screenshot 7 55

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

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

(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?

1 3 5 9 4

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 20 8 None of the above 12

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

2.1 2.5 1.5 1.2 None of the above

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

Screenshot 12 43

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

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

4, 10, 16, 22, 28

52 40 34 46 58

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

-4, 2, 8, 14, 20

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

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

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

750 550 720 645 600

35. (a) Simplify \[5^{4}\ × 5^{6}\]

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

35.(b) Simplify \[7^{5}\ ÷ 7^{2}\]

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

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 6 boxes 2 boxes 3 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.

£13 £9 £12 £15 £6

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?

90 minutes 63 minutes 78 minutes 80 minutes 85 minutes

Time's up