Name: _______________________________________________
Questions for Foundation Calculator
Date: June 2017
1.
The diagram shows the positions of three turbines A, B and C.
Diagram NOT accurately drawn
A is 6 km due north of turbine B.
C is 4.5 km due west of turbine B.
(a) Calculate the distance AC.
...........................................................km
(3)
(b) Calculate the bearing of C from A.
Give your answer correct to the nearest degree.
...........................................................°
(4)
(Total for Question is 7 marks)
2. The diagram shows a semicircle drawn inside a rectangle.
The semicircle has a diameter of 8 cm.
The rectangle is 8 cm by 4 cm.
Work out the area of the shaded region.
Give your answer correct to 3 significant figures.
. . . . . . . . . . . . . . . . . . . . . . . cm2
(Total for Question is 4 marks)
3. The diagram shows the plan of a floor.
The area of the floor is 138 m2.
Work out the value of x.
..........................................................
(Total for Question is 4 marks)
4. Here is a list of the names of five types of quadrilateral.
trapezium
parallelogram
square
rhombus
rectangle
(a) From the list, write down the names of two quadrilaterals which must have all four sides the same
length.
..............................................................................................................................................
(1)
trapezium
parallelogram
square
rhombus
rectangle
(b) From the list, write down the name of the quadrilateral that has only one pair of parallel sides.
..............................................................................................................................................
(1)
trapezium
parallelogram
square
rhombus
rectangle
For one of these quadrilaterals,
the corners are not right angles,
the quadrilateral has rotational symmetry of order 2
and the diagonals cross at right angles.
(c) Write down the name of this quadrilateral.
..............................................................................................................................................
(1)
(Total for Question is 3 marks)
5.
There are yellow discs, red discs, blue discs and green discs in a bag.
Dinesh is going to take at random a disc from the bag.
The table shows each of the probabilities that Dinesh will take a red disc, or a blue disc, or a green disc.
Colour
yellow
Probability
red
blue
green
0.40
0.25
0.15
(a) Work out the probability that he will take a yellow disc.
..............................................................................................................................................
(2)
Dinesh takes at random a disc from the bag.
He writes down the colour of the disc.
He puts the disc back into the bag.
He will do this 60 times.
(b) Work out an estimate for the number of times he takes a red disc from the bag.
..............................................................................................................................................
(2)
(Total for Question is 4 marks)
6. There are 72 guests staying in a hotel.
They are French or German or Spanish.
The two-way table shows some information about the guests.
(a) Complete the two-way table.
(2)
One of these guests is picked at random.
(b) Write down the probability that the guest is female.
...........................................................
(1)
One of the male guests is picked at random.
(c) Write down the probability that this male guest is German.
...........................................................
(1)
(Total for Question is 4 marks)
7. In the space below, use ruler and compasses to construct an equilateral triangle
with sides of length 8 cm.
You must show all your construction lines.
One side of the triangle has already been drawn for you.
________________________________
(Total for Question is 2 marks)
8. The diagram represents a solid made from seven centimetre cubes.
On the centimetre grid below, draw a plan of the solid.
(Total for question = 2 marks)
9.
ABC is a right-angled triangle.
ADB is a straight line.
Work out the size of the angle marked x.
........................................................... °
10.
ABC and DE are parallel lines.
AEG and BEF are straight lines.
Angle AED = 54°
Angle FEG = 70°
Work out the size of the angle marked x.
Give a reason for each stage of your working.
(Total for question = 4 marks)
11.
(a) Write 3500 ml in litres.
........................................................... litres
(1)
(b) Write 3 kilograms in grams
........................................................... grams
(1)
2
2
(c) Change 3 m to cm .
........................................................... cm2
(2)
(Total for question = 4 marks)
12. Here is a solid prism.
Work out the volume of the prism.
. . . . . . . . . . . . . . . . . . . . . . cm3
(Total for Question is 3 marks)
13.
The diagram shows a regular decagon.
Work out the size of angle x.
(4)
14. Here is a cube.
(a) How many vertices does a cube have?
..............................................................................................................................................
(1)
(b) On the grid, draw a net of a cube.
(2)
The diagram shows a cube of side 3 cm.
(c) Work out the total surface area of this cube.
. . . . . . . . . . . . . . . . . . . . . . cm2
(2)
(Total for Question is 5 marks)
15.
(a) Work out the value of 3.14
...........................................................
(1)
(b) Simplify (p3)2
...........................................................
(1)
(c) Simplify
𝑡8
𝑡3
...........................................................
(1)
23 × 2n = 29
(d) Work out the value of n.
...........................................................
(1)
(Total for Question is 4 marks)
16.
(a) Expand
3(x + 4)
(1)
(b) Expand
x(x2 + 2)
(c) Factorise
x − 6x
(2)
2
(1)
(Total for Question is 4 marks)
17. Factorise x2 + 3x − 4
(Total for question is 2 marks)
18. Solve 3(x – 2) = x + 7
x=......................
(Total for Question is 3 marks)
19. Angela and Michelle both work as waitresses at the same restaurant.
This formula is used to work out the total amount of money each waitress gets.
The table shows the number of hours Angela and Michelle each worked last Saturday.
It also shows the tips they got.
Who got the higher total amount of money last Saturday?
You must show clearly how you got your answer.
(Total for Question is 4 marks)
20.
(a) Complete the table of values for y = x2 – 4
x
y
−3
−2
−1
0
−3
0
1
2
3
0
5
(2)
(b) On the grid, draw the graph of y = x2 – 4 for x = –3 to x = 3
(2)
(Total for Question is 4 marks)
21.
Anna drives 45 miles from her home to a meeting.
Here is the travel graph for Anna's journey to the meeting.
Anna's meeting lasts for 1 hour.
She then drives home at a steady speed of 30 miles per hour with no stops.
Complete the travel graph to show this information.
(Total for Question is 2 marks)
22. On the grid, draw the graph of y = 2x − 3 for values of x from −2 to 3
(Total for Question is 4 marks)
(1)
23. Use your calculator to work out
(a)
(1)
(b)
(2)
24. Asif is going on holiday to Turkey.
The exchange rate is £1 = 3.5601 lira.
Asif changes £550 to lira.
(a) Work out how many lira he should get.
Give your answer to the nearest lira.
........................................................... lira
(2)
Asif sees a pair of shoes in Turkey.
The shoes cost 210 lira.
Asif does not have a calculator.
He uses £2 = 7 lira to work out the approximate cost of the shoes in pounds.
(b) Use £2 = 7 lira to show that the approximate cost of the shoes is £60
(2)
(c) Is using £2 = 7 lira instead of using £1 = 3.5601 lira a sensible start to Asif's method to work out the
cost of the shoes in pounds?
You must give a reason for your answer.
(1)
(Total for question = 5 marks)
25. Toby invested £7500 for 2 years in a savings account.
He was paid 4% per annum compound interest.
How much money did Toby have in his savings account at the end of 2 years?
£ ...........................................................
(Total for question is 2 marks)
26. Jane made some almond biscuits which she sold at a fête.
She had:
5 kg of flour
3 kg of butter
2.5 kg of icing sugar
320 g of almonds
Here is the list of ingredients for making 24 almond biscuits.
Jane made as many almond biscuits as she could, using the ingredients she had.
(a) Work out how many almond biscuits she made.
(3)
Jane sold 70% of the biscuits she made for 25p each.
She sold the other 30% at 4 for 55p.
The ingredients Jane used cost her £45 and the total of all other costs was £27
(b) Work out the percentage profit.
(6)
(Total for question = 9 marks)
27. The table shows information about the number of hours that 120 children used a computer last week.
Number of hours
(h)
Frequency
0<h≤2
10
2<h≤4
15
4<h≤6
30
6<h≤8
35
8 < h ≤ 10
25
10 < h ≤ 12
5
Work out an estimate for the mean number of hours that the children used a computer.
Give your answer correct to 2 decimal places.
……………… hours
(Total 4 marks)
28. Two shapes are shown on the grid.
(a) Describe fully the transformation that maps shape P onto shape Q.
(2)
(b) Rotate triangle A 90° clockwise about the point (0, 2).
Label the new triangle B.
(2)