National 5 Practice Papers
Paper A2 (Calculator)
1.
At a certain time the sun is approximately 150,234,102 kilometres from a point on earth.
Light travels at 2.998 × 104 km/s.
Calculate the time take for light to reach Earth from the sun.
Round your answer to 3 significant figures.
[3]
2.
Jill normally walks an average of 24 miles a week. She is training for a charity walk and
increases the amount she walks by 12% each week for the next 4 weeks. How many
miles will she walk in week 4?
[3]
3.
OABCDE is a regular hexagon with centre I.
⃗⃗⃗⃗⃗ and 𝑂𝐷
⃗⃗⃗⃗⃗⃗ respectively.
Vectors u and v are represented by 𝑂𝐸
B
C
I
A
E
O
(a)
(b)
4.
D
v
u
⃗⃗⃗⃗⃗
Express 𝐸𝐷 in terms of u and v.
⃗⃗⃗⃗⃗ in terms of u and v.
Express 𝑂𝐶
[2]
The graph with equation y = kx2 is shown below.
y
x
(-3, 36)
5.
The point (-3, 36) lies on the graph.
Determine the value of k and hence write down the equation of the graph.
[2]
Jack’s car is valued at £3825 this is 15% less than it was valued at last year.
What was the value of Jack’s car last year?
[3]
Paper A2
Page 1
January 2014
National 5 Practice Papers
Paper A2 (Calculator)
6.
Calculate the size of angle MNO in the triangle below.
M
8 cm
N
3 cm
1100
O
7.
Jill is testing if a fertiliser helps the tomatoes to grow faster. After 3 months she
measures the height of 7 tomatoes without any fertiliser being used. Their heights in
centimetres are shown below.
8
(a)
(b)
8.
[3]
6
3
8
5
7
5
Calculate the mean and standard deviation of this sample. (Without fertiliser) [3]
She then measures 7 plants that have had fertiliser used and finds a mean of 7
and a standard deviation of 0.4.
Write down two valid comparisons between the samples.
[2]
A glass ornament in the shape of a cone is partly filled with coloured water.
The cone is 24 centimetres high and has a base of diameter 30 centimetres.
The water is 16 centimetres deep and measures 10 centimetres across the top.
What is the volume of the water?
Give your answer correct to 2 significant figures.
9.
Find the range of values for k such that the equation kx2 – 4x + 2, k ≠ 0,
has no real roots.
Paper A2
Page 2
[5]
[4]
January 2014
National 5 Practice Papers
Paper A2 (Calculator)
10. Part of the graph of y = asinx + b is shown below.
y
4
1
0
360
-2
(a)
(b)
x
What are the values of a and b?
Calculate the x-cordinates of where the graph cuts the x-axis.
[2]
[4]
11. The two cups below are similar.
The smaller cup has a height of 12 cm and a volume of 300 ml. The larger cup has a
height of 18 cm. Calculate the volume in the larger bottle.
[3]
12. A circle with radius 12 centimetres has a sector cut out as shown.
1300
(a) Calculate the area of the sector cut out.
(b) Calculate the circumference of the sector
[3]
[3]
[End of Paper A2]
Paper A2
Page 3
January 2014