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National 5 Maths
Applications Unit Assessment: Practice Test A
You can pass the entire test by getting 21 or more out of 35
Formulae Sheet
Sine rule:
a
b
c


sin A sin B sin C
Cosine rule:
a 2  b2  c 2  2bc cos A
Area of a triangle:
1
A  ab sin C
2
Standard deviation:
s
 (x  x )
n 1
2
where n is the sample size
Assessment Standard 1.1: Trigonometry (need 4 out of 8 to pass plus #2.1)
1)
Sarah wishes to sow grass seed on a triangular plot of ground.
The diagram gives the dimensions of the plot.
Calculate the area of this plot (2)
Success criteria:
 Choose correct formula.
 Substitute correctly.
 Calculator is in ‘DEG’ mode.
 Use squared units for area.
48 m
56°
51 m
2)
The diagram shows an oil tanker (T), a harbour (H) and a beach (B). The
tanker is 34 miles from the harbour and 27 miles from the beach.
T
34
400miles
yards
H
10°
320 yar
27 miles
ds
B
What is the shortest distance (BH) between the beach and the harbour? (3)
Success criteria:
 Choose correct formula to find length in triangle.
 Substitute correctly.
 Remember to take square root.
 Use regular units for length.
3)
Three towns called Parton (P), Queenfield (Q)
and Rosport (R) are shown in the diagram on the
right.
Rosport is 18km from Parton.
Queenfield is 25km from Parton.
Rosport is on a bearing of 072° from Parton.
Calculate the bearing of Rosport from
Queenfield. (3 + #2.1)
Success criteria:
 Choose correct formula to find angle in triangle.
 Substitute and rearrange.
 Use inverse function to find angle
 Find bearing as last step.
 Give bearing with three figures and degree sign.
Assessment Standard 1.2: Vectors (need 5 out of 9 to pass)
4)
The diagrams below show 2 directed line segments a and b.
Success criteria:
 Three vectors drawn.
 All vectors have arrows.
 All vectors labelled.
 Vectors added “nose to tail”
b
a
Using the squares in your jotter, draw the resultant of a + 2b . (3)
5)
The diagram below shows a square based pyramid of height 3 cm. Square
OXYZ has a side length of 8 cm.
The coordinates of X are (8, 0, 0). Z lies on the y-axis.
z
W
Z
y
Y
x
O
X (8, 0, 0)
Write down the coordinates of W. (1)
Success criteria:
 Coordinate written with
brackets and commas.
6)
Three forces are acting on an object. Each force is represented by three
vectors p, q and r as given below.
 2
 5 
 
 
p   3, q   2 ,
1
 4
 
 
1
 
r   6 
 2 
 
Success criteria:
 Answer written as column
vectors with brackets and no
commas
Find the resultant force. (2)
7)
5
 3
Two vectors are given by p   
 2 
.
1
 
and n  
Calculate 2p  3n .
(3)
Success criteria:
 Find vector.
 Square and add components.
 Square root.
 Final answer as surd or decimal.
Assessment Standard 1.3: Fractions and Percentages (need 4 out of 8 to pass)
8)
9)
A company bought a new van for
£34 000. Its value depreciated by
1·6% each year. Find the value of the
van after 4 years. (3)
The diagram shows the size of a
garden:
Success criteria:

Choose correct multiplier

Choose correct power

Power goes with multiplier and not on the price

Units in answer

Answer rounded for money (i.e. 2 decimal places)
3
8 m
4
4
2
m
5
Success criteria:
 Choose whether to add, take away,
multiply or divide
 Give answer in simplest form
Calculate the exact area of the garden in square metres, giving your answer
as either a topheavy fraction or a mixed number. (2)
10)
An athlete gains muscle mass. The athlete increases
their weight by 15%. After the gain, they weighed
86kg.
Find the weight of the athlete before the weight
gain. Give your answer to one decimal place. (3)
Success criteria:
 Choose correct
multiplier
 Use divide to reverse
calculation
 State unrounded answer
 Round as requested
 Units in answer.
Assessment Standard 1.4: Statistics (need 4 out of 8 to pass plus #2.2)
11)
The table below shows the monthly expenditure in 2015 of an American
school baseball team in thousands of dollars.
Success criteria:
Expenditure (thousands of dollars)
Feb
Mar
Apr
May
Jun
8
7
3
5
9
Jan
4

(a) Calculate the mean and standard deviation
of the expenditure during this 6-month
period. (4)
(b) In 2016 the same school had a
mean expenditure of $8000 per
month and a standard deviation
of 1·2 thousand dollars.
Make two valid statements to
compare the expenditure in
2015 and 2016. (#2.2)
12)




Calculate mean and check it looks
reasonable
Complete table
Substitute into formula
Remember brackets and square
root
Units in both answers
Success criteria:




One statement about mean, using words “on
average”
One statement about standard deviation using
words “more varied” or “more consistent”
Both sentences refer to the context
Avoid words “mean” and “standard deviation”
in sentences
The marks of a group of
students in their unit 1 maths
test and their unit 2 maths
test are shown in the scatter
graph on the right.
(a) Determine the gradient
of the line of best fit
shown. (1)
Success criteria:




Identify two points on line.
Memorise formula.
Substitute and calculate.
Simplify.
(b) Find the equation of the
line of best fit in terms of
x and y.
Give the equation in its simplest form. (2)
(c) Estimate the final exam mark of a student who got 80% in the unit 1 test. (1)
Success criteria (b):




Memorise formula.
Use gradient from (a) and choose a point on the line
Substitute
Multiply bracket and rearrange formula to collect like
terms
Success criteria (c):



Show working.
Substitute the given number
into formula from (b)
Calculate answer