Revision Part 1

A: Answer the following questions:

A-1 Calculate:

A-2 Calculate:

A-3 Convert to its decimal equivalent.

0.4
A-4 Convert 1.60 hours into seconds
1.60 = 1

A-5 Work out

A-6 Convert to its decimal equivalent

6.08

A-7 Round 332.642 to 2 significant figures

330 (2 s.f.)

A-8 Find the product

A-9 What is 40 of $140.25

=
A-10 Express in its simplest form

A-11 Find the highest common factor (HCF) for numbers 12 and 24
The factors of 12 is 1,2,3,4,6,12
The factors of 24 is 1,2,3,4,6,8,12
The common factors of 12 and 24 are 1, 2, 3,
4, 6 and 12. So their highest common factor is 12.

A-12 500 gram is what percent of 2.8 Kg?

=

A-13 Solve:

A-14 Solve:

= 0.519

A-15 Solve (a) OR (b)

(a) A company orders $15,000 of office supplies. The series percentage discount
offered by the seller is 20%, 15.25% and 6%. Find the net price.

Solution:
The single equivalent discount = 0.80 × 0.8475 × 0.94 = 0.637
Net Price =

OR
(b) The number of students registered in MU123 course is 423 females and 234 males.
What is the approximate ratio of female to male?
 Solution:
The ratio of females to males is =
OR 180:100

B: Answer the following questions:

B-1 Consider the formula

Find the value of y when

Solution:

B-2 Consider the formula

Find the value of Z when

Solution:

B-3 Find P:

Solution:

B-4 Simplify
Solution:
B-5 If the average speed in kilometers per hour is 150 km/h, what is the distance covered in
45 minutes?
Solution:

B-6 Answer (a) OR (b)

a) Write the product concisely in index form:
OR
b) Write the product concisely in index form : 27

Solution:

OR

C: Answer the following questions:

C-1 Solve the equation Solution:

OR

C-2 Simplify the following:

Solution:
C-3 Consider the following data set:
1.5 Find the mean

Solution:

C-4 Find the median of

Mean of 75 and 77 =

C-5 Answer (a) or (b)

(a) Simplify:

Solution:

OR

(b) Simplify:

Solution:

C-6 Simplify :
Solution:
= 15-17+2 +5pq
= 5pq

C-7 Write the following in short form:

A2B × AB7
 Solutions:

A2+1B1+7 = A3B8

C-8 Find A:
when
Solution:

Answer the following questions (2 points each): Show your calculations.

A-1 Calculate: (
20

A-2 Calculate:

A-3 Convert 590 cm to m

590 cm = 590/100 = 5.9 m

A-4 Convert 1200 hours into weeks

A-5 Round 134.642 to 5 significant figures

134.642 = 134.64 (5 s.f.)

A-6 Round 0.004921 to one significant figure.

0.005

A-7 A computer originally priced at $699 is reduced by 14% in a sale. What is the new
price?
The decrease in price is 14% of 699 = 0.14 x $699 = 97.86
The reduced price is 699 – 97.86 = $601.14

A-8 Express in its simplest form

 =

A-9 Write as mixed number.

A-10 A person weights 70Kg, what is his weight in grams.

= 70 x 1000 = 70,000 gm.

A-11 Round the measurement of 2.7345m to the nearest whole number of meters.
= 3m

A-12 Convert to its decimal equivalent.

= 4.75

A-13 Convert to its percent equivalent value

A-14 Find the missing number that makes the fractions equivalent:

= 80

A-15 The number of students enrolled at MU123 last semester was 240. This semester we
have 350 students enrolled in MU123. Find the percentage of increase. (Show the
formula)

Solution:
Answer the following questions:

B-1 Consider the formula

Find the value of B when

Solution:

B-2 Consider the formula

Find the value of P when

Solution:

B-3 Evaluate the following:

Solution:

B-4 Find the net price for a laptop that retails at $430 and has a trade discount rate of 15%.

Solution:
Discount = 430
Net price
B-5 If a weekly wage of $720 is increased by 2.5%, what is the new weekly wage?

Solution:

The new wage is

B-6 Write the following product concisely in index form:

c) , b)

Solution:

B-7 Simplify:
(a) 18:24:12 (b) 0.5 : 2:25

Solution:

0.5: 2.25 = (100x0.5) : (2.25x2.25) = 50:225 = 2:9 (2 points)

B-8 Solve:

Solution:

Part C: (40 points)

Answer the following SIX questions:

C-1 evaluate

Solution:
C-2 Simplify the following:

a)

Solution:

a)

b)

C-3 a) Find the mean of the scores: 1925; 2650; 4275; 2150; 2675
d) (5 points) Find the median for the scores: 3850; 5300; 8550; 4300
e) Kareem has the following data -4,-8,-4,-2,-5,-2,-3,-4
What is the Range?
f) Find the upper quartile in question b

Solution:

a)

b)

Mean of 4300 and 5300 =

c) Range = Max – min (subtract the least from the greatest) (3 points)
= -2-(-8) = 6 (7 points)

d) Upper quartile =

C-4 Simplify the following:

(a) 15m+ 10m−24m
 Solution: 25m-24m = m

(b) 0.8XY2 + 0.2XY 2

(c) Solution: (0.8 + 0.2)XY 2 = XY 2

C-5 Simplify : 15 − 4pq − q + 1−qp – 2

Solution:
= 15 − 4pq − q + 1−pq − 2
= 15 + 1−2−4pq − pq − q
= 14−5pq − q

C-6 Write the following in short form:

2A4B × 3A4B7

Solutions:

2×3×A4+4B1+7 = 6A8B8

Revision Part 2
Question-1:

a) Simplify:

i) ( -7 + 2 )+ 5 = -5 + 5 = 0
 ii) -7(-2a+b)-(-3b) = 14a + (-7b) +3b = 14a - 7b + 3b = 14a - 4b

iii) (1 - 3²) ÷ (1 – 3²) – (-20) = (1 - 9) ÷ (1 - 9) + 20 = -8 ÷ -8 +20 = 1 +20 = 21

b) Convert the following units:

i) Express 675mm in centimeters.

Ans.: 675 ÷ 10 = 67.5cm

ii) Express 3.5kg in grams

Ans.: 3.5 x 1000 = 3500grams
 iii) A person’s height is given as 1.65m. What will it be in centimeters?
Ans.: 1.65 x 100 = 165cm

c) Round a measurement of 1.059m to:

i) The nearest whole number of meters

Ans.: 1.059m ~ 1.1m ~ 1m

ii) Two significant figures

Ans.: 1.060 m

iii) The harvest of wheat on a farm increases by 50% in one year. If the harvest of
wheat last year was 50,000 bushels, what would the harvest be this year? (2
marks)
 Ans.: 50,000 x 50% = 50,000 x 0.5 = 25,000 bushels is 50% of the harvest
This year harvest = 50,000 + 25,000 = 75,000 bushels

Question-2:

a) Use the appropriate formula to work out:

i) The average speed in kilometers per hour, if a distance of 25km is covered in

45 minutes
Ans.: d = s x t
25 = s X 45
S = 25 ÷ 45
S = 0.555555556
The average speed = 0.555555556 x 60 = 100/3 ~ 33.3333 Kilometers per hour

ii) The distance travelled in kilometers after traveling for 30minutes at an average
speed of 75 kilometers per hour.
Ans.: t = 30 ÷ 60 = 0.5hour
d=sxt
d = 75 x 0.5
d = 37.5kilometers
 iii) The time in seconds to cover a distance of 500 meters at an average speed of 10
meters per seconds.
Ans.: d = s x t
500 = 10 x t
t=d/s
t = 500/10 = 50seconds

b) Naismith’ Rule estimated that the time taken for a walk up a hill is given by the
formula T =

T: is the time for the walk in hours.

D: is the horizontal distances walked in kilometers.
H: is the height climbed in meters.
Estimate how long a walk will take if the horizontal distance is 2km and the height is
217m.

Ans.: H = 217/1000 = 0.217km

D=txh
2 = t x 0.217
t = 2/0.217
 t = 9.22minutes = 9.22/60 ~ 0.15hours

Question-3:

a) Use a factor tree to determine the prime factorization of the

following numbers

i) 500

Ans.:

500 = 5x5x2x5x2 = 2x2x5x5x5 = 22x53

ii) 120
Ans.:

120 = 3x2x5x2x2 = 2x2x2x3x5 = 23x3x5 √

iii) Find the lowest common multiple and highest common factor of 500 and 120.
Ans.:

- LCM for 500,120

500: 500, 1000, 1500, 3000, 3500, 4000, 4500
120: 120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200, 1320, 1440, 1560, 1680,
1800, 1920, 2040, 2160, 2280, 2400, 2520, 2640, 2760, 2880, 3000
 LCM = 3000

- HCF for 500, 120

500: 1,2,4,5,10,50,100,125,250,500
120:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120

HCF = 10
b) The following table gives the pulse rate at rest of each of 30 students (15 male and 15

female) at a large college.

i) Find the mean, median , range and the inter-quartile range of the pulse of
each female and male

Answer:
Mean for males =
(80+60+62+64+66+66+68+68+70+70+72+72+74+76+90)/(15) =
1058/15 ~ 70.53
Mean for females =
(62+62+64+68+65+72+78+78+80+82+88+90+96+100+100)/(15) =
1185/15 = 79

Median for males = 60,62,64,66,66,68,68,70,70,72,72,74,76,80,90

= 70
Median for females= 62,62,64,65,68,72,78,78,80,82,88,90,96,100,100 = 78
Interquartile range for males = 90 - 60 = 30
Interquartile range for females = 100 - 62 = 38 X
 ii) Explain your results. What did you learn from the results found in b part
i?

Question-4:

a) Solve the following equations:

i) 6 (x – 8) = 7 (x + 8)
Ans.: 6x - 48 = 7x + 56
6x - 7x = 56 + 48
-1x = 104
x = 104

ii) 5 (x – 4) = + 8
Ans.: 5x - 20 = 8
5x = 20 + 8
 5x = 28
x = 28/5
x = 5.6

b) This question is based on unit 6:

i) Calculate the slope of the line, which passes through (3,2) and (-1,10)

ii) Find the equation of the line described in part a.

iii) Find the x-intercept and y-intercept of the line described in part a.
Question-5:

Use Microsoft Excel in presenting the following data in bar charts. Explain your results in
40-50 words.

Estimated GDP per capita in Gulf

Cooperation Countries (GCCs) – 2013
The results show that Qatar has the highest GDP among all the GCC while Oman comes in
the bottom of the list with the lowest GDP. Bahrain and Saudi Arabia aren’t so far from
Bahrain, while UAE and Kuwait are somewhere in the middle between the GCC. UAE and
Kuwait needs some extra efforts to reach Qatar while the rest three countries are a way
behind.

Revision Part 3

Question 1: Use the following table to answer the following questions (a) and (b):
Year 2007 2008 2009 2010 2011 2012
Weight
)kg( 94.53 X 93.57 96 90.53 99.37
 a) If the mean is 95, what would X be?
b) Find the Median

Answer:

a)

a) Median:
Rearrange: 90.53, 93.57, 94.53, 96, 96, 99.37
(94.53+96)/2 = 95.26 OR 95.27

Question 2:
a) Solve the equation:

b) Simplify:

c) Simplify:

d) If q = 2 and r = -14, what is ?

e) Simplify:

Answer:
a)
b) XY2 + XY2 = 2XY2
c)
 d)

e)

Question 3:
A printing press charges $400 for the first 100 books and $10 for each additional book plus
$20 delivery cost for each order. Calculate the total cost for an order that consists of 120
books.
Answer:

Question 4: A line passes through the points (5, 3) and (2, 5).
a) Find the equation of the line
b) Graph the line using the above two points.
c) Answer:
a) First, we find the gradient using the following formula:

OR 0.67

Then we use either point to find C, we use point (5,3) and substitute:

The requested equation of the line is:

b)

4
3
21 1 2 3 4 5 6 X
 5

Question 5:
From the following two equations,
P = 70 – 0.2 Q
P = 10 + 0.6 Q
Find P and Q using substitution method

Answer:
P=P
70 – 0.2Q = 10 + 0.6Q
70 – 10 = 0.6Q + 0.2Q
60 = 0.8Q , Then Q = 75

Substitute in one of the above equation, P = 70 – 0.2 x 75

P = 70 – 15 , Then P = 55

Question 6:
a) Ahmed needs money to buy a car. He borrowed $18,000 for 30 months and paid $1575
as an interest. What was the rate of interest?

b) Compute the compound amount on a loan of $5,000 compounded annually for four
years at 5%.

Answer:
 a)

Question 7:
a) Multiply out the brackets

b) Solve the equation:

c) Solve the equation:

Answer:
a)

b) Multiply both sides by 3

c)
Question 8:
a- Amal makes $25.50 an hour when she works overtime. This week she earns $357 as
overtime. How many overtime hours did she work this week?

b- Ahmed borrows $1,000 from his friend and promises to pay him back in two years at 6
percent interest. How much total will Ahmed pay back for the loan?

c- Answer (a):

Answer (b):
,

Question 9:
a) Write down the sales factor corresponding to each of the following percentage
increases or decreases:
i) 0.5% increase
ii) 12% increase
iii) 10% decrease

b) Calculate the Annual Percentage Rate (APR) for an interest rate of 1.3%, charged
monthly.

Answer:
a) i) The scale factor for a 0.5% increase is 1.005
ii) The scale factor for a 12% increase is 1.12
iii) The scale factor for a 10% decrease is 0.90

b) An interest rate of 1.3% charged monthly corresponds to

a scale factor of 1.013
 Therefore, APR = 1.01312 = 1.1676

Question 10:
From the equation: y = − x + 6, answer the following:
a) What is the gradient?
b) Show how to find Y intercept
c) Show how to find X intercept
d) Find a point on the line of the equation
e) Draw the graph of the equation

Answer:
a) The gradient is -2/3
b) when x =0, then y=6
c) when y=0, then 0= -2/3x + x , x=9
d) When x = 0, then y = 6 , the point is (0,6)
e) Students must find at least two points in order to draw the graph (2 points)

Question 11:
a- Multiply out the brackets:

b- Multiply out the brackets:

c- Multiply out the brackets:

d- An office computer costing $8,500 has an estimated life of 6 years and an estimated
scrap value of $400.What is the annual depreciation amount?
Answer:
a)

b)

c)
d) Depreciation = (original cost – scrap value) ÷ service life
e) Depreciation = (8,500 – 400) ÷ 6
Depreciation = 11,600 ÷ 6 = $1,350 annual depreciation
 Revision Part 4

Question 1: Use the following table to answer the following questions (a) and (b):

Year 2005 2006 2007 2008 2009 2010

Exchange
Rates 67 59.05 62.38 54 X 74.75

c) If the mean is 64.86, what would X be?

d) Find the standard deviation.

Answer:
b)

b)
Deviation Square Deviation
54 – 64.86 = -10.86 117.94
59.05 – 64.86 = - 5.81 33.76
62.38 – 64.86 = - 2.48 6.15
67 – 64.86 = 2.03 4.12
72 – 64.86 = 7.14 50.98
 74.75 – 64.86 = 9.89 97.81
Total = 306.64
V

Standard deviation =

Question 2:
f) Solve the equation:

g) Simplify:

h) Simplify:

i) A restaurant charges $100 for the first 50 sandwiches and $2.5 for each additional
sandwich plus $5 delivery cost for each order. Calculate the total cost for an order
that consists of 65 sandwiches.

Answer:
f)

g) (0.5 + 0.1)XY 2 = 0.6XY 2

h)

i)

Question 3: A line passes through the points (2, 4) and (6, 1).
d) Find the equation of the line in the form
e) Graph the line using the above two points.
Answer:
 c) First, we find the gradient using the following formula:

(or just -3/4)

Then we use either point to find C, we use point (6, 1) and substitute:

The requested equation of the line is:

d) Graph the line using the above two points: The graph is expected to be
similar to this:

4 x
3
2
1 x
X
1 2 3 4 5 6

Question 4:
The demand and supply functions for a farm are given by the following equations:

Pd = 80 – 0.4 Qd
Ps = 20 + 0.4 Qs
 Where P is Price and Q is Quantity

a) Calculate the equilibrium price and quantity.

b) Graph the demand and supply functions showing the equilibriums.

Answer: (a)
Pd = P s
80 – 0.4Q = 20 + 0.4Q
80 – 20 = 0.4Q + 0.4Q
60 = 0.8Q , Then Q = 75

Substitute in one of the above equation, Pd = 80 – 0.4 x 75

Pd = 80 – 30 , Then Pd = 50

Answer: (b)
To draw the demand function: Let Q = 0, then P = 80 – 0 = 80, (first point (0, 80))
Let P = 0, then 0 = 80 – 0.4 Q, then Q = 200, (second point (200,0))

To draw the supply function: Let Q = 0, then P = 20, (first point (0, 20))
Let Q = 200, then P = 20+(0.4 x 200) = 100 (second point (200, 100))

The student may suggest any other figures, but the graph should look like this:
P
s
100
80
50
20
Q
75 200
d

Question 5:
c) Amal needs money to buy a laptop. She borrowed $1,500 for 10 months and paid
$68.75 as an interest. What was the rate of interest?

d) Compute the compound amount and the interest on a loan of $10,500 compounded
annually for four years at 10%.

Answer:
 b) ( 2 point)

(2 points)

(1 point)
(2 points)

The compound interest = 15,373.05 – 10,500 = $4873.05

Question 6:

Multiply out the brackets in the following expression:

d) Multiply out the brackets

e) Multiply out the brackets

f) Simplify the expression:

g) Solve the equation:

Answer:

d)
e)
 f)

g) Multiply both sides by 3

(The student may use his own way)

Question 7
The owner of a swimming pool kept records of the number of persons using the pool and the
maximum temperature (Cº) for 12 days. The data was analyzed using Excel and some of the
output is shown below.

ANOVA
df SS MS
Regression 1 15911.92773 15911.92773
Residual 10 50979.73893 5097.973893
Total 11 66891.66667

Coefficients Standard Error t Stat P-value

Intercept 198.9160045 106.8635051 1.861402585 0.092302233
x-variable 7.360953462 4.166500869 1.766699130 0.107727641

(1) Write down the equation of the regression line in standard form.

(2) What information is given by the value of the gradient?

(3) On average, 80% of the persons using the pool were children and the rest were
adults. The admission fees were $2 for a child and $5 for an adult. What would
be the expected income from admission fees on a day when the maximum
temperature was 30 Cº ?

Answer:
 (1) The requested regression equation is : y = 7.4 x + 198.92
(2) The gradient shows that if the temperature is increased by 1 Cº, the number of
people using the pool will increase by about 7-8 persons.
(3) The student must show his skills on how to predict.
Using the above equation, the expected persons =
(7.4 * 30) + 198.92 = 419.75 or 420 person.

Expected income = (420 * 80% * $2) + (420 * 20% * $5)

= 672 + 420 = $1092

Question 8:
Susan worked a total of 58 hours in one week. Eight hours were paid at 1.5 times her hourly
wage (as over time) and 10 hours were paid at the holiday rate of 2 times her hourly wage.
Find her gross earnings for the week if her hourly wage is $14.95.

Answer:

Gross earnings = 179+299+598 = $1076.40

Question 9:
iv) Write down the sales factor corresponding to each of the following percentage
increases or decreases:
v) 0.5% increase
vi) 15% increase
vii) 20% decrease

c) Calculate the Annual Percentage Rate (APR) for an interest rate of 1.5%, charged
monthly.

Answer:
c) i) The scale factor for a 0.5% increase is 1.005
d) ii) The scale factor for a 15% increase is 1.15
iii) The scale factor for a 20% decrease is 0.80

e) An interest rate of 1.5% charged monthly corresponds to

a scale factor of 1.015
 Therefore, APR = 1.01512 = 1.16

Question 10:
a- The original value of a machine was $20,000 and after four years its scrap value is
estimated to be $8000. Find the straight-line depreciation subtracted each year.

b- A printing machine that costs $14,000 is expected to print 25,000,000 labels during its
useful life. If the salvage value of the machine is $1,000 find the depreciation for
printing 2,250,000 labels.

Answer:
a) (20,000 – 8,000)/4 = $3000

b) First we need to find the unit depreciation =

Depreciation = unit depreciation * unit produced

Depreciation = $.00052 x 2250000 = $1170