Academics Mathematics Placement Study Guide - … AMP Test.pdfAcademics Mathematics Placement Study...

COLLEGE OF THE NORTH ATL ANT IC – Q ATAR

Academics Mathematics Placement Study Guide

CNA-QATAR.COM



OverviewThe time for the CNA-Qatar Academic Mathematics Placement (AMP) is two hours. The AMP has two parts: Part 1 can be completed with the use of a calculator and a calculator will be provided for your use. You will not be permitted to use your own calculator or mobile phone. The calculator that will be provided is the Casio fx-85ES, as pictured to the right. It is your responsibility to know how to use this calculator. You will not receive help with the calculators while you are writing the AMP.

Part 2 must be completed WITHOUT the use of a calculator.

The AMP will have 75 multiple choice questions. There are four choices for answers to each question. Questions will cover the following topics:

• Rounding and Place Value • Formula Rearrangement

• Order of Operations • Geometry

• Decimals and Percents • Graphing

• Fractions • Exponents

• Algebraic Expressions • Factoring

• Equations • Rational Expressions

• Word Problems • Trigonometry

This study guide contains sample questions from some of the topics listed above, and represents the average level of difficulty for each section. Not all topics are covered.

VocabularyBelow is a list of words that you may see in the AMP. It is advised that you know the meaning of these words before writing the test.

Area Double Prime

Average Equation Radius

Circumference Evaluate Round

Completely Factor Simplify

Composite Increase Slope

Coordinates Length Solution

Decrease Measure Solve

Denominator Multiply Twice

Diameter Numerator Value

Digit Perimeter Volume

Distance Point x-intercept

Divide Power y-intercept

Academics Mathematics Placement - Study Guide | 2


PART 1 Consists of 55 questions that can be completed with a calculator.

1. Find the GCF and LCM of 32 and 48.

2. Evaluate:

3. Change 120 kilograms (kg) to milligrams (mg).

4. What is 12% of 25?

5. 31% of what number is 15.5?

6. 16 is what percent of 25?

7. Simplify: a)

b)

c)

d)

e)

8. Solve for x:

9. Five more than twice a number is 19. What is the number?

10. A price for a pair of shoes is 400 QR. The price is decreased by 30%. What is the new price?



11. Factor: a)

b)

c)

12. Simplify: a)

b)

c)

13. Find the perimeter:

14. Find the area:

15. What is the height of the box if the volume is 150?

812.8

10

A

B C

10.2

5.1

20

3

h = ?



16. What is the slope of the line given by the equation 3x−9y =−18 ?

17. What is the x-intercept of the line given by the equation 3x−9y =−18 ?

18. What is the position at t = 10 seconds?

19. Using the graph in Question 18, at what time is the position 3 m?

20. Find the measure of ∠C

21. In ΔSRT,∠R = 900,r = 17.5,t = 4.90 . Calculate the length of the missing side.

22. What is the circumference of a circle that has a diameter of 4 units?

A

B

C

9

15



PART 2 Consists of 20 questions to be completed without a calculator.

1. Round to ONE decimal place: 5.6498

2. Which digit is in the tens place? 10.63

3. Evaluate (a) 3×2−25÷ 8+1 (b) 79÷3518

(c) 45− 310

(d) 238−1

23

(e)

79

23−

112

4. Complete the table:

Fraction Decimal Percent

a59

b 1123%

c98

d 0.06%

e 1.26

5. Write an equation to represent the statement: “9 less than twice a number is 17”

6. Simplify x4 ⋅ x9

x2

7. Solve the formula for w: P = 2(L+w)



ANSWER TO SAMPLE QUESTIONS Part 1

1. To find the GCF: 32= 2×2×2×2×248= 2×2×2×2×3

To find the LCM: multiples of 32: 32,64,96,128...

multiples of 48: 48,96,144,192...

2. 250 1+ 0.15×

712

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟= 250 1+ 0.15×0.58333...( )= 250(1+ 0.0875)= 250(1.0875)= 271.875

3. 120 kg= 120 kg×

1000 g1 kg

= 120 000 g×1000 mg

1 g= 120 000 000 mg

4. 12%×25= x

0.12×25= x3= x

5. 31%×x = 15.5

0.31x = 15.50.31x0.31

=15.50.31

x = 50

Common factors…so the GCF is 2×2×2×2= 16

96 is the smallest common multiple, so the LCM is 96



6. 16= x×251625=

25x25

0.64= x64%= x

7. (a) −x2y + 4xy 3−(xy 3−9x2y)

=−x2y + 4xy 3− xy 3+ 9x2y

= 8x2y +3xy 3

(b) ab(b2−4ac)= ab3−4a2bc

(c) (4−7x)2 = (4−7x)(4−7x)

= 16−28x−28x+ 49x2

= 16−56x+ 49x2

(d) 5a5b3( )2 = 5( )2 a5( )2 b3( )2

= 25a10b6

(e) x−1y 4z

x2yz0

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟⎟

−2

=x−1−2y 4−1z

(1)

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟⎟=

x−3y 3z1

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟⎟=

y 3zx3

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟⎟

−2

=x3

y 3z

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟⎟

2

=x6

y 6z2

8. 4(x+ 2)−(x−1)= 9−3x

4x+ 8− x+1= 9−3x4x− x+3x = 9−8−1

6x = 06x6=

06

x = 0

Combine like terms



9. Let x = the number. Then: 2x+5= 192x = 19−52x = 142x2=

142

x = 7

10. Let x = new price. Then: x = 400−30%×400x = 400−0.30×400x = 400−120x = 280

The new price of the shoes is 280 QR.

11. (a) 3x2−5x−2

3x2−6x+ x−2

3x2−6x( )+ x−2( )3x x−2( )+1 x−2( )3x+1( ) x−2( )

(b) 12x3y 3+ 6x4y 2 +3x2y

= 3x2y 4xy 2 + 2x2y +1( )

(c) 4x2−9y 2

= 2x+3y( ) 2x−3y( )



12. (a) x2 + 4x+ 4x2− x−6

=x+ 2( ) x+ 2( )x−3( ) x+ 2( )

=x+ 2( )x−3( )

(b) - = -

=

=

2 5 23 15 15 15

315

5

m m m mn n n n

mn

mn

(c)

y 2−92y 2 +10y

×y 2 +5y

y 2 + y−6=

y +3( ) y−3( )2y y +5( )

×y y +5( )

y +3( ) y−2( )=

y−32 y−2( )

13. P = 8 cm+10 cm+12.8 cm= 30.8 cm

14. A= l×w

= 10.2 cm( ) 5.1 cm( )= 52.02 cm2

15. V = l×w×h

150 m3 = 20 m( ) 3 m( ) h( )150 m3 = 60 m2( ) h( )150 m3

60 m2=

60 m2( ) h( )60 m2

2.5 m= h

Cancel Combine factors ( x + 2 )



16. 3x−9y =−18−9y =−3x−18−9y−9=−3x−18−9

y =13x+ 2

So the slope of the line is 13

.

17. 3x−9y =−183x−9(0)=−18

3x =−183x3=−183

x =−6

18. 5 m

19. 3 seconds

20. cos∠C =915

∠C = cos−1915

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

∠C = 53

21.

17.52 = 4.92 + s2

306.25= 24.01+ s2

306.25−24.01= s2

282.24= s2

282.24 = s16.8 m= s

22. If the diameter is 4 units, then the radius is 4÷ 2= 2 units . The circumference is then

C = 2πr = 2π 2( )= 12.57 units.

Slope-intercept form

The x-intercept happens when y=0

R

4.9

S

T

17.5



Part 2 1. 5.6 2. 1 3. (a) 3×2−25÷ 8+1= 6−32÷ 8+1

= 6−4+1= 3

(b)

79÷3518=

79×1835=

79×9×27×5

=25

(c)

45−

310=

4×25×2

−310

=810−

310

=510=

12

(d) 2

38−1

23= (2−1)+

38−

23

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

= 1+924−

1624

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟

=2424+

924−

1624

⎛

⎝⎜⎜⎜⎜

⎞

⎠⎟⎟⎟⎟=

1724

(e)

79

23−

112

=

79

2×43×4

−1

12

=

79

812−

112

=

79712

=79×

127=

43

Cannot subtract 16 from 9... We need to borrow from the 1

The 1 becomes2424



4.

Fraction Decimal Percent

(a)59

5÷ 9= 0.555...0.5555...×100= 55.56%

(b)

11×3+ 23

÷100

=353×

1100

=35300=

35÷5300÷5

=760

7÷ 60= 0.11666... 1123%

(c)98

9÷ 8= 1.1251.125×100= 112.5%

(d)

0.06÷100

=0.06×100100×100

=6

10000=

6÷ 210000÷ 2

=3

5000

0.06÷100= 0.0006

0.06%

(e)

126100

=126÷ 2100÷ 2

=6350

1.261.26×100= 126%

5. Let x = the number, then the equation is 2x−9= 17 6. x

4 ⋅x9

x2= x4+9−2 = x11

7. P = 2l+ 2w

P−2l= 2wP−2l2=

2w2

P−2l2=w

P−2l2=w

Do not cancel the 2


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