algebra ready-sample-test
TRANSCRIPT
This is a sample test for the
algebra–ready placement test
at the Harbor College
The solution and a link to a review
are given for each problem. The review–links
of all the topics may be accessed here.
This is an interactive PowerPoint file.
Using it in Slideshare is not interactive.
So for best result, download it using the button
below. Run it in the presentation–mode. download button
A
B
C
D
Question 1.
Answer for Question 1:
2842
The reduced form of is
67
34
47
23
Solution to Q1
2842
The correct answer is 2/3.
To reduce a fraction, we divide the numerator
and the denominator by their greatest common
factor (i.e. the largest number that can go into
both numbers) which is 14.
=
Link to reviewNext Question
Solution to Q1
2842
The correct answer is 2/3.
To reduce a fraction, we divide the numerator
and the denominator by their greatest common
factor (i.e. the largest number that can go into
both numbers) which is 14.
=÷1428
42 ÷14= 2
3
Correct!
Next Question
A
B
C
D
Question 1. 2842
The reduced form of
67
34
47
23
is
A
B
C
D
Question 2.
Answer for Question 2:
56
14
=
42
512
712
1324
Link to reviewNext Question
Solution to Q2
56
14
=Convert into fractions
with LCD = 1212(5 x 2 – 1 x 3)
=
712
The correct answer is .
712
Correct!
Next Question
A
B
C
D
Question 2. 56
14
=
42
512
712
1324
A
B
C
D
Question 3.
Answer for Question 3:
2714
187
=÷
34
94
98
38
Solution to Q3
2714
187
=
÷
2714 18
7x
The answer is . 34
reciprocate and multiply
Link to reviewNext Question
Solution to Q3
2714
187
=
÷
2714 18
7x
3
22
= 34
The answer is . 34
reciprocate and multiply
1
Correct!
Question 3. 2714
187
=÷
Next Question
A
B
C
D
34
94
98
38
A
B
C
D
Question 4.
Answer for Question 4:
42
3 143
=
3
42
1
41
1
41
3
Next Question
Solution to Q4
3 143
= 3 – 1 43
= 243
141=
The answer is .141
Link to review
Correct!
Next Question
A
B
C
D
Question 4.
42
3 143
=
3
42
1
41
1
41
3
A
B
C
D
Answer for Question 5:
,43
,98
32
43
98
43
98
32
98
98
43
<
<
<
< 32
43
32
32
<
<
<
<
Question 5. Arrange
from the smallest to the largest.
Solution to Q5
, 43
32
We cross multiply to compare the fractions.
The answer is B:
So
98
32
, similarly we have that
43
98
<32
<
43
<43
98
< .
← larger
Solution to Q5
, 43
32
We cross multiply to compare the fractions.
The answer is B:
So
98
32
, similarly we have that
43
98
<32
<
43
<43
98
< .
← larger
43
=
Or multiply by the LCD = 36
36 x98
=32
=36 x 36 x
Link to reviewNext Question
9 4 12
27 32 24
the largestthe middle the smallest
Question 5. Arrange
from the smallest to the largest.
Correct!
Next Question
A
B
C
D
,43
,98
32
43
98
43
98
32
98
98
43
32
43
32
32
<
<
<
<
<
<
<
<
Question 6. A bag has 48 pieces of candies.
Joe ate 7/8 of the whole bag. How many
pieces of candies did Joe eat?
D
B
C
A 42
36
40
30
Answer for Question 6:
Link to reviewNext Question
Solution to Q6
48 x = 4287
6
The answer is 42.
Question 6. A bag has 48 pieces of candies.
Joe ate 7/8 of the whole bag. How many
pieces of candies did Joe eat?
Correct!
Next Question
42
36
40
30D
B
C
A
6
4
0
–4
A
D
C
B
Question 7. –3 – (–5) – (–2) =
Answer for Question 7:
Link to reviewNext Question
Solution to Q7
The answer is 4.
–3 – (–5) – (–2)
= –3 + 5 + 2
= 4
6
4
0
–4
Correct!
Next Question
Question 7. –3 – (–5) – (–2) =
A
D
C
B
39
37
35
34
A
B
D
C
Question 8.
Answer for Question 8:
33 =32 x 36
Solution to Q8
33 =32 x 36
3338
2+6=8
The answer is 35.
Link to reviewNext Question
Solution to Q8.
33 =32 x 36
3338
= 35
2+6=8 8–3=5
The answer is 35.
39
37
35
34
Correct!
Next Question
Question 8.33 =
32 x 36
A
B
D
C
2
4
6
8
A
B
C
D
Question 9. 24 ÷ 6 x 2
Answer for Question 9:
Link to reviewNext Question
Solution to Q9
The answer is 8.
24 ÷ 6 X 2
= 4 x 2
= 8
Correct!
Next Question
2
4
6
8
A
B
C
D
Question 9. 24 ÷ 6 x 2
15
–9
6
0D
B
C
A
Question 10. 6 – 3(–3) =
Answer for Question 10:
Link to reviewNext Question
Solution to Q10
The answer is 8.
6 – 3(–3)
= 6 + 9
= 15
Correct!
Next Question
Question 10. 6 – 3(–3) =
15
–9
6
0D
B
C
A
A
D
C
B
Question 11. 2.3 – 0.45 + 0.08 =
Answer for Question 11:
1.93
1.83
1.73
2.03
Link to reviewNext Question
Solution to Q11
The answer is 1.93.
2.3 – 0.45 + 0.08
= 1.85 + 0.08
= 1.93
Correct!
Next Question
Question 11. 2.3 – 0.45 + 0.08 =
1.93
1.83
1.73
2.03A
D
C
B
A
B
C
D
Question 12. 1.22 x 0.5 =
Answer for Question 12:
0.36
0.6
0.24
0.72
Link to reviewNext Question
Solution to Q12
The answer is 0.72.
1.22 x 0.5
= 1.44 x 0.5
= 0.72
Correct!
Next Question
Question 12. 1.22 x 0.25 =
A
B
C
D
0.36
0.6
0.24
0.72
D
B
C
A
Question 13. 0.108 ÷ 1.8 =
Answer for Question 13:
0.6
0.06
0.006
0.0006
Link to reviewNext Question
Solution to Q13
The answer is 0.6.
0.108 ÷ 1.8
= 1.08 ÷ 18
= 0.6
Correct!
Next Question
A
B
C
D
Question 13. 0.108 ÷ 1.8 =
0.6
0.06
0.006
0.0006
A
B
D
Question 14.
Answer for Question 14:
–0.5
–0.8
–0.7
43
– 1.35 =
C –0.6
Link to reviewNext Question
Solution to Q14
The answer is –0.6.
43
– 1.35
= 0.75 – 1.35
= –0.6
Correct!
Next Question
A
B
D
Question 14.
–0.5
–0.8
–0.7
43
– 1.35 =
C –0.6
A
B
D
Question 15. 2.3 X 103 =
Answer for Question 15:
C
0.00023
0.023
230
2300
Link to reviewNext Question
Solution to Q15
The answer is 230.
2.3 X 103
= 2.3 x 1,000
= 2300
Correct!
Next Question
A
B
D
Question 15. 2.3 X 103 =
C
0.00023
0.023
230
2300
C
B
D
Question 16. How many grams of pure alcohol
are there in 300 grams of cough syrup that is
5% alcohol?
Answer for Question 16:
A
1.5 g
150 g
15 g
0.15 g
Solution to Q16
The answer is 15 grams.
5% of 300 is
1005
x 300
Link to reviewNext Question
Solution to Q16
The answer is 15 grams.
5% of 300 is
1005
x 300
= 15
3
Correct!
Next Question
Question 16. How many grams of pure alcohol
are there in 300 grams of cough syrup that is
5% alcohol?
C
B
D
A
1.5 g
150 g
15 g
0.15 g
A
B
D
Question 17. Which of the following
percentages is the closest to 2/7.
Answer for Question 17:
C 30%
20%
10%
40%
Solution to Q17
The answer is C: 30%
72
= 0.28…
Link to reviewNext Question
Correct!
Next Question
A
B
D
Question 17. Which of the following
percentages is the closest to 2/7.
C 30%
20%
10%
40%
A
C
D
Question 18. Arrange the numbers 60%, 2/3,
0.61 from the smallest to the largest .
Answer for Question 18:
B
60%, 2/3, 0.61
60%, 0.61, 2/3,
2/3, 0.61, 60%,
0.61, 60%, 2/3,
Solution to Q18
The answer is B:
Link to reviewNext Question
60%, 0.61, 2/3,
60% = 0.60
2/3 ≈ 0.66
Correct!
Next Question
A
C
D
Question 18. Arrange the numbers 60%, 2/3,
0.61 from the smallest to the largest .
B
60%, 2/3, 0.61
60%, 0.61, 2/3,
2/3, 0.61, 60%,
0.61, 60%, 2/3,
B
C
D
Question 19. Joe got a raise from $15/hr to
$18/hr. What is the % increase in Joe’s hourly
wages?
Answer for Question 19:
A
3%,
18%,
15%,
20%,
Solution to Q19
The answer is A:
Link to reviewNext Question
20%
From $15 Joe got a of raise of 3$.
so the % increase is 3/15 = 20% .
Correct!
Next Question
B
C
D
Question 19. Joe got a raise from $15/hr to
$18/hr. What is the % increase in Joe’s hourly
wages?
A
3%,
18%,
15%,
20%,
B
C
A
Question 20. Let x = 4, then 6 – 5x is
Answer for Question 20:
D –14
–4
14
4
Solution to Q20
The answer is A:
Link to reviewNext Question
–14
Set x = 4 in 6 – 5x, we get
6 – 5(4)
= 6 – 20
= –14
Correct!
Next Question
B
C
A
Question 20. Let x = 4, then 6 – 5x is
D –14
–4
14
4
B
C
A
Question 21. If x = 3, y = 6, then xy – x – y is
Answer for Question 21:
D 9
0
6
–3
Solution to Q21
The answer is 9.
Link to reviewNext Question
Set x = 3, y = 6 in xy – x – y
we have 3(6) – 3 – 6 = 9
Correct!
Next Question
B
C
A
Question 21. If x = 3, y = 6, then xy – x – y is
D 9
0
6
–3
B
D
A
Question 22. If 3x – 2 = 16, then x is
Answer for Question 22:
C
12
8
6
4
Solution to Q22
The answer is x = 6.
Link to reviewNext Question
3x – 2 = 16
add 2 to both sides 3x = 18
divide both sides by 3 x = 6
Correct!
Next Question
B
D
A
Question 22. If 3x – 2 = 16, then x is
C
12
8
6
4
B
D
C
Question 23.
If b = 2, and a – 2b = 10 then a =
Answer for Question 23:
A 14
8
–12
6
Solution to Q23
The answer is a = 14.
Link to reviewNext Question
If b = 2, the a – 2(2) = 10 so a = 14.
Correct!
Next Question
B
D
C
Question 23.
If b = 2, and a – 2b = 10 then a =
A 14
8
–12
6
A
D
C
Question 24. A medium bag of chocolates has
24 pieces and a small bag has 6 pieces.
We bought 2 medium bags and 4 small bags.
How many pieces of chocolates we have in
total?
Answer for Question 24:
B
80
72
96
60
Solution to Q24
The answer is 72.
Link to reviewNext Question
We have 2 x 24 + 4 x 6 = 72.
Correct!
Next Question
A
D
C
Question 24. A medium bag of chocolates has
24 pieces and a small bag has 6 pieces.
We bought 2 medium bags and 4 small bags.
How many pieces of chocolates we have in
total?
B
80
72
96
60
A
D
B
Question 25. From experience, it’s sunny every
5 out of 7 days at Sunny Hills. In a period of
140 days, how many sunny days are expected?
Answer for Question 25:
C
60
80
100
120
Solution to Q25
The answer is 100.
Link to reviewNext Question
We have that 75
140x
=
700 = 7x or
100 = x
Correct!
Next Question
A
D
B
Question 25. From experience, it’s sunny every
5 out of 7 days at Sunny Hills. In a period of
140 days, how many sunny days are expected?
C
60
80
100
120
D
C
B
Question 26. A bag of chocolates cost $24 and
a bag of peanuts cost $6. We bought 2 bags of
chocolates and 6 bags of peanuts. What is the
difference between the cost for chocolates and
the cost for the peanuts?
Answer for Question 26:
A $12
$10
$8
$6
Solution to Q26
The answer is $12.
Link to reviewNext Question
The chocolates cost 2 x 24 = $48,
the peanuts cost 6 x 6 = $36,
so the difference is 48 – 36 = $12.
Correct!
D
C
B
Question 26. A bag of chocolates cost $24 and
a bag of peanuts cost $6. We bought 2 bags of
chocolates and 6 bags of peanuts. What is the
difference between the cost for chocolates and
the cost for the peanuts?
A $12
$10
$8
$6 Next Question
A
C
B
Question 27.
A triangle has sides with lengths of
Answer for Question 27:
D
ft, 1½ ft and 2 ft, what’s its perimeter? 1 23
ft4 56
ft5 16
ft5 56
ft4 16
Solution to Q27
The answer is 5 1/6 ft.
Link to reviewNext Question
The perimeter is
+1 23
1 12
+ 2
= 1 + 1 + 2 + 2/3 + 1/2
= 4 + 1 16
= 5 16
Correct!
Next Question
A
B
Question 27.
A triangle has sides with lengths of
ft, 1½ ft and 2 ft, what’s its perimeter? 1 23
ft4 56
ft5 16
ft5 56
ft4 16C
D
A
D
B
Question 28.
The perimeter of a square is 16 ft,
what is the area?
Answer for Question 28:
C
256 ft2
144 ft2
16 ft2
12 ft2
Solution to Q28
The answer 16 ft2.
Link to reviewNext Question
The perimeter is 16 ft so the square is
4 ft x 4 ft with area 4 x 4 = 16 ft2
Correct!
Next Question
A
D
B
Question 28.
The perimeter of a square is 16 ft,
what is the area?
C
256 ft2
144 ft2
16 ft2
12 ft2
A
B
Question 29.
Which of the following is the closest to the
circumference of a circle with a 8–ft radius?
Answer for Question 29:
20 ft
30 ft
40 ft
50 ft
C
D
Solution to Q29
The answer D: 50 ft.
Link to reviewNext Question
The circumference of circle is 2πr
where π ≈ 3.14,
if r = 8 then the circumference is
16 π ≈ 16 x 3.1 ≈ 50.
Correct!
Next Question
A
B
20 ft
30 ft
40 ft
50 ft
C
D
Question 29.
Which of the following is the closest to the
circumference of a circle with a 8–ft radius?
A
D
Question 30.
Which of the following pictures represents
A, B and C on the real line most accurately
if A = 3, B = 9 and C = 12?
Answer for Question 30:
C
B0
0
0
0
Solution to Q30
The answer is B.
Link to reviewNext Question
0 6 1293
Correct!
Next Question
A
D
Question 30.
Which of the following pictures represents
A, B and C on the real line most accurately
if A = 3, B = 9 and C = 12?
C
B0
0
0
0
A
D
Question 31.
The vertices of a rectangle are (1, 1), (6, 1),
(1, 8), and (6, 8). What is the perimeter of
this rectangle?
Answer for Question 31:
C
B
20
24
30
36
Solution to Q31
The answer is 24.
Link to reviewNext Question
We have the following 5 x 7 rectangle:
(1, 1) (6, 1)
(6, 8)(1, 8)
So the perimeter is
5 + 5 + 7 + 7
= 245
7
Correct!
Next Question
0
A
D
Question 31.
The vertices of a rectangle are (1, 1), (6, 1),
(1, 8), and (6, 8). What is the perimeter of
this rectangle?
C
B
20
24
30
36
A
D
Question 32.
The vertices of a rectangle are (–1, 1), (4, 1),
(–1, 3), and (4, 3). What is the area of this
rectangle?
Answer for Question 32:
B
C
36
24
20
10
Solution to Q32
The answer is 20.
Link to reviewNext Question
We have the following 5 x 4 rectangle:
(–1, 1) (4, 1)
(4, 3)(–1, 3) So the area is
5 x 4
= 205
4
Correct!
Next Question
A
D
Question 32.
The vertices of a rectangle are (–1, 1), (4, 1),
(–1, 3), and (4, 3). What is the area of this
rectangle?
B
C
36
34
20
10
A
D
Question 33.
The following are the temperatures recorded
from 1 pm to 5 pm, what is the largest
difference in the temperature during this time
period given this data?
Answer for Question 33:
B
C
20o
15o
10o
5o
1 pm 2 pm 3 pm
(1, 16o)
(2, 10o)
(4, 20o)
(3, 17o)
(5, 11o)
4 pm 5 pm
Solution to Q33
The answer is 100.
Link to reviewNext Question
The highest temperature is 20o and the
lowest is 10o so the largest difference is
20 – 10 = 10o
Correct!
A
D
Question 33.
The following are the temperatures recorded
from 1 pm to 5 pm, what is the largest
difference in the temperature during this time
period given this data?
B
C
20o
15o
10o
5o
1 pm 2 pm 3 pm
(1, 16o)
(2, 10o)
(4, 20o)
(3, 17o)
(5, 11o)
4 pm 5 pm
Next Question
C
D
Question 34. Given the following right triangle,
what is the length of A?
Answer for Question 34:
B
A 8 ft
8 ½ ft
9 ft
9 ½ ft
10 ft
6 ft
A
Solution to Q34
The answer is 8 ft.
Link to reviewNext Question
By Pythagorean Theorem that
A2 + 62 = 102
A2 + 36 = 100
A2 = 64
A = 8
Next Question
C
D
Question 34. Given the following right triangle,
what is the length of A?
B
A 8 ft
8 ½ ft
9 ft
9 ½ ft
10 ft
6 ft
A
Correct!
A
D
Question 35. Which of the following value is
closest to √20?
Answer for Question 35:
B
C
7.5
6.5
4.5
3.5
Solution to Q35
The answer is 4.5 ft.
Link to review
√16 < √20 < √25
4 < √20 < 5
So √20 ≈ 4.5
Correct!
A
D
Question 35. Which of the following value is
closest to √20?
B
C
7.5
6.5
4.5
3.5