Free Printable Math Major 112 College and Advanced Algebra

1.

Simplify fully:
√32 + 5√32

a)

6√32

b)

24√8

c)

24√2

d)

6√8

2.

Rationalise the Denominator:
³/_√5

a)

³^√5/₅

b)

³^√5/₂₅

c)

^√5/₅

d)

^√5/3

3.

Simplify fully:
2√45 - 5√45 + 9√16

a)

-9√5 + 36

b)

-3√45 + 144

c)

6√16

d)

6√106

4.

Which one would you multiply by to rationalise this denominator:
^√5/_{(√2 - 1)}

a)

(√2 - 1)

b)

√2

c)

√2 + 1

d)

√5

5.

Solve the simultaneous equations (there are two separate solutions):
y = x² + 7x - 2
y = 2x - 6

a)

x = 4, y = 2; x = 3, y = 5

b)

x = -4, y = 2; x = -1, y = -8

c)

x = -2, y = -10; x = 3, y = 0

d)

x = 1, y = -4; x = 0; y = -6

6.

Simplify fully:
√32

a)

4√8

b)

16√2

c)

4√2

d)

4√4

7.

Simplify as far as possible

a)

6/5x

b)

(x-4)/(x-2)

c)

(x+3)/(x+2)

d)

(x+3)/(x-4)

8.

Simplify as far as possible

a)

4/x

b)

x/4

c)

1/4x

d)

4x

9.

Simplify as far as possible

a)

A.4x³/(x+2)

b)

B.4x³/(x+10)

c)

C.2x³/(5x+1)

d)

D. 2x³/(x+5)

10.

a)

A

b)

B

c)

C

d)

D

11.

a)

A

b)

B

c)

C

d)

D

12.

a)

A

b)

B

c)

C

d)

D

13.

Which of the following is the radical form of the exponential expression $3^{\frac{5}{2}}$ ?

a)

$\sqrt{3^5}$

b)

$\sqrt{5^3}$

c)

$\sqrt{2^3}$

d)

$\sqrt{5^2}$

14.

Simplify: $\sqrt{108x^8y^2}$

a)

$36x^4y^2$

b)

$6x^4y\sqrt{3}$

c)

$2x^4y\sqrt{27}$

d)

$6x^4y$

15.

Simplify: $3\sqrt{75x^2y^3z}$

a)

$3xy\sqrt{3yz}$

b)

$5xy\sqrt{3yz}$

c)

$15xy\sqrt{3yz}$

d)

$75xy\sqrt{3yz}$

16.

Simplify: $2\sqrt{162x^{10}y^8}$

a)

$18x^5y^4\sqrt{2}$

b)

$18x^5y^4$

c)

$9x^5y^4\sqrt{2}$

d)

$9x^5y^4$

17.

Perform the indicated operation: $4\sqrt{10}+6\sqrt{40}$

a)

$10\sqrt{40}$

b)

$16\sqrt{40}$

c)

$10\sqrt{10}$

d)

$16\sqrt{10}$

18.

Perform the indicated operation: $-10\sqrt{48}+3\sqrt{27}$

a)

$31\sqrt{3}$

b)

$-31\sqrt{3}$

c)

$13\sqrt{3}$

d)

$-13\sqrt{3}$

19.

Perform the indicated operation: $\sqrt{2x}\left(3\sqrt{6x}+\sqrt{7x^2}\right)$

a)

$4x\sqrt{3}+x\sqrt{14x}$

b)

$6x\sqrt{3}+x\sqrt{14x}$

c)

$4x^2\sqrt{3}+x^2\sqrt{14x}$

d)

$3\sqrt{12x}+\sqrt{14x^2}$

20.

Perform the indicated operation: $\sqrt{\frac{30x^9}{160x^5}}$

a)

$4x^2\sqrt{3}$

b)

$\frac{x^2\sqrt{3}}{4}$

c)

$4x\sqrt{3}$

d)

$\frac{x\sqrt{3}}{4}$

21.

K varies directly as twice of D. Which of the following equation correctly represents the relationship between K and D?

a)

$K=2kD$

b)

$K=kD^2$

c)

$K=\frac{kD}{2}$

d)

$2K=kD$

22.

M varies jointly as N and O, and inversely as P. Which of the following equations correctly represents the relationship between the variables?

a)

$NO=\frac{kM}{P}$

b)

$M=\frac{kN}{OP}$

c)

$P=kMNO$

d)

$M=\frac{kNO}{P}$

23.

H varies directly as C, if H=7 and C=11. What is the constant of variation?

a)

7/11

b)

11/7

c)

7

d)

11

24.

H varies directly as the square of C, if H=100 and C=5. What is the constant of variation?

a)

25

b)

10

c)

4

d)

2

25.

The mass of a vase is directly proportional to its volume. When the volume is $30cm^3$ , the mass is $420g$ . What is the mass of the vase if its volume is $80cm^3?$

(a)

26.

Twenty-four students went on a field trip. There were also 8 adults on the trip. The expression 0.5(24+8) represents the cost to buy everyone a dolphin eraser. What is the total cost of the erasers?

a)

16

b)

32

c)

20

d)

24

27.

Which expression represents "the quotient of 10 and 2, plus 3"? Choose the correct answer.

a)

10 / (2+3)

b)

(10X2)+3

c)

10-2+3

d)

10/2 + 3

28.

Which expression is NOT equal to 8?

a)

3X8/4+2

b)

3X(8/4)+2

c)

(3X8)/(4+2)

d)

(3X8)/4+2

29.

Which expression means 6 fewer than 15?

a)

15-6

b)

15/6

c)

15*6

d)

15+6

30.

Evaluate: 8+12/4-3

a)

2

b)

8

c)

14

d)

44

31.

Evaluate: 9X5-16/2

a)

37

b)

7

c)

9

d)

39

32.

What is the value of the expression below?

5X16-4+2/2

a)

61

b)

77

c)

40

d)

39

33.

5X[16-(4+2)]÷2

a)

25

b)

20

c)

35

d)

40

34.

{[11+7-(2X3)]+8}÷2

a)

10

b)

12

c)

27

d)

Aunt Sally

35.

240÷8 - 3

a)

229

b)

27

c)

235

d)

48

36.

7 ² - 3 · 3

a)

40

b)

84

c)

138

d)

33

37.

Solve.

a)

1

b)

3

c)

9

d)

18

38.

Solve

a)

24

b)

288

c)

14

d)

36

39.

Simplify the expression:

$\frac{2}{3}+\frac{7}{4}$

a)

$\frac{29}{12}$

b)

$\frac{9}{12}$

c)

$\frac{9}{7}$

d)

$\frac{29}{3}$

40.

Simplify the expression:

$\frac{2}{3}\cdot\frac{7}{4}$

a)

$\frac{8}{21}$

b)

$\frac{14}{12}$

c)

$\frac{7}{6}$

d)

$\frac{21}{8}$

41.

Expand the product:

$\left(x-3\right)\left(x^2+5\right)$

a)

$x^3+5x^2-3x$

b)

$x^3-15$

c)

$x^3-3x^2+5x-15$

d)

$x^3+5x^2-3x-15$

42.

Explain how to plot the point $\left(x,y\right)=\left(5,-2\right)$

a)

From the origin, go up 5, then left 2

b)

From the origin, go right 5, then down 2

c)

From the origin, go up 5, then right 2

d)

From the origin, go left 5, then down 2

43.

Simplify the expression:

$\sqrt[]{50}$

a)

$5\sqrt[]{2}$

b)

$2\sqrt[]{5}$

c)

$25$

d)

$25\sqrt[]{2}$

44.

Simplify the expression:

$\frac{4x^2-x}{2x}$

a)

$\frac{2x-x}{x}$

b)

$\frac{2x-1}{2}$

c)

$\frac{4x-1}{2}$

d)

$\frac{4x-1}{x}$

45.

Solve the equation for x:

$4x+1=7x-6$

a)

$x=2$

b)

$x=3$

c)

$x=\frac{8}{3}$

d)

$x=\frac{7}{3}$

46.

Factor the following expression:

$x^2-5x-6$

a)

$\left(x-6\right)\left(x+1\right)$

b)

$\left(x-3\right)\left(x-2\right)$

c)

$\left(x+3\right)\left(x-2\right)$

d)

$\left(x+6\right)\left(x-1\right)$

47.

Solve 6x²-36=0

a)

x=6

b)

x=√6

c)

x=6, x=-6

d)

x=√6, x=-√6

48.

Solve x²-2x-3=0

a)

x=-3, x=-1

b)

x=-3, x=1

c)

x=-1, x=3

d)

x=1, x=3

49.

Solve |4y-3|=5

a)

y=2

b)

y=2, y=-2

c)

y=-1/2

d)

y=2, y=-1/2

50.

What value do you need to add to both sides of the equation x²+4x=1 to complete the square?

a)

4

b)

2

c)

-4

d)

-2

Math Major 112 College and Advanced Algebra

Total questions: 50

Worksheet time: 2hrs 55mins

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