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WorksheetsMathematics Evaluation
Total questions: 71
Worksheet time: 50mins
Which of the following statements is correct ?
A. 0.0010 has one significant figures
B. 200 has two significant figures
C. 100.00 has five significant figures
D. 0.003280 has three significant figures
If x to the ¾ power equals 8, x is equal to:
A. – 9
B. 6
C. 16
D. 9
Factor the expression x^3 + 8 as completely as possible:
A. ( x – 2 ) ( x^2 + 2x + 4 )
B. ( x + 4 ) ( x^2 + 2x + 2 )
C. ( - x + 2 ) ( - x^2 + 2x + 2 )
D. ( x + 2 ) ( x^2 – 2x + 4 )
The number 34,787.00 has how many significant digits?
A. 5
B. 6
C. 7
D. 3
Which of the following is a prime number ?
A. 377
B. 313
C. 357
D. 333
When rounded-off to four significant figures, 102.4886 becomes:
A. 102.4
B. 102.4889
C. 102.48
D. 102.5
Which of the following is not a rational number?
A. 5
B. 0.227272727....
C. 1/4
D. √2
The most significant digit of the number 0.2015 is
A. 0
B. 1
C. 2
D. 5
Solve for the value of x of the equation: x = 10
A. 0.618
B. 1.258
C. 1.852
D. 0.453
If xy^9 = 27 and yz^8 = 16, then what is the value of x: y: z ?
A. 1:3:6
B. 3:1:2
C. 6:2:1
D. 6:4:3
Round-off 7.65 into two significant digits
A. 7.6
B. 7.7
C. 7.0
D. 8.0
The Number 0.005328 has how many significant digits?
A. 8
B. 5
C. 4
D. 7
38.5 to the x power = 6.5 to the x -2 power, solve for x using logarithms.
A. 2.70
B. 2.10
C. -2.10
D. -2.02
Solve the value of x: 2/3 - 2/3 = 4.
A. 8
B. 1/8
C. – 8
D. All of these
If 3x = 4y, then 2/2 * 3x/4y = ?
A. 3/4
B. 4/3
C. 27/64
D. 9/16
If log x = -1/n, then the value of x is:
A. 10^(1/n)
B. 10^(-1/n)
C. 10^n
D. 10^(-n)
In a morning walk, three persons step off together. Their steps measure 75 cm, 80 cm and 90 cm respectively. What is the minimum distance each should walk so it can cover the same distance in complete steps?
3600 cm
4500 cm
7200 cm
540,000 cm
Determine the absolute value of the complex number 3 + 4i.
4
8
5
6
Find the value of x: 20 x = x−
4, -5
-4, -5
-4, 5
No Solution
If y = x + 1/x , x cannot be equal to 0, then the equation (x^2 – 3x + 1)(x^2 – 5x + 1) = 6x^2 reduces to:
y^2 – 8y + 9 = 0
y^2 – 8y + 7 = 0
y^2 + 8y – 9 = 0
y^2 – 8y + 7 = 0
Find the value of x to satisfy the following equations: x + y = 7; x + 2y = 34
3
4
2
5
What are all the ordered triples of real numbers (x, y , z ) which satisfy the following equations? ( x + y)( x + y + z ) = 384; ( y + z )( x + y + z ) = 288; (x + z ) ( x + y + z ) = 480
I only
II only
I and II
none of these
Solve for the constant “m” in x^2 – 4x + 3m = 0 if one root exceeds the other by 2.
1
3
2
5
If a, b and c be three real numbers such that a + 2b + 4c = 0. Then, the equation ax^2 + bx + c = 0.
has its roots lying within - 1 < x < 0
has both the roots complex
has its roots lying within 2 < x < 6
has one of its roots equal to ½
If x – 1/x = 1 , find the value of x^3 – 1/x^3.
1
2
3
4
Solve for x: x + x^1 - x = 1.
13/25
17/25
16/25
22/25
Which of the following statement is NOT correct?
π^0 = 1
e^0 = 1
0^0 = 1
ln 1 = 0
The equation whose roots are twice the roots of the equation x^2 – 3x + 3 = 0 is:
x^2 – 3x + 6 = 0
x^2 – 6x + 12 = 0
x^2 – 4x + 8 = 0
x^2 – 8x + 6 = 0
Solve the value of x in the equation : 38.5 x = 6.5 (x-2)
-2.10
-5.01
3.8
-3.1
Simplify: 35 log x + log x + log x
9 log x
og 9xl
15 log x
Given the equation 2x^2 + x - 10 = 0. Find the product of roots.
5
-1/2
-5
½
Given: log x = 5y + log y. Find the value of x.
x = 5y
x = 5ay
x = ya
If the sum of the roots of a quadratic equation is 12 and the product is 36, then what is the difference of the roots?
1
0
3
6
What is the logarithm of negative number?
zero
rational
irrational
complex
Solve the value of x: 9x^2 - 8x = 0.
1/8
-1
8
¼
Solve the value of x : 1.4 = (0.0613/x) 1.32
0.5471
0.04751
0.7541
0.4571
The surface area of A of a hollow cone is given by A = πrL. Determine, correct to 1 decimal place, the surface area when r = 3.0 cm and L = 8.5 cm.
80.11 cm²
80.1 cm²
80.1106 cm²
80.0 cm²
What are the roots of the cubic equation x^3 – 8x – 3 = 0?
x = - 7.90 , -3 , - 0.38
x = -3, -2, 2
x = -3, -0.38, 2
x = - 2.62, -0.38, 3
What is the solution of the equation 50x² + 5x - 2 = 1, where x is a real-valued variable?
-6.12 or -3.88
-0.52 or 0.700
7.55
no solution
Which of the following is a happy number?
143
69
88
100
How many real solutions does the equation : x^7 + 14x^5 + 16x^3 + 30x – 560 = 0 have?
1
3
5
7
What is the discriminant of the equation: 4x² – 8x + 5 = 0?
8
16
-16
-8
What is the discriminant of the equation: 4x^2 – 8x + 5 = 0 ?
8
–16
16
–8
How many positive real root(s) in the given equation 4x^3 – 2x^2 + x – 3.
2
1
3
0
What is the natural logarithm of xy e ?
1
xy
2.718xy
2.718
What is the value of (2/3)^(0.001) ?
antilog(log(0.001))
antilog(log(0.001))
antilog(log(0.001))
antilog(log(0.001))
Factor the expression 3x^3 – 3x^2 – 18x
3x(x – 3)(x+2)
3x(x+3)(x – 2)
3x(x+3)(x+2)
3x(x – 3)(x – 2)
Which of the following best describe 8 + 0i ?
irrational number
real number
imaginary
surd
Simplify the given fraction (3x^2 - 1x + 3)/(x^1 + 3x + 2x + 2)
2x/(3x + 1)
1/(x + 1)
1/(x + 1)
1/(x + 1)
Find the equation of whose roots are the reciprocal of the roots of 2x^2 – 3x – 5 = 0.
5x^2 - 3x - 2 = 0
5x^2 - 12x + 10 = 0
5x^2 + 3x - 2 = 0
5x^2 - 15x + 2 = 0
Resolve (x+ 2) / (x^2 – 7 x + 12) into partial fraction.
6 / (x – 4) – 2 / (x – 3)
6 / (x – 4) – 5 / (x – 3)
6 / (x – 4) + 7 / (x – 3)
6 / (x – 4) + 5 / (x – 3)
One root of the equation 5x^2 + 13x + m = 0 is reciprocal of the other m equals:
0
5
6
1/6
If x = 111..., then what is the value of x?
0.723
0.675
0.618
0.876
If i (squared) = –1, then the sum i + i(squared) + i(cubed) + ... to 1000 terms is equal to:
– i
– 1
0
i
Find the value of x: log3(x^2 – 8x) = 2.
-1
9
1 and 9
9
What is the smallest positive value of x in (x^2 + 4x + 4) to be reciprocal of (x^2 – 4x + 4)?
sq rt of 3
sq rt of 5
3
5
What is the least common multiple (LCM) of 15 and 18?
90
45
108
75
What is the greatest common factor (GCF) of 70 and 112?
2
14
7
35
Two tankers contain 825 liters and 675 liters of kerosene oil respectively. Find the maximum capacity of container which can measure the kerosene oil of both tankers when used an exact number of times.
50 liters
75 liters
150 liters
25 liters
What is the base-10 logarithm of (1000)3?
3
6
9
27
What is the value of the square root of – 64 x square root of – 225?
8i
– 120
8i/15
– 120 i
What is the smallest counting number that is divisible by each of the fifteen counting number?
360,360
100,000
1000
100
The time of swing t seconds, of a simple pendulum is given by the equation below. Determine the time correct to 3 decimal places, given that L = 12.0 and g = 9.81.
6.949
6.950
6.94
7.00
Determine the sum of the positive valued solutions to the simultaneous equations: xy = 15, yz = 35, zx = 21.
17
19
15
20
What is the value of log (x^2/x)?
2x log x
x log x
x^2 log x
(x log x)/x
Solve the value of x: x^2 + x = 9.
2.52
1.823
3
1
If (x + 4) is a factor of x^3 - 2x^2 + 7x + k, what is the value of k?
2
4
3
5
Two reviewees attempt to solve a problem that reduces to a quadratic equation. One of the reviewees made a mistake in the constant term and gave an answer of 8 and 2 for the roots. The other reviewee made a mistake in the coefficient of the first degree term and gave an answer of –9 and –1 for the roots. If you are to check their solutions, what would be the correct quadratic equation?
x^2 – 3x + 9 = 0.
x^2 – 12x + 10 = 0.
x^2 – 10x + 9 = 0.
x^2 – 15x + 20 = 0.
Solve the simultaneous equations: 2x^2 – 3y^2 = 6, 3x^2 + 2y^2 = 35.
x = 3 or -3 and y = 2 or – 2
x = 3 or – 3 and y = -2 or 1
x = 3 or -3 and y = -2 or – 1
x = 3 or -3 and y = 1 or – 1
Find the factor of x^3 - x^2 - x - 1.
2x(x - 1)(x + 1)
2(x - 1)(x + 1)
2(x + 1)(x + 1)
2(x - 1)(x + 1)
What is equivalent to 0.227272727227...?
7/44
5/22
11/44
5/54
