1.
- Solve the following inequality: 28-5x < x - 4.
Correct Answer
C. (C) x>5.33
Explanation
To solve the inequality, we need to isolate the variable x.
First, we can simplify the inequality by combining like terms:
28 - 5x < x - 4
Next, we can move all the x terms to one side of the inequality by subtracting x from both sides:
28 - 5x - x < -4
Simplifying further, we get:
28 - 6x < -4
Now, we can isolate the variable x by moving the constant term to the other side of the inequality by subtracting 28 from both sides:
-6x < -4 - 28
Simplifying, we get:
-6x < -32
To solve for x, we divide both sides of the inequality by -6. However, since we are dividing by a negative number, the inequality sign flips:
x > -32/-6
Simplifying, we get:
x > 5.33
Therefore, the correct answer is (C) x > 5.33.
2.
- Which of the following is NOT a measure of central tendencies?
Correct Answer
C. (C) Decile
Explanation
Decile is not a measure of central tendency because it is a measure of dispersion or variability. Central tendency measures summarize the center or average of a distribution, while measures of dispersion describe how spread out the data is. Deciles divide the data into ten equal parts, providing information about the distribution of the data rather than its central value.
3.
Simplify without using tables: 1^{3}/_{4} + 3^{1}/_{5} x 1^{2}/_{3} + ^{1}/_{12}
Correct Answer
D. D. 7^{1}/_{6}
Explanation
To simplify the given expression, we need to follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right). In this case, there are no parentheses or exponents, so we start with multiplication and division.
First, we multiply 31/5 by 12/3, which gives us 372/15.
Next, we add 13/4 to 372/15. To add these fractions, we need to find a common denominator, which is 60.
Converting 13/4 to have a denominator of 60, we get 195/60.
Converting 372/15 to have a denominator of 60, we get 1488/60.
Adding 195/60 and 1488/60, we get 1683/60.
Finally, we simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 3.
Dividing 1683 by 3 and dividing 60 by 3, we get 561/20.
Therefore, the simplified expression is 561/20, which is equivalent to 71/6.
4.
- What is the length of an arc, which subtends an angle 60^{0} at the centre of a circle of radius 0.5m?
Correct Answer
D. (D) 0.52
Explanation
The length of an arc can be calculated using the formula L = rθ, where L is the length of the arc, r is the radius of the circle, and θ is the angle in radians. In this case, the radius is given as 0.5m and the angle is given as 600. To convert the angle from degrees to radians, we use the formula θ = (π/180) * angle. Substituting the values into the formula, we get L = 0.5 * (π/180) * 600 = 0.52m. Therefore, the correct answer is (D) 0.52.
5.
- Evaluate 7 - 35 = (mod 8).
Correct Answer
B. (B) -4
6.
- Esther was facing S20°W. She turned 90° in the clockwise direction. What direction is she facing now?
Correct Answer
B. (B) N70°W
Explanation
Esther was originally facing in the direction of S20°W. When she turns 90° in the clockwise direction, she will be facing in the opposite direction, which is N70°E. However, since the options are given in terms of cardinal directions, we need to convert N70°E to its corresponding cardinal direction. N70°E is equivalent to N20°W, so Esther is facing N70°W.
7.
- What is the area of a circle whose radius is 7cm. (Take π = ^{22}/_{7} ).
Correct Answer
C. (C) 154cm^{2}
Explanation
The formula to calculate the area of a circle is A = πr^2, where A is the area and r is the radius. In this case, the radius is given as 7cm. Plugging in the values, we get A = (22/7) * (7^2) = (22/7) * 49 = 154cm^2. Therefore, the correct answer is (C) 154cm^2.
8.
- Find the circumference of a circle whose diameter is 10cm. (Take π = ^{22}/_{7} ).
Correct Answer
A. (A) 31.42cm
Explanation
The circumference of a circle can be found by multiplying the diameter by π. In this case, the diameter is given as 10cm. Therefore, the circumference can be calculated as 10cm x (22/7) = 31.42cm.
9.
- Write 123.6 in standard form.
Correct Answer
C. (C) 1.236 X 10^{2}
Explanation
.
10.
- Write in a combined inequality the following: x<3, x> -2.
Correct Answer
A. (A) -2<x<3
Explanation
The correct answer is (A) -2
11.
- If y varies inversely as the square of x, and y = 1^{1}/_{4} when x = 4, find the value of y when x = ^{1}/_{2}
Correct Answer
C. (C) 10
Explanation
Inverse variation means that as one variable increases, the other variable decreases, and vice versa. In this case, y varies inversely as the square of x. This can be represented by the equation y = k/x^2, where k is a constant.
To find the value of k, we can use the given information that when x = 4, y = 11/4. Plugging these values into the equation, we get 11/4 = k/4^2, which simplifies to 11/4 = k/16. Solving for k, we find that k = 44.
Now, we can use this value of k to find the value of y when x = 1/2. Plugging these values into the equation, we get y = 44/(1/2)^2, which simplifies to y = 44/(1/4), or y = 44 * 4. Therefore, y = 176.
Therefore, the value of y when x = 1/2 is 176, which is not one of the given answer choices. Therefore, the correct answer is not provided.
12.
Find the three lowest values of x , given that x is the integer : 18 + 5x > 1
Correct Answer
C. C. -1 , -2 , -3
Explanation
The given inequality is 18 + 5x > 1. To find the three lowest values of x that satisfy this inequality, we need to solve for x. Subtracting 18 from both sides of the inequality gives us 5x > -17. Dividing both sides by 5 gives us x > -3.4. Since x must be an integer, the three lowest values of x that satisfy the inequality are -1, -2, and -3. Therefore, the correct answer is C. -1, -2, -3.
13.
Given C = 5(F -32)/9 , find F when C = 35
Correct Answer
D. (D) 95
Explanation
The given equation C = 5(F - 32)/9 represents the conversion formula from Celsius to Fahrenheit. To find F when C = 35, we substitute C = 35 into the equation and solve for F.
35 = 5(F - 32)/9
7*9 = F - 32
F = 95
14.
Find the equation of the lines passing through the following pair of points: A (2, 3) and B(3, 9)
Correct Answer
A. A. y = 6x - 9
Explanation
The equation of a line passing through two points (x₁, y₁) and (x₂, y₂) can be found using the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we use the formula (y₂ - y₁) / (x₂ - x₁).
For the given points A (2, 3) and B (3, 9), the slope is (9 - 3) / (3 - 2) = 6 / 1 = 6.
Substituting the slope and one of the points into the slope-intercept form, we get y = 6x - 9.
Therefore, the correct answer is A. y = 6x - 9.
15.
- Use logarithm tables to evaluate the following: 608 x 4.85 ÷ 276.
Correct Answer
A. (A) 10.69
16.
- Factorise 2x^{2} + 9x + 7
Correct Answer
C. (C) (x+1)(2x+7)
Explanation
The given expression is a quadratic trinomial, and we need to factorize it. The factors of the trinomial will have the form (ax + b)(cx + d), where a, b, c, and d are constants. To factorize the expression 2x^2 + 9x + 7, we need to find two numbers that multiply to give 2 * 7 = 14 and add up to give 9. The numbers that satisfy these conditions are 2 and 7. Therefore, the expression can be factorized as (x + 1)(2x + 7), which matches option (C).
17.
- Three times a certain number added to 14 is the same as when two times the number is subtracted from 6. What is the number?
Correct Answer
B. (B) -8/5
18.
Simplify √147 - √75 + √12
Correct Answer
C. C. 4√3
Explanation
To simplify the expression, we need to find the square roots of 147, 75, and 12. The square root of 147 is 7√3, the square root of 75 is 5√3, and the square root of 12 is 2√3. Therefore, the expression simplifies to 7√3 - 5√3 + 2√3, which further simplifies to 4√3. Hence, the correct answer is C. 4√3.
19.
The operation * on the set Q of rational numbers is defined by
Correct Answer
B. (B) -8.5
20.
Express ^{8.75}/_{0.025} in standard form
Correct Answer
D. (D) 3.5 x 10^{2}
Explanation
The given expression can be simplified by dividing 8.75 by 0.025, which equals 350. In standard form, this can be written as 3.5 x 10^2, where the exponent 2 indicates that the decimal point is moved two places to the right. Therefore, the correct answer is (D) 3.5 x 10^2.
21.
- The angles of a pentagon are x^{0}, 2x^{0}, (x + 30)^{0}, (x - 10)^{0} and (x + 40)^{0}. Find x.
Correct Answer
C. (C) 80°
Explanation
The sum of the interior angles of a pentagon is equal to 540 degrees. Therefore, we can set up the following equation: x0 + 2x0 + (x + 30)0 + (x - 10)0 + (x + 40)0 = 540. Simplifying this equation, we get 5x0 + 60 = 540. Subtracting 60 from both sides, we get 5x0 = 480. Dividing both sides by 5, we get x0 = 96. Therefore, x = 96/10 = 9.6. Since the options are given in degrees, we round x to the nearest whole number, which is 10. The correct answer is (C) 80 degrees.
22.
The operation delta ∆ on the set Z of integers is defined by a ∆ b = 2a + 3b - 1
Correct Answer
C. C. e = ( 1 - a )/3
Explanation
The given operation delta ∆ on the set Z of integers is defined as a∆ b = 2a + 3b - 1. In order to find e, we need to substitute e for b in the equation. So, we have a∆ e = 2a + 3e - 1. Comparing this with the given options, we can see that option C, e = (1 - a)/3, matches the equation. Therefore, the correct answer is C. e = (1 - a)/3.
23.
- Which of the following statements is true?
Correct Answer
B. (B) The angle of elevation and the angle of depression are different angles, but they have the same measure
Explanation
The angle of elevation and the angle of depression are different angles because they are measured in different positions. However, they have the same measure because they are formed by a horizontal line and a line of sight that is inclined upwards or downwards from the horizontal.
24.
- A bicycle depreciates in value by about 15% each year. If Regina bought a bicycle for ₦6800 in 1988, find the value 3years later.
Correct Answer
A. (A) ₦4176
Explanation
To find the value of the bicycle 3 years later, we need to calculate the depreciation for each year. The bicycle depreciates by 15% each year, so after the first year, the value will be 85% of the original value. After the second year, it will be 85% of the value in the first year, and after the third year, it will be 85% of the value in the second year. Therefore, the value 3 years later will be 85% of 85% of 85% of ₦6800. Calculating this gives us ₦4176, which is option (A).
25.
- Given the corner points of solution of inequation on some trading equipment are A (3 , -2), B (2 , 3), C (-5, 2), D (4 , 3). Minimize cost Z=3x+y.
Correct Answer
D. (D) -13
Explanation
The given question asks for the minimum value of the cost function Z=3x+y. To find the minimum value, we need to evaluate the cost function at each corner point and determine the smallest value. Evaluating Z at point A (3, -2), we get Z=3(3)+(-2)=7. Evaluating Z at point B (2, 3), we get Z=3(2)+(3)=9. Evaluating Z at point C (-5, 2), we get Z=3(-5)+(2)=-13. Evaluating Z at point D (4, 3), we get Z=3(4)+(3)=15. The smallest value is -13, which is the minimum cost. Therefore, the correct answer is (D) -13.
26.
- The mean of 2, 5, (x+1), (x+2), 7 and 9 is 6. Find the median
Correct Answer
C. (C) 6.5
Explanation
To find the median, we first need to arrange the numbers in ascending order: 2, 5, (x+1), (x+2), 7, 9. The mean of these numbers is given as 6. Since the median is the middle value when the numbers are arranged in ascending order, we can set up an equation to find the value of x. The sum of the numbers is 2 + 5 + (x+1) + (x+2) + 7 + 9 = 6 * 6 = 36. Simplifying this equation gives 2x + 26 = 36, which leads to x = 5. Therefore, the numbers are 2, 5, 6, 7, 7, 9, and the median is (x+1) = 6.5.
27.
- Given two functions h (x)=3x+2 and g(x)= x-1, find hg (x ).
Correct Answer
D. (D) 3x - 1
Explanation
The function hg(x) represents the composition of function g(x) and function h(x). To find hg(x), we substitute the expression for g(x) into h(x), which gives us h(g(x)). Substituting g(x) = x - 1 into h(x) = 3x + 2, we get h(g(x)) = 3(x - 1) + 2 = 3x - 3 + 2 = 3x - 1. Therefore, the correct answer is (D) 3x - 1.
28.
Simplify
Correct Answer
C. C.
29.
If tanx= ^{8}/_{15}_{,} find the value of
Correct Answer
B. (B) 3.21
30.
The lengths of the adjacent sides of a right-angled triangle are x cm and (x-1) cm. If the length of the hypotenuse is √13, find the value of x.
Correct Answer
B. (B) 3
Explanation
In a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Using this property, we can set up the equation x^2 + (x-1)^2 = 13. Simplifying this equation gives x^2 + x^2 - 2x + 1 = 13. Combining like terms gives 2x^2 - 2x - 12 = 0. Factoring out a 2 gives 2(x^2 - x - 6) = 0. Factoring further gives 2(x-3)(x+2) = 0. Setting each factor equal to 0 gives x-3 = 0 or x+2 = 0. Solving for x gives x = 3 or x = -2. Since we are looking for the length of a side, x cannot be negative, so the value of x is 3.