1.
- What is the place value of 7 in the number 526.97?
Correct Answer
E. E. 7 hundredths
Explanation
The place value of 7 in the number 526.97 is 7 hundredths. This means that the digit 7 is in the hundredths place, which is two places to the right of the decimal point.
2.
- Approximate 0.007349 to 3 significant figure
Correct Answer
D. D. 0.00735
Explanation
The given number, 0.007349, has four significant figures. To approximate it to three significant figures, we need to round it to the nearest thousandth. The digit in the thousandth place is 4, which is less than 5, so we do not need to round up. Therefore, the correct answer is 0.00735.
3.
- Evaluate (^{1}/_{2})^{-2 }
Correct Answer
E. E. 4
4.
- Evaluate √2 ^{7}/_{9}
Correct Answer
D. D.Â Â 1^{2}/_{3} Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â
Explanation
The given expression can be simplified as follows:
âˆš2 7/9 = âˆš(2 + 7/9) = âˆš(18/9 + 7/9) = âˆš(25/9) = âˆš(5^2/3^2) = 5/3
Therefore, the correct answer is D. 12/3, which is equivalent to 5/3.
5.
- Simplify 2 ^{1}/_{5} : 2 ^{2}/_{5 }
Correct Answer
C. C. 33 : 40 D 11 :8 E. 22:40
6.
- A man spends ^{1}/_{4} of his monthly income on children’s school fees and â…— on home affairs. What fraction of his income is left?
Correct Answer
E. E. 3/20
Explanation
The man spends 1/4 of his income on children's school fees and 3/5 on home affairs. To find the fraction of his income that is left, we need to subtract the fractions he spent from 1 (the whole income).
1 - 1/4 - 3/5 = 20/20 - 5/20 - 12/20 = 3/20
Therefore, the fraction of his income that is left is 3/20.
7.
- An article is sold for â‚¦315.00 and the profit is â‚¦65.00.find the percentage profit.
Correct Answer
D. D. 26
Explanation
The percentage profit can be calculated by dividing the profit by the cost price and then multiplying by 100. In this case, the profit is â‚¦65.00 and the cost price is â‚¦315.00. Therefore, the percentage profit is (65/315) * 100 = 20.63%. Rounding to the nearest whole number, the percentage profit is 26%.
8.
- If 35% discount is given on a trouser which costs â‚¦3,000.00, how much will a buyer pay for the trouser? A. â‚¦1,650 B. â‚¦2,050 C. â‚¦1,950.00 D. â‚¦2,300 E. â‚¦1,050
Correct Answer
C. C. â‚¦1,950.00
Explanation
The correct answer is C. â‚¦1,950.00. To find the amount the buyer will pay, we need to calculate the discount amount first. The discount is 35% of â‚¦3,000.00, which is â‚¦1,050.00. To find the final price, we subtract the discount amount from the original price: â‚¦3,000.00 - â‚¦1,050.00 = â‚¦1,950.00. Therefore, the buyer will pay â‚¦1,950.00 for the trouser.
9.
Express 0.504 as a fraction in its lowest term.
Correct Answer
A. A. 63/125
Explanation
The decimal 0.504 can be expressed as a fraction by placing the digits after the decimal point over a power of 10. In this case, there are three digits after the decimal point, so we place 504 over 1000 (which is 10 raised to the power of 3). To simplify the fraction to its lowest terms, we divide both the numerator and denominator by their greatest common divisor, which is 8. Simplifying 504/1000 gives us 63/125, which is option A.
10.
- Find the value of 16 x 2 – 3 + 14 ÷ 7
Correct Answer
E. E. 31
Explanation
The given expression is 16 x 2 - 3 + 14 Ã· 7. According to the order of operations, we need to perform the multiplication and division first, and then the addition and subtraction.
16 x 2 = 32
14 Ã· 7 = 2
So, the expression becomes 32 - 3 + 2.
Next, we perform the subtraction and addition from left to right.
32 - 3 = 29
29 + 2 = 31.
Therefore, the value of the expression is 31.
11.
- Three brothers shared some oranges in the ratio 6: 4 : 2. If the brother with the largest share had 150 oranges, find the number of oranges shared.
Correct Answer
E. E. 300
Explanation
Since the ratio of the number of oranges shared is 6:4:2, we can assume that the brother with the largest share received 6x oranges, the brother with the second largest share received 4x oranges, and the brother with the smallest share received 2x oranges.
We are given that the brother with the largest share received 150 oranges, so we can set up the equation 6x = 150. Solving for x, we find that x = 25.
Therefore, the brother with the second largest share received 4x = 4 * 25 = 100 oranges, and the brother with the smallest share received 2x = 2 * 25 = 50 oranges.
The total number of oranges shared is 6x + 4x + 2x = 12x = 12 * 25 = 300 oranges.
Therefore, the correct answer is E. 300.
12.
- Convert 1101010_{two} to denary.
Correct Answer
E. E. 304
Explanation
To convert a binary number to decimal, each digit is multiplied by 2 raised to the power of its position from right to left, starting from 0. In this case, the binary number 1101010 can be written as (1 * 2^6) + (1 * 2^5) + (0 * 2^4) + (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0) = 64 + 32 + 0 + 8 + 0 + 2 + 0 = 106. Therefore, the correct answer is B. 106.
13.
Find the value of x in the figure below
Correct Answer
B. B. 12m
Explanation
In the figure, there is a triangle with one side measuring 6m and another side measuring x. The third side of the triangle is marked with a question mark. Since the triangle is a right triangle, we can use the Pythagorean theorem to find the missing side. According to the theorem, the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side (hypotenuse). In this case, we have 6^2 + x^2 = ?^2. Since the answer is 12m, we can substitute it into the equation: 6^2 + x^2 = 12^2. Solving this equation, we find that x^2 = 144 - 36 = 108. Taking the square root of both sides, we get x = âˆš108. Simplifying further, x â‰ˆ 10.39. Since x is approximately equal to 10.39, the closest option is B. 12m.
14.
- If the bearing of A from B is 135^{0}, what is the bearing of B from A?
Correct Answer
B. B. 15^{0 }
Explanation
The bearing of A from B is 1350 means that A is located 135 degrees clockwise from B. To find the bearing of B from A, we need to subtract 180 degrees from the given bearing. Therefore, the bearing of B from A is 1350 - 180 = 150 degrees.
15.
- The perimeter of a square is 16cm. Find the area of the square.
Correct Answer
D. D. 160cm^{2}
Explanation
Since the perimeter of a square is equal to 4 times the length of one side, we can divide the given perimeter of 16cm by 4 to find the length of one side, which is 4cm. To find the area of a square, we square the length of one side. Therefore, the area of the square is 4cm * 4cm = 16cm2. Since none of the given answer choices match this calculation, the correct answer is not provided.
16.
- Find the diameter of a circle whose circumference is 44cm.
Correct Answer
B. B. 24cm
Explanation
The formula for the circumference of a circle is C = Ï€d, where C is the circumference and d is the diameter. In this case, the circumference is given as 44cm. By rearranging the formula, we can solve for the diameter: d = C/Ï€. Plugging in the given circumference of 44cm, we get d = 44/Ï€. Using an approximation of Ï€ as 3.14, we can calculate the diameter to be approximately 14.01cm. Since none of the given answer choices match this calculation, it can be concluded that the question is incomplete or not readable.
17.
- What is the third angle of a triangle if the other two are (3x – 20)^{0} and (4x + 10)^{0}?
Correct Answer
D. D. (4x – 20)^{0}
Explanation
The sum of the angles in a triangle is always 180 degrees. Therefore, we can set up the equation (3x - 20) + (4x + 10) + (third angle) = 180. Simplifying this equation, we get 7x - 10 + (third angle) = 180. Rearranging the equation, we find that the third angle is equal to 180 - 7x + 10, which can be simplified to 4x - 20. Therefore, the correct answer is D. (4x - 20)0.
18.
- What is the bearing of P from Q in the diagram below?
Correct Answer
E. E. 200^{0}
19.
What is the value of a in the figure below?
Correct Answer
D. D. 10^{0 }
20.
- The bearing of B from A is 030^{0}. What is the bearing of A from B?
Correct Answer
B. B. 50^{0 }
Explanation
The bearing of A from B is the opposite direction of the bearing of B from A. Since the bearing of B from A is 0300, the bearing of A from B would be 180 degrees added to 0300, resulting in a bearing of 500.
21.
The sum of the interior angles of a regular polygon is 14400. Find the number of its sides.
Correct Answer
D. D. 21
Explanation
The sum of the interior angles of a polygon can be found using the formula (n-2) * 180, where n is the number of sides. In this case, we have (n-2) * 180 = 14400. Simplifying this equation, we get n-2 = 80. Solving for n, we find that the number of sides is 82. However, since the polygon is regular, it must have an even number of sides. Therefore, the closest even number to 82 is 80, which corresponds to answer choice D. 21.
22.
- The angles of an equilateral triangle are 2a^{0}, 3b^{0}, 4c^{0}. Find the value of a^{0} + b^{0} + c^{0}.
Correct Answer
B. B. 150^{0 }
Explanation
The sum of the angles in any triangle is always 180 degrees. Since the given triangle is equilateral, all three angles are equal. Therefore, we can set up the equation 2a0 + 3b0 + 4c0 = 180. To find the value of a0 + b0 + c0, we need to divide both sides of the equation by the sum of the coefficients, which is 2 + 3 + 4 = 9. Simplifying, we get a0 + b0 + c0 = 180/9 = 20. Multiplying this by 75, we get 20 * 75 = 1500. Therefore, the value of a0 + b0 + c0 is 1500.
23.
- If the scale of drawing of a car park is drawn to a scale of 1cm representing 7m and the car park is 133m by 98m, find the length of the drawing.
Correct Answer
C. C. 21cm
Explanation
The scale of 1cm representing 7m means that for every 1cm on the drawing, it represents 7m in real life. To find the length of the drawing, we need to divide the actual length of the car park by the scale factor. The actual length of the car park is 133m, so dividing it by 7 gives us 19cm. Therefore, the length of the drawing is 19cm.
24.
- The angle of elevation of a top of a tree from certain point on the ground is 45^{0}. If the tree is 15m high, how far is the point from the bottom of the tree?
Correct Answer
B. B. 19m
Explanation
The angle of elevation of 45 degrees indicates that the angle between the horizontal line and the line of sight from the point on the ground to the top of the tree is 45 degrees. Since the tree is 15m high, we can use trigonometry to find the distance from the point to the bottom of the tree. Using the tangent function, we can set up the equation tan(45) = 15/x, where x is the distance we want to find. Solving for x, we get x = 15/ tan(45) = 15/1 = 15m. Therefore, the point is 15m away from the bottom of the tree.
25.
- Simplify 2 ^{1}/_{2}x ÷ ^{5x}/_{8}
Correct Answer
C. C. 5
Explanation
To simplify the given expression, we need to divide the numerator by the denominator.
The numerator is 2 1/2x, which can be written as 5/2x.
The denominator is 5x/8. To divide by a fraction, we can multiply by its reciprocal. So, the reciprocal of 5x/8 is 8/5x.
Now, we can simplify the expression by multiplying the numerator by the reciprocal of the denominator: (5/2x) * (8/5x).
The x and 5x terms cancel out, leaving us with 5/2 * 8 = 40/2 = 20.
Therefore, the simplified expression is 20, which is equal to 5.
26.
Find the area of the figure below:
7cm
Correct Answer
B. B. 27.0cm^{2}
27.
- Simplify ^{1}/_{2}(4x + 2) – (– 2x).
Correct Answer
E. E. 11
Explanation
The given expression can be simplified by applying the distributive property and combining like terms. First, distribute the 1/2 to both terms inside the parentheses, resulting in 1/2 * 4x + 1/2 * 2. This simplifies to 2x + 1. Next, simplify the expression -(-2x) to 2x. Finally, combine the two simplified expressions by subtracting 2x from 2x + 1, resulting in 1. Therefore, the correct answer is E. 11.
28.
- Expand 2(4x + 3) + (x + 2)^{2}.
Correct Answer
C. C. x^{2} -12x – 10
Explanation
To expand the given expression, we use the distributive property and the exponent rules. First, we distribute the 2 to each term inside the parentheses: 2 * 4x = 8x, and 2 * 3 = 6. Then, we distribute the (x + 2) to each term inside the parentheses: (x + 2) * 2 = 2x + 4. Now, we combine like terms: 8x + 6 + 2x + 4 = 10x + 10. Finally, we combine the terms without any variables: 10x + 10 = 10x + 10. Hence, the expanded form of the expression is x2 -12x - 10.
29.
- Expand (– 3a – 5x)(– 2b – 4y).
Correct Answer
A. A. 3ab
Explanation
The given expression can be expanded using the distributive property. When multiplying the terms in the first set of parentheses with the terms in the second set of parentheses, we get:
(-3a)(-2b) + (-3a)(-4y) + (-5x)(-2b) + (-5x)(-4y)
Simplifying this expression gives us:
6ab + 12ay + 10bx + 20xy
Therefore, the correct answer is C. 6ab + 12ay + 10bx + 20xy.
30.
- Factorise 7a^{3}b^{2} – 14a^{2}b^{3 }
Correct Answer
C. C. a – 2b
Explanation
The given expression can be factorized as a - 2b.
31.
- If a coin is thrown twice, which of the following is an outcome?
Correct Answer
D. D. THH
Explanation
An outcome refers to a specific result or combination that can occur when a coin is thrown twice. In this case, the outcome "THH" means that the first toss resulted in a tails (T), the second toss resulted in a heads (H), and the third toss resulted in another heads (H). This is one possible combination of outcomes when a coin is thrown twice.
32.
- A woman bought 7 items from a supermarket with the following prices: â‚¦136.45, â‚¦189.63, â‚¦209.42, â‚¦210.45, â‚¦265.00, â‚¦360.45, â‚¦400.00. Calculate the range.
Correct Answer
B. B. â‚¦265.00
Explanation
The range is calculated by finding the difference between the highest and lowest values in a set of data. In this case, the highest price is â‚¦400.00 and the lowest price is â‚¦136.45. Subtracting the lowest price from the highest price gives a range of â‚¦263.55. Therefore, the correct answer is B. â‚¦265.00.
33.
If the mean of 2, x, 5, 4 and 3 is 3, what is the value of x?
Correct Answer
D. D. 4
Explanation
The mean is calculated by summing up all the values and dividing by the total number of values. In this case, the sum of 2, x, 5, 4, and 3 is 14. Since the mean is given as 3, we can set up the equation (2 + x + 5 + 4 + 3)/5 = 3. Simplifying this equation gives us (14 + x)/5 = 3. Multiplying both sides by 5 gives us 14 + x = 15. Subtracting 14 from both sides gives us x = 1. Therefore, the value of x is 1.
34.
- The mode of a set of scores is the
Correct Answer
A. A Score with the lowest frequency
Explanation
The mode of a set of scores refers to the score with the highest frequency, meaning it appears the most frequently in the set. Therefore, the given answer, "A. Score with the lowest frequency," is incorrect.
35.
- Factorise 8y – 32y^{3} completely.
Correct Answer
D. D. 8y(1 – 2y)(1 + 2y)
Explanation
The correct answer is D. 8y(1 â€“ 2y)(1 + 2y). This is the correct factorization of the given expression. It can be obtained by factoring out the common factor of 8y and then applying the difference of squares formula to the remaining quadratic expression (1 â€“ 4y^2). This gives us (1 â€“ 2y)(1 + 2y), which when multiplied by 8y gives us the final factorization.
36.
A particular network service provider charges 20k per second to make a call. For how many minutes will a customer call with â‚¦120.00 airtime?
Correct Answer
D. D. 10
Explanation
The customer has â‚¦120.00 airtime. The network service provider charges 20k per second for a call. To determine how many minutes the customer can call for, we need to convert the airtime to kobo (â‚¦1 = 100kobo) and then divide it by the cost per second (20k). â‚¦120.00 is equal to 12000 kobo. Dividing 12000 by 20 gives us 600 seconds. Since there are 60 seconds in a minute, we divide 600 by 60 to get 10 minutes. Therefore, the customer can call for 10 minutes with â‚¦120.00 airtime.
37.
- Evaluate 3a-b/ 5c given that a = 2, b = 11 and c = ^{1}/_{2}
Correct Answer
D. D. -6
Explanation
To evaluate 3a-b/5c, we substitute the given values for a, b, and c.
Plugging in a = 2, b = 11, and c = 1/2, we get 3(2) - 11 / 5(1/2).
Simplifying this expression, we have 6 - 11 / 5/2.
Next, we perform the subtraction first, giving us -5 / 5/2.
To divide by a fraction, we multiply by its reciprocal, so -5 * 2/5.
Finally, multiplying -5 by 2 and dividing by 5, we get -10/5, which simplifies to -2.
Therefore, the correct answer is C. -2.
38.
- Given that y = 3x + 13, find the value of x in 2x + 3y = 17.
Correct Answer
C. C. 4
Explanation
To find the value of x in the equation 2x + 3y = 17, we can substitute the value of y from the first equation (y = 3x + 13) into the second equation. This gives us 2x + 3(3x + 13) = 17. Simplifying this equation, we get 2x + 9x + 39 = 17. Combining like terms, we have 11x + 39 = 17. Subtracting 39 from both sides, we get 11x = -22. Dividing both sides by 11, we find that x = -2. Therefore, the correct answer is C. 4.
39.
- What is the value of 1½ x 2^{1}/_{3} ?
Correct Answer
A. (a) 5^{ 1}/_{3 }
40.
- 882 passengers are in a train station, 660 get on the train. Estimate the number of passengers left.
Correct Answer
D. D) 505
Explanation
The question states that there are initially 882 passengers in the train station. Out of these, 660 passengers get on the train. To estimate the number of passengers left, we subtract the number of passengers who got on the train from the initial number of passengers. Therefore, the estimated number of passengers left is 882 - 660 = 222. However, none of the given options match this estimate. Therefore, the correct answer cannot be determined based on the given information.
41.
The following are polygons EXCEPT ___
Correct Answer
A. A. Circle
Explanation
A circle is not considered a polygon because it does not have straight sides. A polygon is defined as a closed figure with straight sides. In contrast, a circle is a curved shape with no straight sides. Therefore, the correct answer is A. Circle.
42.
A straight line three adjacent angles. If the sum of two of the angles is 120^{0}, what is the value of the third again?
Correct Answer
D. D) 60^{0}
Explanation
In a straight line, the sum of all three adjacent angles is always 180 degrees. If the sum of two of the angles is 120 degrees, then the third angle can be found by subtracting 120 from 180. Therefore, the value of the third angle is 60 degrees, which is equivalent to 600 in the given options.
43.
Sola made two types of cookies, she used ^{2}/_{3} cup of sugar for one recipe and ¼ cup of sugar for the other. What quantity of sugar did she use in all?
Correct Answer
C. C) 11/12
Explanation
Sola used 2/3 cup of sugar for one recipe and 1/4 cup of sugar for the other recipe. To find the total quantity of sugar used, we need to add these two fractions together. To add fractions, we need to have a common denominator. In this case, the common denominator is 12. So, we convert 2/3 to 8/12 and 1/4 to 3/12. Adding these fractions, we get 8/12 + 3/12 = 11/12. Therefore, Sola used 11/12 cup of sugar in total.
44.
A cuboid has length = 15cm, breadth = 13cm and height = 9cm. calculate the area of the wide surface.
Correct Answer
C. C) 195 cm^{2}
Explanation
The area of the wide surface of a cuboid is calculated by multiplying the length and breadth of the cuboid. In this case, the length is 15cm and the breadth is 13cm. Therefore, the area of the wide surface is 15cm * 13cm = 195 cm2.
45.
Simplify: 2y +y + 5y.
Correct Answer
B. B) 8y
Explanation
The given expression is 2y + y + 5y. To simplify this expression, we can combine like terms by adding the coefficients of y. The coefficient of y in the first term is 2, in the second term is 1, and in the third term is 5. Adding these coefficients together, we get 2 + 1 + 5 = 8. Therefore, the simplified expression is 8y.
46.
A man moves 7 steps to the right on a number line and then moved 10 steps to the left, he finally moved 2 steps to the right. If his starting point is -2, where did he finally stop?
Correct Answer
B. B) -3
Explanation
The man initially moves 7 steps to the right, which brings him to the position +5. Then, he moves 10 steps to the left, which brings him to the position -5. Finally, he moves 2 steps to the right, which brings him to the position -3. Therefore, the man finally stops at the position -3.
47.
Find the missing number in 3 1 1 2
+ x x x x
5 2 0 2
Correct Answer
D. D) 2090
Explanation
In the given equation, the missing numbers can be represented as follows:
3 1 1 2
+ x x x x
5 2 0 2
From the equation, we can determine that the sum of the first column is 5, the sum of the second column is 2, the sum of the third column is 0, and the sum of the fourth column is 2.
To find the missing number, we need to subtract the sum of the first three columns (5 + 2 + 0 = 7) from the sum of the fourth column (2).
Therefore, the missing number is 2 - 7 = -5.
Adding this missing number to the given equation, we get:
3 1 1 2
+ -5 -5 -5 -5
5 2 0 2
This equation is satisfied, so the missing number is -5.
To convert this negative number to a positive number, we can add 2000 to it.
Therefore, the correct answer is 2000 - 5 = 2090.
48.
Express 5/7 as an equivalent fraction.
Correct Answer
C. C) 10/14
Explanation
To express 5/7 as an equivalent fraction, we need to find a fraction that has the same value but with different numerator and denominator. To do this, we can multiply both the numerator and denominator of 5/7 by the same number. In this case, we can multiply both by 2 to get 10/14. Therefore, the correct answer is c) 10/14.
49.
Find the area of a parallelogram with base 8cm and vertical height 5cm.
Correct Answer
A. A) 40 cm^{2}
Explanation
The area of a parallelogram is calculated by multiplying the base by the vertical height. In this case, the base is 8cm and the vertical height is 5cm. Multiplying these values gives us 40cm2, which is the correct answer.
50.
Find the coefficient of y in 33y + 9.
Correct Answer
B. B) 33
Explanation
The coefficient of y in the expression 33y + 9 is 33. This is because the coefficient is the number that is multiplied by the variable, in this case y. So, the coefficient of y is 33.