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Questions and Answers
Between which two integers does -2.5 lie? (Select all that apply)
The measure of each interior angle of a regular polygon is 140°. The number of sides that polygon has is _____
If the larger angle of a parallelogram is 30° less than twice the smaller angle, what is the measure of the larger angle?
If 5% of a number is 42, then the number is _____
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If ξ = {all digits in our number system}, A = {x : x is prime} and B = {x : x is even}, then B-A is _____
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The square root of 0.09 is _____
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The marked price of an article is ₹850 and the retailer gives a discount of 6%. Find the selling price of the article.
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Find the value of x in the equation: (4/64) = (3/4 - 3x).
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Find the values of the letters A and B in the addition: A6A + 5B8 = B61.
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Construct a quadrilateral ABCD in which AB=3.5 cm, BC=2.5 cm, DC=4.1 cm, ∠B=120°, and ∠C=90°.
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Find the value of X: √900X = 30.
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Name the shaded region in the given circle.
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Find the measure of angle x in the following figures.
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In a school of 4500 students, if the PT teacher wants to make students sit in rows where the number of students in each row is the same as the number of rows, how many students are left out?
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In the following figure, O is the center of the circle. If PT is tangent to the circle at point T, find the measure of ∠x and ∠y.
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Find 5 rational numbers between -3 and -4.
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Simplify: { (1/4) - (1/3) } ÷ (1/2).
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Let ξ = {x : x Є N, 5 ≤ x ≤ 20}, X = {x : x Є N, 10 ≤ x ≤ 20}, Y = {x : x Є N, 2x < 30}. Find a. n(X ∪ Y), b. n(X ∩ Y), c. n(X′).
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Find the smallest number by which 10584 should be multiplied so that the product is a perfect cube? Also, find the cube root of the product.
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In a 2-digit number, the sum of the digits is 7. If the difference of the 2-digit number and the number obtained by reversing the digits is 9, then find the numbers.
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Study Notes
Number Systems
- Rational numbers can be written in the form of p/q, where q is not equal to zero.
- To find rational numbers between two given rational numbers one can take the average of the two numbers.
- To find the multiplicative inverse of a number, simply reciprocate it.
- The square root of a number is the value that when multiplied by itself gives the original number.
Algebra
- To solve for an unknown variable, we can use basic mathematical operations (addition, subtraction, multiplication, and division) to isolate the variable on one side of the equation.
Geometry
- A regular polygon is a polygon with all sides and all angles equal.
- The measure of each interior angle of a regular polygon can be calculated by: (n-2) x 180 / n, where n is the number of sides of the polygon.
- A convex polygon is a polygon where all interior angles are less than 180 degrees.
- A tangent to a circle is a line that touches the circle at exactly one point.
- The angle between a tangent and a radius drawn to the point of contact is always 90 degrees.
Number Theory
- A perfect cube is a number that can be obtained by multiplying a number by itself three times.
- The number 10584 can be factored into 2 x 2 x 2 x 3 x 3 x 7 x 7. To make it a perfect cube, we need to multiply it by 3 x 7 to have three sets of each factor.
Arithmetic
- A discount is a reduction in the original price of a product.
- The selling price of an article is the price at which it is sold after deducting the discount from the marked price.
Sets
- A set is a collection of well-defined objects.
- The union of two sets is the set of all elements that are in either set.
- The intersection of two sets is the set of all elements that are in both sets.
- The complement of a set is the set of all elements that are not in the set.
Problem Solving
- Divisibility Rule of 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
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